Inflation from axion monodromy based on Berg, E.P. & Sj ors, - - PowerPoint PPT Presentation

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Inflation from axion monodromy based on Berg, E.P. & Sj ors, - - PowerPoint PPT Presentation

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Inflation from axion monodromy based on Berg, E.P. & Sj ors, arXiv:0912.1341 (hep-th) and Flauger, McAllister, E.P., Westphal & Xu, arXiv:0907.2916 (hep-th) Enrico Pajer Cornell University, Ithaca KITP Mar 2010 Outline 1

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SLIDE 1

Inflation from axion monodromy

based on Berg, E.P. & Sj¨

  • rs, arXiv:0912.1341 (hep-th) and

Flauger, McAllister, E.P., Westphal & Xu, arXiv:0907.2916 (hep-th) Enrico Pajer

Cornell University, Ithaca

KITP Mar 2010

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SLIDE 2

Outline

1 Motivations 2 Inflation from axion monodromy 3 Dante’s Inferno 4 Conclusions

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 2 / 43

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SLIDE 3

Outline

1 Motivations 2 Inflation from axion monodromy 3 Dante’s Inferno 4 Conclusions

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 3 / 43

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SLIDE 4

Cosmological data

We are living in the golden age of

  • bservational cosmology:

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 4 / 43

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SLIDE 5

Cosmological data

We are living in the golden age of

  • bservational cosmology: COBE

goes to Stockholm,

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 4 / 43

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SLIDE 6

Cosmological data

We are living in the golden age of

  • bservational cosmology: COBE

goes to Stockholm, WMAP has measured the CMB with percent

  • accuracy. . .

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 4 / 43

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SLIDE 7

Cosmological data

We are living in the golden age of

  • bservational cosmology: COBE

goes to Stockholm, WMAP has measured the CMB with percent

  • accuracy. . .

and now Planck: the satellite, launched on May 2009, finished the first full sky map (95%) on Feb 14th!

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 4 / 43

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SLIDE 8

The picture emerging from the data

A mechanism whose main parameter is unknown by at least 10

  • rders of manitude and nevertheless works?

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 5 / 43

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SLIDE 9

The picture emerging from the data

A mechanism whose main parameter is unknown by at least 10

  • rders of manitude and nevertheless works?

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 5 / 43

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SLIDE 10

The picture emerging from the data

A mechanism whose main parameter is unknown by at least 10

  • rders of manitude and nevertheless works? Inflation

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 5 / 43

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SLIDE 11

The picture emerging from the data

A mechanism whose main parameter is unknown by at least 10

  • rders of manitude and nevertheless works? Inflation

Inflation does not solve the horizon and flatness problem but can arguably alleviate it. It provides a mechanism that shifts in the past the initial condition problem.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 5 / 43

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SLIDE 12

The picture emerging from the data

A mechanism whose main parameter is unknown by at least 10

  • rders of manitude and nevertheless works? Inflation

Inflation does not solve the horizon and flatness problem but can arguably alleviate it. It provides a mechanism that shifts in the past the initial condition problem. Neverless it is a spectacular model to generate cosmological perturbations.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 5 / 43

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SLIDE 13

The picture emerging from the data

A mechanism whose main parameter is unknown by at least 10

  • rders of manitude and nevertheless works? Inflation

Inflation does not solve the horizon and flatness problem but can arguably alleviate it. It provides a mechanism that shifts in the past the initial condition problem. Neverless it is a spectacular model to generate cosmological perturbations. The simplest models of inflation is compatible with the data

[see e.g. WMAP7] , i.e. small, scale-invariant but slightly red tilted,

Gaussian, adiabatic primordial curvature perturbations.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 5 / 43

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SLIDE 14

The picture emerging from the data

A mechanism whose main parameter is unknown by at least 10

  • rders of manitude and nevertheless works? Inflation

Inflation does not solve the horizon and flatness problem but can arguably alleviate it. It provides a mechanism that shifts in the past the initial condition problem. Neverless it is a spectacular model to generate cosmological perturbations. The simplest models of inflation is compatible with the data

[see e.g. WMAP7] , i.e. small, scale-invariant but slightly red tilted,

Gaussian, adiabatic primordial curvature perturbations. What is left to do?

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 5 / 43

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SLIDE 15

Different approaches

A lot is left to do: Precision measurements The broad predictions of the simplest model of inflation are veryfied at the percent level.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 6 / 43

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SLIDE 16

Different approaches

A lot is left to do: Precision measurements The broad predictions of the simplest model of inflation are veryfied at the percent level. Precision measurements, e.g. Planck, will provide new tests.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 6 / 43

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SLIDE 17

Different approaches

A lot is left to do: Precision measurements The broad predictions of the simplest model of inflation are veryfied at the percent level. Precision measurements, e.g. Planck, will provide new tests. Departures from the simplest model? E.g. what non-Gaussian signal do we look for? How significant are anomalies?

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 6 / 43

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SLIDE 18

Different approaches

A lot is left to do: Precision measurements The broad predictions of the simplest model of inflation are veryfied at the percent level. Precision measurements, e.g. Planck, will provide new tests. Departures from the simplest model? E.g. what non-Gaussian signal do we look for? How significant are anomalies?

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 6 / 43

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SLIDE 19

Different approaches

A lot is left to do: Precision measurements The broad predictions of the simplest model of inflation are veryfied at the percent level. Precision measurements, e.g. Planck, will provide new tests. Departures from the simplest model? E.g. what non-Gaussian signal do we look for? How significant are anomalies? Theoretical soundness Initial conditions

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 6 / 43

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SLIDE 20

Different approaches

A lot is left to do: Precision measurements The broad predictions of the simplest model of inflation are veryfied at the percent level. Precision measurements, e.g. Planck, will provide new tests. Departures from the simplest model? E.g. what non-Gaussian signal do we look for? How significant are anomalies? Theoretical soundness Initial conditions Is inflation natural?

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 6 / 43

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SLIDE 21

Different approaches

A lot is left to do: Precision measurements The broad predictions of the simplest model of inflation are veryfied at the percent level. Precision measurements, e.g. Planck, will provide new tests. Departures from the simplest model? E.g. what non-Gaussian signal do we look for? How significant are anomalies? Theoretical soundness Initial conditions Is inflation natural? EFT approach: fine tuning and symmetries

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 6 / 43

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SLIDE 22

Different approaches

A lot is left to do: Precision measurements The broad predictions of the simplest model of inflation are veryfied at the percent level. Precision measurements, e.g. Planck, will provide new tests. Departures from the simplest model? E.g. what non-Gaussian signal do we look for? How significant are anomalies? Theoretical soundness Initial conditions Is inflation natural? EFT approach: fine tuning and symmetries Fundamental theory approach: when symmetries are broken and fine tuning is possible?

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 6 / 43

slide-23
SLIDE 23

Different approaches

A lot is left to do: Precision measurements The broad predictions of the simplest model of inflation are veryfied at the percent level. Precision measurements, e.g. Planck, will provide new tests. Departures from the simplest model? E.g. what non-Gaussian signal do we look for? How significant are anomalies? Theoretical soundness Initial conditions Is inflation natural? EFT approach: fine tuning and symmetries Fundamental theory approach: when symmetries are broken and fine tuning is possible? Non trivial correlations between observables

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 6 / 43

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SLIDE 24

Exciting signatures in the sky

Obervables that could deeply impact our picture of the early universe: Tensor modes:

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 7 / 43

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SLIDE 25

Exciting signatures in the sky

Obervables that could deeply impact our picture of the early universe: Tensor modes:

Detectable in the T anisotropies or in the polarization of the CMB. Current bound on the tensor-to-scalar ratio: r < .20

[WMAP7+SN] .

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 7 / 43

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SLIDE 26

Exciting signatures in the sky

Obervables that could deeply impact our picture of the early universe: Tensor modes:

Detectable in the T anisotropies or in the polarization of the CMB. Current bound on the tensor-to-scalar ratio: r < .20

[WMAP7+SN] .

A detection would support inflation and determine the high scale (order GUT) where it took place.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 7 / 43

slide-27
SLIDE 27

Exciting signatures in the sky

Obervables that could deeply impact our picture of the early universe: Tensor modes:

Detectable in the T anisotropies or in the polarization of the CMB. Current bound on the tensor-to-scalar ratio: r < .20

[WMAP7+SN] .

A detection would support inflation and determine the high scale (order GUT) where it took place.

non-Gaussianity:

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 7 / 43

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SLIDE 28

Exciting signatures in the sky

Obervables that could deeply impact our picture of the early universe: Tensor modes:

Detectable in the T anisotropies or in the polarization of the CMB. Current bound on the tensor-to-scalar ratio: r < .20

[WMAP7+SN] .

A detection would support inflation and determine the high scale (order GUT) where it took place.

non-Gaussianity:

Detectable e.g. in the three-point function of T perturbations. Current bounds are of the order a percent (shape dependent).

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 7 / 43

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SLIDE 29

Exciting signatures in the sky

Obervables that could deeply impact our picture of the early universe: Tensor modes:

Detectable in the T anisotropies or in the polarization of the CMB. Current bound on the tensor-to-scalar ratio: r < .20

[WMAP7+SN] .

A detection would support inflation and determine the high scale (order GUT) where it took place.

non-Gaussianity:

Detectable e.g. in the three-point function of T perturbations. Current bounds are of the order a percent (shape dependent). A detection would rule out the simplest class of models (a slowly rolling single canonically normalized field).

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 7 / 43

slide-30
SLIDE 30

Exciting signatures in the sky

Obervables that could deeply impact our picture of the early universe: Tensor modes:

Detectable in the T anisotropies or in the polarization of the CMB. Current bound on the tensor-to-scalar ratio: r < .20

[WMAP7+SN] .

A detection would support inflation and determine the high scale (order GUT) where it took place.

non-Gaussianity:

Detectable e.g. in the three-point function of T perturbations. Current bounds are of the order a percent (shape dependent). A detection would rule out the simplest class of models (a slowly rolling single canonically normalized field). It tell us about the interaction of the inflaton and give us more information than a single number.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 7 / 43

slide-31
SLIDE 31

Exciting signatures in the sky

Obervables that could deeply impact our picture of the early universe: Tensor modes:

Detectable in the T anisotropies or in the polarization of the CMB. Current bound on the tensor-to-scalar ratio: r < .20

[WMAP7+SN] .

A detection would support inflation and determine the high scale (order GUT) where it took place.

non-Gaussianity:

Detectable e.g. in the three-point function of T perturbations. Current bounds are of the order a percent (shape dependent). A detection would rule out the simplest class of models (a slowly rolling single canonically normalized field). It tell us about the interaction of the inflaton and give us more information than a single number.

Isocurvature modes, curvature, features in the spectrum, . . .

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 7 / 43

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SLIDE 32

An example of a precious synergy

And example of a synergy between theory and observation in inflation from axion mondromy

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 8 / 43

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SLIDE 33

Tensor modes and the Lyth bound

The detection of tensor modes, e.g. in the B-mode polarization, would fix the scale of inflation close to the GUT scale.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 9 / 43

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SLIDE 34

Tensor modes and the Lyth bound

The detection of tensor modes, e.g. in the B-mode polarization, would fix the scale of inflation close to the GUT scale. Measuring tensor modes puts a lower bound on the range of variation of the inflaton

[Lyth 98]

∆φ Mpl > r 0.01

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 9 / 43

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SLIDE 35

Tensor modes and the Lyth bound

The detection of tensor modes, e.g. in the B-mode polarization, would fix the scale of inflation close to the GUT scale. Measuring tensor modes puts a lower bound on the range of variation of the inflaton

[Lyth 98]

∆φ Mpl > r 0.01 In a fundamental theory a flat potential over a superplanckian distance is hard to control, e.g. η-problem.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 9 / 43

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SLIDE 36

Tensor modes and the Lyth bound

The detection of tensor modes, e.g. in the B-mode polarization, would fix the scale of inflation close to the GUT scale. Measuring tensor modes puts a lower bound on the range of variation of the inflaton

[Lyth 98]

∆φ Mpl > r 0.01 In a fundamental theory a flat potential over a superplanckian distance is hard to control, e.g. η-problem. This is the main motivation to consider axion monodromy inflation

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 9 / 43

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SLIDE 37

Tensor modes and the Lyth bound

The detection of tensor modes, e.g. in the B-mode polarization, would fix the scale of inflation close to the GUT scale. Measuring tensor modes puts a lower bound on the range of variation of the inflaton

[Lyth 98]

∆φ Mpl > r 0.01 In a fundamental theory a flat potential over a superplanckian distance is hard to control, e.g. η-problem. This is the main motivation to consider axion monodromy inflation

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 9 / 43

slide-38
SLIDE 38

Tensor modes and the Lyth bound

The detection of tensor modes, e.g. in the B-mode polarization, would fix the scale of inflation close to the GUT scale. Measuring tensor modes puts a lower bound on the range of variation of the inflaton

[Lyth 98]

∆φ Mpl > r 0.01 In a fundamental theory a flat potential over a superplanckian distance is hard to control, e.g. η-problem. This is the main motivation to consider axion monodromy inflation

Schematically

Tensor modes ⇒ High scale ⇒ Large field ⇒ more UV-sensitive

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 9 / 43

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SLIDE 39

UV-sensitivity

EFT approach: learn about higher scales studying UV-sensitive

  • bservables.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 10 / 43

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SLIDE 40

UV-sensitivity

EFT approach: learn about higher scales studying UV-sensitive

  • bservables.

Inflation is a UV-sensitive mechanism. Schematically V (φ) = 1 2m2φ2 +

  • n

λn φn Mn−4

pl

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 10 / 43

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SLIDE 41

UV-sensitivity

EFT approach: learn about higher scales studying UV-sensitive

  • bservables.

Inflation is a UV-sensitive mechanism. Schematically V (φ) = 1 2m2φ2 +

  • n

λn φn Mn−4

pl

Within string theory and supergravity many models suffer from an η-problem.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 10 / 43

slide-42
SLIDE 42

UV-sensitivity

EFT approach: learn about higher scales studying UV-sensitive

  • bservables.

Inflation is a UV-sensitive mechanism. Schematically V (φ) = 1 2m2φ2 +

  • n

λn φn Mn−4

pl

Within string theory and supergravity many models suffer from an η-problem. We need to invoke a symmetry, e.g. shift symmetry.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 10 / 43

slide-43
SLIDE 43

UV-sensitivity

EFT approach: learn about higher scales studying UV-sensitive

  • bservables.

Inflation is a UV-sensitive mechanism. Schematically V (φ) = 1 2m2φ2 +

  • n

λn φn Mn−4

pl

Within string theory and supergravity many models suffer from an η-problem. We need to invoke a symmetry, e.g. shift symmetry. Then we need a fundamental theory (UV-finite) to ask if, how and where the symmetry is broken.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 10 / 43

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SLIDE 44

Outline

1 Motivations 2 Inflation from axion monodromy 3 Dante’s Inferno 4 Conclusions

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 11 / 43

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SLIDE 45

Axion monodromy

Two difficulties for large field models in a UV theory Space: ∆φ > Mpl is often impossible (e.g. brane inflation, Natural inflation)

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 12 / 43

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SLIDE 46

Axion monodromy

Two difficulties for large field models in a UV theory Space: ∆φ > Mpl is often impossible (e.g. brane inflation, Natural inflation) Flatness: ǫ, η ≪ 1 is rare (e.g. η problem)

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 12 / 43

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SLIDE 47

Axion monodromy

Two difficulties for large field models in a UV theory Space: ∆φ > Mpl is often impossible (e.g. brane inflation, Natural inflation) Flatness: ǫ, η ≪ 1 is rare (e.g. η problem)

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 12 / 43

slide-48
SLIDE 48

Axion monodromy

Two difficulties for large field models in a UV theory Space: ∆φ > Mpl is often impossible (e.g. brane inflation, Natural inflation) Flatness: ǫ, η ≪ 1 is rare (e.g. η problem) Axion monodromy addresses both

[(Silverstein & Westphal)(1+McAllister)]

Invoke a shift symmetry on an “angular” field.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 12 / 43

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SLIDE 49

Axion monodromy

Two difficulties for large field models in a UV theory Space: ∆φ > Mpl is often impossible (e.g. brane inflation, Natural inflation) Flatness: ǫ, η ≪ 1 is rare (e.g. η problem) Axion monodromy addresses both

[(Silverstein & Westphal)(1+McAllister)]

Invoke a shift symmetry on an “angular” field. The symmetry is broken in a controlled way inducing a monodromy.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 12 / 43

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SLIDE 50

Axion monodromy

Two difficulties for large field models in a UV theory Space: ∆φ > Mpl is often impossible (e.g. brane inflation, Natural inflation) Flatness: ǫ, η ≪ 1 is rare (e.g. η problem) Axion monodromy addresses both

[(Silverstein & Westphal)(1+McAllister)]

Invoke a shift symmetry on an “angular” field. The symmetry is broken in a controlled way inducing a monodromy. This enlarges the field space and provides the potential for inflation.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 12 / 43

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SLIDE 51

Axions in field theory

Axions are scalar fields with only derivative couplings and might arise e.g. from the breaking of a U(1) symmetry

[Peccei & Quinn 77]

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 13 / 43

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SLIDE 52

Axions in field theory

Axions are scalar fields with only derivative couplings and might arise e.g. from the breaking of a U(1) symmetry

[Peccei & Quinn 77]

Hence they enjoy a continuous shift symmetry at all orders in perturbation theory φ(x) → φ(x) + constant

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 13 / 43

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SLIDE 53

Axions in field theory

Axions are scalar fields with only derivative couplings and might arise e.g. from the breaking of a U(1) symmetry

[Peccei & Quinn 77]

Hence they enjoy a continuous shift symmetry at all orders in perturbation theory φ(x) → φ(x) + constant Continuous shift symmetry is broken to a discrete shift symmetry by non-perturbative effects

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 13 / 43

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SLIDE 54

Axions in field theory

Axions are scalar fields with only derivative couplings and might arise e.g. from the breaking of a U(1) symmetry

[Peccei & Quinn 77]

Hence they enjoy a continuous shift symmetry at all orders in perturbation theory φ(x) → φ(x) + constant Continuous shift symmetry is broken to a discrete shift symmetry by non-perturbative effects The axion decay constant f determines the periodicity of the canonically normalized axion L ⊃ 1 2(∂φ)2 + Λ4 cos φ f

  • ⇒ φ(x) → φ(x) + 2πf

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 13 / 43

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SLIDE 55

A simple example

A canonically normalized axion with a shift symmetry V (φ) = const

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 14 / 43

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SLIDE 56

A simple example

A canonically normalized axion with a shift symmetry V (φ) = const + Λ4 cos φ f

  • Non-perturbative effects are exponentially suppressed. They lead

to a very exciting phenomenology, see Raphael Flauger’s talk!

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 14 / 43

slide-57
SLIDE 57

A simple example

A canonically normalized axion with a shift symmetry V (φ) = const + Λ4 cos φ f

  • + 1

2m2φ2 Non-perturbative effects are exponentially suppressed. They lead to a very exciting phenomenology, see Raphael Flauger’s talk! Break the shift symmetry explicitely in a controlled way.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 14 / 43

slide-58
SLIDE 58

A simple example

A canonically normalized axion with a shift symmetry V (φ) = const + Λ4 cos φ f

  • + 1

2m2φ2 Non-perturbative effects are exponentially suppressed. They lead to a very exciting phenomenology, see Raphael Flauger’s talk! Break the shift symmetry explicitely in a controlled way. m controls the breaking: in the limit m → 0 the potential is flat. Higher corrections are suppressed in m/Λ for some cutoff Λ

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 14 / 43

slide-59
SLIDE 59

A simple example

A canonically normalized axion with a shift symmetry V (φ) = const + Λ4 cos φ f

  • + 1

2m2φ2 Non-perturbative effects are exponentially suppressed. They lead to a very exciting phenomenology, see Raphael Flauger’s talk! Break the shift symmetry explicitely in a controlled way. m controls the breaking: in the limit m → 0 the potential is flat. Higher corrections are suppressed in m/Λ for some cutoff Λ

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 14 / 43

slide-60
SLIDE 60

A simple example

A canonically normalized axion with a shift symmetry V (φ) = const + Λ4 cos φ f

  • + 1

2m2φ2 Non-perturbative effects are exponentially suppressed. They lead to a very exciting phenomenology, see Raphael Flauger’s talk! Break the shift symmetry explicitely in a controlled way. m controls the breaking: in the limit m → 0 the potential is flat. Higher corrections are suppressed in m/Λ for some cutoff Λ What happens beyond the effective description? Is the shift symmetry broken above the cutoff? Are non-perturbative effects always negligible?

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 14 / 43

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SLIDE 61

The phenomenology

Observables tensor modes.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 15 / 43

slide-62
SLIDE 62

The phenomenology

Observables tensor modes. ns depends on the details of the monodromy potential.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 15 / 43

slide-63
SLIDE 63

The phenomenology

Observables tensor modes. ns depends on the details of the monodromy potential. Non-pertubative effects lead to oscillations in the spectrum and large resonant non-Gaussianity (Raphael’s talk tomorrow)

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 15 / 43

slide-64
SLIDE 64

The phenomenology

Observables tensor modes. ns depends on the details of the monodromy potential. Non-pertubative effects lead to oscillations in the spectrum and large resonant non-Gaussianity (Raphael’s talk tomorrow)

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 15 / 43

slide-65
SLIDE 65

The phenomenology

Observables tensor modes. ns depends on the details of the monodromy potential. Non-pertubative effects lead to oscillations in the spectrum and large resonant non-Gaussianity (Raphael’s talk tomorrow)

Chaotic Inflation

0.92 0.94 0.96 0.98 1.0 1.02

ns

IIA Nil manifolds µ10/32/3 N = 50 N = 60 Linear Axion Inflation µ3 N = 50 N = 60

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 15 / 43

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SLIDE 66

The phenomenology

Observables tensor modes. ns depends on the details of the monodromy potential. Non-pertubative effects lead to oscillations in the spectrum and large resonant non-Gaussianity (Raphael’s talk tomorrow)

Chaotic Inflation

0.92 0.94 0.96 0.98 1.0 1.02

ns

IIA Nil manifolds µ10/32/3 N = 50 N = 60 Linear Axion Inflation µ3 N = 50 N = 60

Can we implement this idea in string theory? What do we learn?

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 15 / 43

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SLIDE 67

Axion in string theory

String theory seen from a low energy 4D observer: Model independent axions such as dualizing Bµν or Cµν

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 16 / 43

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SLIDE 68

Axion in string theory

String theory seen from a low energy 4D observer: Model independent axions such as dualizing Bµν or Cµν Model dependent axions from integrating a p-form over a p-cycle

  • f the compact manifold

c(x) =

  • Σp

Cp , b(x) =

  • Σ2

B2

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 16 / 43

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SLIDE 69

Axion in string theory

String theory seen from a low energy 4D observer: Model independent axions such as dualizing Bµν or Cµν Model dependent axions from integrating a p-form over a p-cycle

  • f the compact manifold

c(x) =

  • Σp

Cp , b(x) =

  • Σ2

B2 The shift symmetry is valid at all order in perturbation theory but broken non-pertubatively, e.g by world-sheet instantons or brane instantons.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 16 / 43

slide-70
SLIDE 70

Axion in string theory

String theory seen from a low energy 4D observer: Model independent axions such as dualizing Bµν or Cµν Model dependent axions from integrating a p-form over a p-cycle

  • f the compact manifold

c(x) =

  • Σp

Cp , b(x) =

  • Σ2

B2 The shift symmetry is valid at all order in perturbation theory but broken non-pertubatively, e.g by world-sheet instantons or brane instantons. The axion decay constant f is determined by geometrical data of the compactification.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 16 / 43

slide-71
SLIDE 71

Axion in string theory

String theory seen from a low energy 4D observer: Model independent axions such as dualizing Bµν or Cµν Model dependent axions from integrating a p-form over a p-cycle

  • f the compact manifold

c(x) =

  • Σp

Cp , b(x) =

  • Σ2

B2 The shift symmetry is valid at all order in perturbation theory but broken non-pertubatively, e.g by world-sheet instantons or brane instantons. The axion decay constant f is determined by geometrical data of the compactification. In controlled setups f < Mpl

[Banks et al 03]

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 16 / 43

slide-72
SLIDE 72

Shift symmetry

The 4D axion b(x) from Bij = b(x)ωij, with ω a two-form. In (bosonic) closed string theory, the vertex operator for b at zero momentum integrated over the world-sheet is V (k = 0) =

  • ws

d2σǫαβ∂αXi∂βXjωijb =

  • ts

B In perturbation theory the world-sheet wraps topologically trivial cycles hence V (k = 0) = 0, only derivative coplings.

[Wen & Witten, Dine & Seiberg 86]

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 17 / 43

slide-73
SLIDE 73

Shift symmetry

The 4D axion b(x) from Bij = b(x)ωij, with ω a two-form. In (bosonic) closed string theory, the vertex operator for b at zero momentum integrated over the world-sheet is V (k = 0) =

  • ws

d2σǫαβ∂αXi∂βXjωijb =

  • ts

B In perturbation theory the world-sheet wraps topologically trivial cycles hence V (k = 0) = 0, only derivative coplings.

[Wen & Witten, Dine & Seiberg 86]

Breaking of the shift symmetry

Two ingredients can invalidate the above argument: Non-perturbative effects

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 17 / 43

slide-74
SLIDE 74

Shift symmetry

The 4D axion b(x) from Bij = b(x)ωij, with ω a two-form. In (bosonic) closed string theory, the vertex operator for b at zero momentum integrated over the world-sheet is V (k = 0) =

  • ws

d2σǫαβ∂αXi∂βXjωijb =

  • ts

B In perturbation theory the world-sheet wraps topologically trivial cycles hence V (k = 0) = 0, only derivative coplings.

[Wen & Witten, Dine & Seiberg 86]

Breaking of the shift symmetry

Two ingredients can invalidate the above argument: Non-perturbative effects World sheet with boundaries, i.e. D-branes

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 17 / 43

slide-75
SLIDE 75

The ingredients

The setup

[McAllister, Silverstein & Westphal 08]

Type IIB orientifolds.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 18 / 43

slide-76
SLIDE 76

The ingredients

The setup

[McAllister, Silverstein & Westphal 08]

Type IIB orientifolds. N = 1, 4D: an axion c(x) from RR field C2 c(x) =

  • Σ2

C2 .

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 18 / 43

slide-77
SLIDE 77

The ingredients

The setup

[McAllister, Silverstein & Westphal 08]

Type IIB orientifolds. N = 1, 4D: an axion c(x) from RR field C2 c(x) =

  • Σ2

C2 . Wrapping a 5-brane over Σ2 induces a monodromy for c(x) (world-sheets with boundary).

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 18 / 43

slide-78
SLIDE 78

The ingredients

The setup

[McAllister, Silverstein & Westphal 08]

Type IIB orientifolds. N = 1, 4D: an axion c(x) from RR field C2 c(x) =

  • Σ2

C2 . Wrapping a 5-brane over Σ2 induces a monodromy for c(x) (world-sheets with boundary). If the 5-brane is in a warped region the potential is flat.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 18 / 43

slide-79
SLIDE 79

The ingredients

The setup

[McAllister, Silverstein & Westphal 08]

Type IIB orientifolds. N = 1, 4D: an axion c(x) from RR field C2 c(x) =

  • Σ2

C2 . Wrapping a 5-brane over Σ2 induces a monodromy for c(x) (world-sheets with boundary). If the 5-brane is in a warped region the potential is flat. Moduli stabilization ´ a la KKLT does not spoil the shift symmetry.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 18 / 43

slide-80
SLIDE 80

The ingredients

The setup

[McAllister, Silverstein & Westphal 08]

Type IIB orientifolds. N = 1, 4D: an axion c(x) from RR field C2 c(x) =

  • Σ2

C2 . Wrapping a 5-brane over Σ2 induces a monodromy for c(x) (world-sheets with boundary). If the 5-brane is in a warped region the potential is flat. Moduli stabilization ´ a la KKLT does not spoil the shift symmetry. Non-perturbative corrections (e.g. to the K¨ ahler potential) induce small ripples

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 18 / 43

slide-81
SLIDE 81

Linear potential for the inflaton

The shift symmetry can be broken in the presence of boundaries.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 19 / 43

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SLIDE 82

Linear potential for the inflaton

The shift symmetry can be broken in the presence of boundaries. Consider a D5-brane wrapped on a two-cycle Σ2. The DBI action −T5

  • d6xe−Φ
  • det (Gind + Bind)

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 19 / 43

slide-83
SLIDE 83

Linear potential for the inflaton

The shift symmetry can be broken in the presence of boundaries. Consider a D5-brane wrapped on a two-cycle Σ2. The DBI action −T5

  • d6xe−Φ
  • det (Gind + Bind)

The shift b(x) → b(x) + const of b(x) =

  • Σ2 B2 stores

some potential energy. V (b) = T5

  • L4 + b2 ∼ T5b

for large b Linear inflaton potential (and breaks SUSY). COBE normalization and control require to red-shift T5. Via S-duality, NS5 gives a monodromy for c.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 19 / 43

slide-84
SLIDE 84

4D N = 1 data

Effective action of O3/O7 Calabi-Yau

  • rientifolds (σΩ = −Ω).

[Grimm & Louis 04]

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 20 / 43

slide-85
SLIDE 85

4D N = 1 data

Effective action of O3/O7 Calabi-Yau

  • rientifolds (σΩ = −Ω).

[Grimm & Louis 04]

Assume complex structure moduli and dilaton are stabilized by fluxes at a higher scale.

[Kachru et al 03]

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 20 / 43

slide-86
SLIDE 86

4D N = 1 data

Effective action of O3/O7 Calabi-Yau

  • rientifolds (σΩ = −Ω).

[Grimm & Louis 04]

Assume complex structure moduli and dilaton are stabilized by fluxes at a higher scale.

[Kachru et al 03]

h1,1

+ orientifold-even K¨

ahler moduli from two-/four-cycle volumes complexified by

  • C4

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 20 / 43

slide-87
SLIDE 87

4D N = 1 data

Effective action of O3/O7 Calabi-Yau

  • rientifolds (σΩ = −Ω).

[Grimm & Louis 04]

Assume complex structure moduli and dilaton are stabilized by fluxes at a higher scale.

[Kachru et al 03]

h1,1

+ orientifold-even K¨

ahler moduli from two-/four-cycle volumes complexified by

  • C4

h1,1

− orientifold-odd K¨

ahler moduli from

  • B2 and
  • C2

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 20 / 43

slide-88
SLIDE 88

4D N = 1 data

Effective action of O3/O7 Calabi-Yau

  • rientifolds (σΩ = −Ω).

[Grimm & Louis 04]

Assume complex structure moduli and dilaton are stabilized by fluxes at a higher scale.

[Kachru et al 03]

h1,1

+ orientifold-even K¨

ahler moduli from two-/four-cycle volumes complexified by

  • C4

h1,1

− orientifold-odd K¨

ahler moduli from

  • B2 and
  • C2

Supermultiplets Ga ≡ 2π

  • ca − iba

gs

  • ,

Tα ≡ iρα + 1 2cαβγvβvγ + gs 4 cαbcGb(G − ¯ G)c , intersection numbers cIJK =

  • ωI ∧ ωJ ∧ ωK

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 20 / 43

slide-89
SLIDE 89

4D N = 1 data

Tree-level K¨ ahler and super-potential

[Grimm & Louis 04]

K = −2 log VE = −2 log 1 6cαβγvα(T, G)vβ(T, G)vγ(T, G)

  • W

= W0 ca and ba enjoy a shift symmetry (world-sheet argument).

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 21 / 43

slide-90
SLIDE 90

4D N = 1 data

Tree-level K¨ ahler and super-potential

[Grimm & Louis 04]

K = −2 log VE = −2 log 1 6cαβγvα(T, G)vβ(T, G)vγ(T, G)

  • W

= W0 ca and ba enjoy a shift symmetry (world-sheet argument). No-scale structure of K ⇒ Tα are not stabilized.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 21 / 43

slide-91
SLIDE 91

4D N = 1 data

Tree-level K¨ ahler and super-potential

[Grimm & Louis 04]

K = −2 log VE = −2 log 1 6cαβγvα(T, G)vβ(T, G)vγ(T, G)

  • W

= W0 ca and ba enjoy a shift symmetry (world-sheet argument). No-scale structure of K ⇒ Tα are not stabilized. Non-perturbative corrections (ED3 or gaugino condensation on D7’s) stabilize Tα

[Kachru et al. 03]

W = W0 +

h1,1

+

  • α=1

Aαe−aαTα ,

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 21 / 43

slide-92
SLIDE 92

4D N = 1 data

Tree-level K¨ ahler and super-potential

[Grimm & Louis 04]

K = −2 log VE = −2 log 1 6cαβγvα(T, G)vβ(T, G)vγ(T, G)

  • W

= W0 ca and ba enjoy a shift symmetry (world-sheet argument). No-scale structure of K ⇒ Tα are not stabilized. Non-perturbative corrections (ED3 or gaugino condensation on D7’s) stabilize Tα

[Kachru et al. 03]

W = W0 +

h1,1

+

  • α=1

Aαe−aαTα ,

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 21 / 43

slide-93
SLIDE 93

4D N = 1 data

Tree-level K¨ ahler and super-potential

[Grimm & Louis 04]

K = −2 log VE = −2 log 1 6cαβγvα(T, G)vβ(T, G)vγ(T, G)

  • W

= W0 ca and ba enjoy a shift symmetry (world-sheet argument). No-scale structure of K ⇒ Tα are not stabilized. Non-perturbative corrections (ED3 or gaugino condensation on D7’s) stabilize Tα

[Kachru et al. 03]

W = W0 +

h1,1

+

  • α=1

Aαe−aαTα ,

Non-perturbative breaking of shift symmetry

Non-perturbative effects could spoil the shift symmetry. In fact they induce an η-problem for ba, analogous to D3-brane inflation.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 21 / 43

slide-94
SLIDE 94

Moduli stabilization

The supersymmetric conditions ensuring a minimum are = DαW = −Aαaαe−aαTα − W vα 2VE , = DaW = Wπcαacvαbc VE

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 22 / 43

slide-95
SLIDE 95

Moduli stabilization

The supersymmetric conditions ensuring a minimum are = DαW = −Aαaαe−aαTα − W vα 2VE , = DaW = Wπcαacvαbc VE DαW = 0 fixes Tα (complex equation)

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 22 / 43

slide-96
SLIDE 96

Moduli stabilization

The supersymmetric conditions ensuring a minimum are = DαW = −Aαaαe−aαTα − W vα 2VE , = DaW = Wπcαacvαbc VE DαW = 0 fixes Tα (complex equation) DaW = 0 fixes ony ba = 0

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 22 / 43

slide-97
SLIDE 97

Moduli stabilization

The supersymmetric conditions ensuring a minimum are = DαW = −Aαaαe−aαTα − W vα 2VE , = DaW = Wπcαacvαbc VE DαW = 0 fixes Tα (complex equation) DaW = 0 fixes ony ba = 0 ca still enjoys a shift symmetry

[L¨ ust et al 06, Grimm 07]

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 22 / 43

slide-98
SLIDE 98

Moduli stabilization

The supersymmetric conditions ensuring a minimum are = DαW = −Aαaαe−aαTα − W vα 2VE , = DaW = Wπcαacvαbc VE DαW = 0 fixes Tα (complex equation) DaW = 0 fixes ony ba = 0 ca still enjoys a shift symmetry

[L¨ ust et al 06, Grimm 07]

Non-perturbative breaking of shift symmetry

It is crucial to know how the shift symmetry is broken. Moduli stabilization ´ a la KKLT is incompatible with ba shift symmetry.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 22 / 43

slide-99
SLIDE 99

The axion decay constant

Which values can f take? Direct KK reduction from C2 = c(x)ω/2π gives f2 M2

pl

= gsπ2 3VE ω ∧ ∗ω (2π)10(α′)3

  • ∝ L2

c

VE .

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 23 / 43

slide-100
SLIDE 100

The axion decay constant

Which values can f take? Direct KK reduction from C2 = c(x)ω/2π gives f2 M2

pl

= gsπ2 3VE ω ∧ ∗ω (2π)10(α′)3

  • ∝ L2

c

VE . Using N = 1 4D data one finds −1 2f2 (∂c)2 = ⊂ M2

plKG ¯ G |∂G|2 ,

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 23 / 43

slide-101
SLIDE 101

The axion decay constant

Which values can f take? Direct KK reduction from C2 = c(x)ω/2π gives f2 M2

pl

= gsπ2 3VE ω ∧ ∗ω (2π)10(α′)3

  • ∝ L2

c

VE . Using N = 1 4D data one finds −1 2f2 (∂c)2 = ⊂ M2

plKG ¯ G |∂G|2 ,

f2 M2

pl

= gs 8π2 cα−−vα VE .

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 23 / 43

slide-102
SLIDE 102

The axion decay constant

Which values can f take? Direct KK reduction from C2 = c(x)ω/2π gives f2 M2

pl

= gsπ2 3VE ω ∧ ∗ω (2π)10(α′)3

  • ∝ L2

c

VE . Using N = 1 4D data one finds −1 2f2 (∂c)2 = ⊂ M2

plKG ¯ G |∂G|2 ,

f2 M2

pl

= gs 8π2 cα−−vα VE .

Axion decay constant in string theory

In controlled setups gs ≪ 1 and L ≫ α′, hence f ≪ Mpl.

[Banks et al. 03]

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 23 / 43

slide-103
SLIDE 103

Constraints from the moduli stabilization

A series of constraints follow from consistency and computability

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 24 / 43

slide-104
SLIDE 104

Constraints from the moduli stabilization

A series of constraints follow from consistency and computability small coupling ⇒ gs ≪ 1

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 24 / 43

slide-105
SLIDE 105

Constraints from the moduli stabilization

A series of constraints follow from consistency and computability small coupling ⇒ gs ≪ 1 small world-sheet instantons ⇒ vα >

1 π√gs

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 24 / 43

slide-106
SLIDE 106

Constraints from the moduli stabilization

A series of constraints follow from consistency and computability small coupling ⇒ gs ≪ 1 small world-sheet instantons ⇒ vα >

1 π√gs

no higher instantons ⇒ Tα > Nα

π , with Nα 50 D7-branes

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 24 / 43

slide-107
SLIDE 107

Constraints from the moduli stabilization

A series of constraints follow from consistency and computability small coupling ⇒ gs ≪ 1 small world-sheet instantons ⇒ vα >

1 π√gs

no higher instantons ⇒ Tα > Nα

π , with Nα 50 D7-branes

no destabilization ⇒ V (φCMB) < Umod

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 24 / 43

slide-108
SLIDE 108

Constraints from the moduli stabilization

A series of constraints follow from consistency and computability small coupling ⇒ gs ≪ 1 small world-sheet instantons ⇒ vα >

1 π√gs

no higher instantons ⇒ Tα > Nα

π , with Nα 50 D7-branes

no destabilization ⇒ V (φCMB) < Umod High scale inflation and KKLT stabilization lead an upper bound on the volume (lower bound on ms/Mpl) τα ≪ 73 − 8 log vαπ√gs 2gs

  • ,

VE < h(1,1)

+

√gs 1.8 · 104 ,

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 24 / 43

slide-109
SLIDE 109

The amplitude of modulations

Non-perturbative corrections leads to ripples on the linear potential V (φ) = µ3φ + bµ3f cos φ f

  • Enrico Pajer

(Cornell) Inflation from axion monodromy KITP Mar 2010 25 / 43

slide-110
SLIDE 110

The amplitude of modulations

Non-perturbative corrections leads to ripples on the linear potential V (φ) = µ3φ + bµ3f cos φ f

  • F-term corrections need instantons with four fermionic zero

modes, e.g. non-BPS instantons. Few is known due to the lack of

  • holomorphicity. Educated guess:

K = −2 log

  • VE + e−SED1 cos(c)
  • = −2 log
  • VE + e− 2πv+

√gs cos(c)

  • .

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 25 / 43

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SLIDE 111

The amplitude of modulations

Non-perturbative corrections leads to ripples on the linear potential V (φ) = µ3φ + bµ3f cos φ f

  • F-term corrections need instantons with four fermionic zero

modes, e.g. non-BPS instantons. Few is known due to the lack of

  • holomorphicity. Educated guess:

K = −2 log

  • VE + e−SED1 cos(c)
  • = −2 log
  • VE + e− 2πv+

√gs cos(c)

  • .

D-term is protected by holomorphicity, corrections should be small.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 25 / 43

slide-112
SLIDE 112

The amplitude of modulations

Expanding as x = x0 + e−SED1x1 + . . . , the moduli stabilization gives VSUGRA = Umod,0

  • 1 + e−SED1 cos c
  • K(1) + 2Re W(1)

W(0)

  • Enrico Pajer

(Cornell) Inflation from axion monodromy KITP Mar 2010 26 / 43

slide-113
SLIDE 113

The amplitude of modulations

Expanding as x = x0 + e−SED1x1 + . . . , the moduli stabilization gives VSUGRA = Umod,0

  • 1 + e−SED1 cos c
  • K(1) + 2Re W(1)

W(0)

  • Hence the estimate size of the ripples is

bf = Umod,0 φ µ3φ e−SED1

  • K(1) + 2Re W(1)

W(0)

  • <

2c0 · 109M4

pl

gs V2

E

e−2/gs

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 26 / 43

slide-114
SLIDE 114

The amplitude of modulations

Expanding as x = x0 + e−SED1x1 + . . . , the moduli stabilization gives VSUGRA = Umod,0

  • 1 + e−SED1 cos c
  • K(1) + 2Re W(1)

W(0)

  • Hence the estimate size of the ripples is

bf = Umod,0 φ µ3φ e−SED1

  • K(1) + 2Re W(1)

W(0)

  • <

2c0 · 109M4

pl

gs V2

E

e−2/gs Exponentially suppressed in v+/√gs > 1/(πgs).

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 26 / 43

slide-115
SLIDE 115

The amplitude of modulations

Expanding as x = x0 + e−SED1x1 + . . . , the moduli stabilization gives VSUGRA = Umod,0

  • 1 + e−SED1 cos c
  • K(1) + 2Re W(1)

W(0)

  • Hence the estimate size of the ripples is

bf = Umod,0 φ µ3φ e−SED1

  • K(1) + 2Re W(1)

W(0)

  • <

2c0 · 109M4

pl

gs V2

E

e−2/gs Exponentially suppressed in v+/√gs > 1/(πgs). Enhanced by high moduli stabilization barrier.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 26 / 43

slide-116
SLIDE 116

Backreaction

The most serious inflaton-dependent backreaction we identified:

  • Σ C2 = 0 induces δND3(φ) =

φ 2πf units of D3 charge on the NS5.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 27 / 43

slide-117
SLIDE 117

Backreaction

The most serious inflaton-dependent backreaction we identified:

  • Σ C2 = 0 induces δND3(φ) =

φ 2πf units of D3 charge on the NS5.

D3-charge changes the warp factor and hence all warped volumes h(y) → h(y) + δh(y, φ)

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 27 / 43

slide-118
SLIDE 118

Backreaction

The most serious inflaton-dependent backreaction we identified:

  • Σ C2 = 0 induces δND3(φ) =

φ 2πf units of D3 charge on the NS5.

D3-charge changes the warp factor and hence all warped volumes h(y) → h(y) + δh(y, φ) T α are warped 4-cycle volumes and are stabilized.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 27 / 43

slide-119
SLIDE 119

Backreaction

The most serious inflaton-dependent backreaction we identified:

  • Σ C2 = 0 induces δND3(φ) =

φ 2πf units of D3 charge on the NS5.

D3-charge changes the warp factor and hence all warped volumes h(y) → h(y) + δh(y, φ) T α are warped 4-cycle volumes and are stabilized. The inflaton-dependent shift of T α can make the potential too steep.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 27 / 43

slide-120
SLIDE 120

Backreaction

The most serious inflaton-dependent backreaction we identified:

  • Σ C2 = 0 induces δND3(φ) =

φ 2πf units of D3 charge on the NS5.

D3-charge changes the warp factor and hence all warped volumes h(y) → h(y) + δh(y, φ) T α are warped 4-cycle volumes and are stabilized. The inflaton-dependent shift of T α can make the potential too steep.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 27 / 43

slide-121
SLIDE 121

Backreaction

The most serious inflaton-dependent backreaction we identified:

  • Σ C2 = 0 induces δND3(φ) =

φ 2πf units of D3 charge on the NS5.

D3-charge changes the warp factor and hence all warped volumes h(y) → h(y) + δh(y, φ) T α are warped 4-cycle volumes and are stabilized. The inflaton-dependent shift of T α can make the potential too steep. This correction is suppressed by δN D3(φ)/N D3 but not by warping (because it comes from the CS term).

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 27 / 43

slide-122
SLIDE 122

Backreaction

The most serious inflaton-dependent backreaction we identified:

  • Σ C2 = 0 induces δND3(φ) =

φ 2πf units of D3 charge on the NS5.

D3-charge changes the warp factor and hence all warped volumes h(y) → h(y) + δh(y, φ) T α are warped 4-cycle volumes and are stabilized. The inflaton-dependent shift of T α can make the potential too steep. This correction is suppressed by δN D3(φ)/N D3 but not by warping (because it comes from the CS term). Can we fix it?

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 27 / 43

slide-123
SLIDE 123

Dipole suppression

The tadpole is canceled by the anti-NS5, so the total δN D3(φ) is zero

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 28 / 43

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SLIDE 124

Dipole suppression

The tadpole is canceled by the anti-NS5, so the total δN D3(φ) is zero Depending on the geometry there can be a dipole suppression u/d

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 28 / 43

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SLIDE 125

Dipole suppression

The tadpole is canceled by the anti-NS5, so the total δN D3(φ) is zero Depending on the geometry there can be a dipole suppression u/d

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 28 / 43

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SLIDE 126

Dipole suppression

The tadpole is canceled by the anti-NS5, so the total δN D3(φ) is zero Depending on the geometry there can be a dipole suppression u/d

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 28 / 43

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SLIDE 127

Dipole suppression

The tadpole is canceled by the anti-NS5, so the total δN D3(φ) is zero Depending on the geometry there can be a dipole suppression u/d We constructed a toy model that present this suppresion.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 28 / 43

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SLIDE 128

Light KK modes

A large flux on the brane suppresses the KK masses.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 29 / 43

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SLIDE 129

Light KK modes

A large flux on the brane suppresses the KK masses. E.g. for a spacetime filling D5 wrapped on a 2-cycle of volume v2

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 29 / 43

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SLIDE 130

Light KK modes

A large flux on the brane suppresses the KK masses. E.g. for a spacetime filling D5 wrapped on a 2-cycle of volume v2 When

  • B2 ≡ b = 0, then

m2

KK,b ≃

v2 v2 + b2 m2

KK

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 29 / 43

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SLIDE 131

Light KK modes

A large flux on the brane suppresses the KK masses. E.g. for a spacetime filling D5 wrapped on a 2-cycle of volume v2 When

  • B2 ≡ b = 0, then

m2

KK,b ≃

v2 v2 + b2 m2

KK

large inflaton vev implies light KK modes. Typically mKK,b ∼ H.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 29 / 43

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SLIDE 132

Light KK modes

A large flux on the brane suppresses the KK masses. E.g. for a spacetime filling D5 wrapped on a 2-cycle of volume v2 When

  • B2 ≡ b = 0, then

m2

KK,b ≃

v2 v2 + b2 m2

KK

large inflaton vev implies light KK modes. Typically mKK,b ∼ H.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 29 / 43

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SLIDE 133

Light KK modes

A large flux on the brane suppresses the KK masses. E.g. for a spacetime filling D5 wrapped on a 2-cycle of volume v2 When

  • B2 ≡ b = 0, then

m2

KK,b ≃

v2 v2 + b2 m2

KK

large inflaton vev implies light KK modes. Typically mKK,b ∼ H.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 29 / 43

slide-134
SLIDE 134

Light KK modes

A large flux on the brane suppresses the KK masses. E.g. for a spacetime filling D5 wrapped on a 2-cycle of volume v2 When

  • B2 ≡ b = 0, then

m2

KK,b ≃

v2 v2 + b2 m2

KK

large inflaton vev implies light KK modes. Typically mKK,b ∼ H. Notice that problems arise with large vevs.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 29 / 43

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SLIDE 135

Outline

1 Motivations 2 Inflation from axion monodromy 3 Dante’s Inferno 4 Conclusions

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 30 / 43

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SLIDE 136

Back to the Lyth bound

There is a dichotomy which becomes evident with more than one inflaton.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 31 / 43

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SLIDE 137

Back to the Lyth bound

There is a dichotomy which becomes evident with more than one inflaton. The bound is on the effective inflaton φeff, i.e. the length of the inflationary trajectory ∆φeff ≡

  • dφeff

Quantum corrections grow with the vev’s of fundamental fields.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 31 / 43

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SLIDE 138

Back to the Lyth bound

There is a dichotomy which becomes evident with more than one inflaton. The bound is on the effective inflaton φeff, i.e. the length of the inflationary trajectory ∆φeff ≡

  • dφeff

Quantum corrections grow with the vev’s of fundamental fields.

The Lyth bound

The consequences of the Lyth bound are generically different in multi-field inflation

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 31 / 43

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SLIDE 139

Back to the Lyth bound

There is a dichotomy which becomes evident with more than one inflaton. The bound is on the effective inflaton φeff, i.e. the length of the inflationary trajectory ∆φeff ≡

  • dφeff

Quantum corrections grow with the vev’s of fundamental fields.

The Lyth bound

The consequences of the Lyth bound are generically different in multi-field inflation How complicate a potential can provide this classical trajectories?

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 31 / 43

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SLIDE 140

A simple model

The potential is as simple as this: V (r(x), θ(x)) = W(r) + Λ4

  • 1 − cos

r fr − θ fθ

  • Enrico Pajer

(Cornell) Inflation from axion monodromy KITP Mar 2010 32 / 43

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SLIDE 141

A simple model

The potential is as simple as this: V (r(x), θ(x)) = W(r) + Λ4

  • 1 − cos

r fr − θ fθ

  • Two (canonically normalized) axions {r, θ}, with respective axion

decay constants {fr, fθ}.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 32 / 43

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SLIDE 142

A simple model

The potential is as simple as this: V (r(x), θ(x)) = W(r) + Λ4

  • 1 − cos

r fr − θ fθ

  • Two (canonically normalized) axions {r, θ}, with respective axion

decay constants {fr, fθ}. The shift symmetry of r is broken by a monodromy term W(r). This could be anything. For illustration W(r) = m2r2/2.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 32 / 43

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SLIDE 143

A simple model

The potential is as simple as this: V (r(x), θ(x)) = W(r) + Λ4

  • 1 − cos

r fr − θ fθ

  • Two (canonically normalized) axions {r, θ}, with respective axion

decay constants {fr, fθ}. The shift symmetry of r is broken by a monodromy term W(r). This could be anything. For illustration W(r) = m2r2/2. A non-perturbative effect involves a linear combination of r and θ.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 32 / 43

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SLIDE 144

A simple model

The potential is as simple as this: V (r(x), θ(x)) = W(r) + Λ4

  • 1 − cos

r fr − θ fθ

  • Two (canonically normalized) axions {r, θ}, with respective axion

decay constants {fr, fθ}. The shift symmetry of r is broken by a monodromy term W(r). This could be anything. For illustration W(r) = m2r2/2. A non-perturbative effect involves a linear combination of r and θ. θ enjoys a shift symmetry to all order in perturbation theory broken only by non-perturbative effects to θ → θ + 2πfθ.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 32 / 43

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SLIDE 145

The infernal potential

The potential on the two-field space

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 33 / 43

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SLIDE 146

The infernal potential

The potential on the two-field space The periodicity in θ is evident in polar coordinates. Hence the name...

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 33 / 43

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SLIDE 147

Solution of the infernal dynamics

In the regime

  • A. fr ≪ fθ ≪ Mpl,
  • B. Λ4 ≫ frm2r0,

r can be integrated out (mr > H), i.e. r = r(θ) and one finds the effective single field potential Veff(φeff) = 1 2 m2

eff φ2 eff ,

meff ≡ m fr fθ where φeff ≃ cos(fr/fθ)θ + sin(fr/fθ)r.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 34 / 43

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SLIDE 148

Solution of the infernal dynamics

In the regime

  • A. fr ≪ fθ ≪ Mpl,
  • B. Λ4 ≫ frm2r0,

r can be integrated out (mr > H), i.e. r = r(θ) and one finds the effective single field potential Veff(φeff) = 1 2 m2

eff φ2 eff ,

meff ≡ m fr fθ where φeff ≃ cos(fr/fθ)θ + sin(fr/fθ)r.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 34 / 43

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SLIDE 149

The extra dial and the η-problem

The η-problem is alleviated

Since meff = m(fr/fθ), even if m ∼ H and hence r would have an η-problem, a mild hierachy fr/fθ ∼ O(.1) gives slow-roll inflation. Intuitively φeff is mostly θ which has a shift symmetry.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 35 / 43

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SLIDE 150

The extra dial and the field range

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 36 / 43

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SLIDE 151

The extra dial and the field range

What about the field range?

∆φeff ≃ 15Mpl, but...

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 36 / 43

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SLIDE 152

The extra dial and the field range

What about the field range?

∆φeff ≃ 15Mpl, but... whole inflationary dynamics is takes place inside 0 < θ < 2πfθ , 0 < r < 15Mpl fr fθ

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 36 / 43

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SLIDE 153

The extra dial and the field range

What about the field range?

∆φeff ≃ 15Mpl, but... whole inflationary dynamics is takes place inside 0 < θ < 2πfθ , 0 < r < 15Mpl fr fθ Provided fr/fθ ∼ O(10−1 − 10−2), chaotic inflation takes place in a region subplanckian in size.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 36 / 43

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SLIDE 154

Summary of the effective model

Phenomenology: Dante’s Inferno gives prediction similar to a single-field slow-roll chaotic model.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 37 / 43

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SLIDE 155

Summary of the effective model

Phenomenology: Dante’s Inferno gives prediction similar to a single-field slow-roll chaotic model. The precise numbers depend on the details of the monodromy term W(r).

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 37 / 43

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SLIDE 156

Summary of the effective model

Phenomenology: Dante’s Inferno gives prediction similar to a single-field slow-roll chaotic model. The precise numbers depend on the details of the monodromy term W(r). Generically, observable tensor modes are generated.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 37 / 43

slide-157
SLIDE 157

Summary of the effective model

Phenomenology: Dante’s Inferno gives prediction similar to a single-field slow-roll chaotic model. The precise numbers depend on the details of the monodromy term W(r). Generically, observable tensor modes are generated.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 37 / 43

slide-158
SLIDE 158

Summary of the effective model

Phenomenology: Dante’s Inferno gives prediction similar to a single-field slow-roll chaotic model. The precise numbers depend on the details of the monodromy term W(r). Generically, observable tensor modes are generated. Theoretical considerations: The inflaton is mostly an axion with a shift symmetry (only non-perturbative corrections) which alleviates the η-problem.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 37 / 43

slide-159
SLIDE 159

Summary of the effective model

Phenomenology: Dante’s Inferno gives prediction similar to a single-field slow-roll chaotic model. The precise numbers depend on the details of the monodromy term W(r). Generically, observable tensor modes are generated. Theoretical considerations: The inflaton is mostly an axion with a shift symmetry (only non-perturbative corrections) which alleviates the η-problem. The whole large-field inflationary dynamics takes place within a region subplanckian in size.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 37 / 43

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SLIDE 160

Summary of the effective model

Phenomenology: Dante’s Inferno gives prediction similar to a single-field slow-roll chaotic model. The precise numbers depend on the details of the monodromy term W(r). Generically, observable tensor modes are generated. Theoretical considerations: The inflaton is mostly an axion with a shift symmetry (only non-perturbative corrections) which alleviates the η-problem. The whole large-field inflationary dynamics takes place within a region subplanckian in size. Issues related to the large vev’s of the axions are alleviated

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 37 / 43

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SLIDE 161

A cartoon of Dante’s Inferno

New ingredients: two two-cycles Σr and Σθ

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 38 / 43

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SLIDE 162

The two axions

Non-perturbative effects (e.g. ED1) and the monodromy term (5-brane) can wrap two overlapping but non-identiacal two-cycles.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 39 / 43

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SLIDE 163

The two axions

Non-perturbative effects (e.g. ED1) and the monodromy term (5-brane) can wrap two overlapping but non-identiacal two-cycles. We can choose a basis of two-cycles such that only one axion has a monodromy, say r.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 39 / 43

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SLIDE 164

The two axions

Non-perturbative effects (e.g. ED1) and the monodromy term (5-brane) can wrap two overlapping but non-identiacal two-cycles. We can choose a basis of two-cycles such that only one axion has a monodromy, say r. We expect the effective potential of the form V (r(x), θ(x)) = W(r) + Λ4

  • 1 − cos

r fr − θ fθ

  • Enrico Pajer

(Cornell) Inflation from axion monodromy KITP Mar 2010 39 / 43

slide-165
SLIDE 165

The two axions

Non-perturbative effects (e.g. ED1) and the monodromy term (5-brane) can wrap two overlapping but non-identiacal two-cycles. We can choose a basis of two-cycles such that only one axion has a monodromy, say r. We expect the effective potential of the form V (r(x), θ(x)) = W(r) + Λ4

  • 1 − cos

r fr − θ fθ

  • Big advantage: we do not need to carefully understand W(r) like

in the single field case

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 39 / 43

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SLIDE 166

The two axions

Non-perturbative effects (e.g. ED1) and the monodromy term (5-brane) can wrap two overlapping but non-identiacal two-cycles. We can choose a basis of two-cycles such that only one axion has a monodromy, say r. We expect the effective potential of the form V (r(x), θ(x)) = W(r) + Λ4

  • 1 − cos

r fr − θ fθ

  • Big advantage: we do not need to carefully understand W(r) like

in the single field case Even if W(r) has an η-problem, inflation can work provided fr ≪ fθ.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 39 / 43

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SLIDE 167

Smaller axion vev’s

Constraints from consistency and computabiility are the same as in the single field case.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 40 / 43

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SLIDE 168

Smaller axion vev’s

Constraints from consistency and computabiility are the same as in the single field case. The main difference is that now ∆r ≃ ∆φfr fθ ≪ ∆φ ∼ 15Mpl

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 40 / 43

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SLIDE 169

Smaller axion vev’s

Constraints from consistency and computabiility are the same as in the single field case. The main difference is that now ∆r ≃ ∆φfr fθ ≪ ∆φ ∼ 15Mpl A smaller ∆r implies less induced D3 charge, so less backreaction.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 40 / 43

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SLIDE 170

Smaller axion vev’s

Constraints from consistency and computabiility are the same as in the single field case. The main difference is that now ∆r ≃ ∆φfr fθ ≪ ∆φ ∼ 15Mpl A smaller ∆r implies less induced D3 charge, so less backreaction. KK-modes are heavier mKK,b ∼ mKK b ≃ mKK ∆φ fθ fr ≫ mKK ∆φ .

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 40 / 43

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SLIDE 171

Smaller axion vev’s

Constraints from consistency and computabiility are the same as in the single field case. The main difference is that now ∆r ≃ ∆φfr fθ ≪ ∆φ ∼ 15Mpl A smaller ∆r implies less induced D3 charge, so less backreaction. KK-modes are heavier mKK,b ∼ mKK b ≃ mKK ∆φ fθ fr ≫ mKK ∆φ . The shift of 4-cycle volumes is not a problem since it involves r while the inflaton is mostly θ which enjoys a shift symmetry.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 40 / 43

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SLIDE 172

Outline

1 Motivations 2 Inflation from axion monodromy 3 Dante’s Inferno 4 Conclusions

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 41 / 43

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SLIDE 173

To do list

There are many possible further directions Construct a more explicit model.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 42 / 43

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SLIDE 174

To do list

There are many possible further directions Construct a more explicit model. Investigate perturbative moduli stabilization.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 42 / 43

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SLIDE 175

To do list

There are many possible further directions Construct a more explicit model. Investigate perturbative moduli stabilization. Better understand the non-perturbative effects, also in light of their phenomenological consequences.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 42 / 43

slide-176
SLIDE 176

To do list

There are many possible further directions Construct a more explicit model. Investigate perturbative moduli stabilization. Better understand the non-perturbative effects, also in light of their phenomenological consequences. Find a more controlled monodromy.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 42 / 43

slide-177
SLIDE 177

To do list

There are many possible further directions Construct a more explicit model. Investigate perturbative moduli stabilization. Better understand the non-perturbative effects, also in light of their phenomenological consequences. Find a more controlled monodromy. Investigate the phenomenological consequences of the two-field model

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 42 / 43

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SLIDE 178

To do list

There are many possible further directions Construct a more explicit model. Investigate perturbative moduli stabilization. Better understand the non-perturbative effects, also in light of their phenomenological consequences. Find a more controlled monodromy. Investigate the phenomenological consequences of the two-field model . . .

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 42 / 43

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SLIDE 179

Conclusions

Cosmology offers a handle on high scale physics.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 43 / 43

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SLIDE 180

Conclusions

Cosmology offers a handle on high scale physics. Embedding axion monodromy inflation into string theory provides some insight into the possible origin of the flatness of the potential, i.e. shift symmetry.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 43 / 43

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SLIDE 181

Conclusions

Cosmology offers a handle on high scale physics. Embedding axion monodromy inflation into string theory provides some insight into the possible origin of the flatness of the potential, i.e. shift symmetry. The effective field theory approach hides many of the possible difficulties that can arise in a UV-finite theory of gravity.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 43 / 43

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SLIDE 182

Conclusions

Cosmology offers a handle on high scale physics. Embedding axion monodromy inflation into string theory provides some insight into the possible origin of the flatness of the potential, i.e. shift symmetry. The effective field theory approach hides many of the possible difficulties that can arise in a UV-finite theory of gravity. Phenomenologically axion monodromy fits existing data.

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 43 / 43

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SLIDE 183

Conclusions

Cosmology offers a handle on high scale physics. Embedding axion monodromy inflation into string theory provides some insight into the possible origin of the flatness of the potential, i.e. shift symmetry. The effective field theory approach hides many of the possible difficulties that can arise in a UV-finite theory of gravity. Phenomenologically axion monodromy fits existing data. It suggests exciting signal for the near future such as tensor modes, r ≃ 0.07, and possibly oscillations in the scalar spectrum and resonant non-Gaussianity (see Raphael’s talk tomorrow).

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 43 / 43

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SLIDE 184

Conclusions

Cosmology offers a handle on high scale physics. Embedding axion monodromy inflation into string theory provides some insight into the possible origin of the flatness of the potential, i.e. shift symmetry. The effective field theory approach hides many of the possible difficulties that can arise in a UV-finite theory of gravity. Phenomenologically axion monodromy fits existing data. It suggests exciting signal for the near future such as tensor modes, r ≃ 0.07, and possibly oscillations in the scalar spectrum and resonant non-Gaussianity (see Raphael’s talk tomorrow).

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 43 / 43

slide-185
SLIDE 185

Conclusions

Cosmology offers a handle on high scale physics. Embedding axion monodromy inflation into string theory provides some insight into the possible origin of the flatness of the potential, i.e. shift symmetry. The effective field theory approach hides many of the possible difficulties that can arise in a UV-finite theory of gravity. Phenomenologically axion monodromy fits existing data. It suggests exciting signal for the near future such as tensor modes, r ≃ 0.07, and possibly oscillations in the scalar spectrum and resonant non-Gaussianity (see Raphael’s talk tomorrow).

Enrico Pajer (Cornell) Inflation from axion monodromy KITP Mar 2010 43 / 43