Probing Inflation with CMB Polarization Daniel Baumann High Energy - - PowerPoint PPT Presentation

Probing Inflation with CMB Polarization

Daniel Baumann

High Energy Theory Group Harvard University

Chicago, July 2009

“How likely is it that B-modes exist at the r=0.01 level?”

Daniel Baumann

High Energy Theory Group Harvard University

Chicago, July 2009

the organizers

“I don’t know!”

Daniel Baumann

High Energy Theory Group Harvard University

Chicago, July 2009

“What can we learn from a B-mode detection at the r=0.01 level?”

Daniel Baumann

High Energy Theory Group Harvard University

Chicago, July 2009

Based on CMBPol Mission Concept Study: Probing Inflation with CMB Polarization

Daniel Baumann, Mark G. Jackson, Peter Adshead, Alexandre Amblard, Amjad Ashoorioon, Nicola Bartolo, Rachel Bean, Maria Beltran, Francesco de Bernardis, Simeon Bird, Xingang Chen, Daniel J. H. Chung, Loris Colombo, Asantha Cooray, Paolo Creminelli, Scott Dodelson, Joanna Dunkley, Cora Dvorkin, Richard Easther, Fabio Finelli, Raphael Flauger, Mark P. Hertzberg, Katherine Jones-Smith, Shamit Kachru, Kenji Kadota, Justin Khoury, William H. Kinney, Eiichiro Komatsu, Lawrence M. Krauss, Julien Lesgourgues, Andrew Liddle, Michele Liguori, Eugene Lim, Andrei Linde, Sabino Matarrese, Harsh Mathur, Liam McAllister, Alessandro Melchiorri, Alberto Nicolis, Luca Pagano, Hiranya V. Peiris, Marco Peloso, Levon Pogosian, Elena Pierpaoli, Antonio Riotto, Uros Seljak, Leonardo Senatore, Sarah Shandera, Eva Silverstein, Tristan Smith, Pascal Vaudrevange, Licia Verde, Ben Wandelt, David Wands, Scott Watson, Mark Wyman, Amit Yadav, Wessel Valkenburg, and Matias Zaldarriaga

White Paper of the Inflation Working Group

arXiv: 0811.3919

• 1. B-modes
• 2. Non-Gaussianity

Outline

• 1. Classical Dynamics of Inflation
• 2. Quantum Fluctuations from Inflation
• 3. Current Observational Evidence

PART 1: THE PRESENT PART 2: THE FUTURE

Part 1: THE PRESENT

Inflation

The Quantum Origin of Structure in the Early Universe

Inflation

Guth (1980)

ds2 = dt2 − a(t)2 dx2

A period of accelerated expansion sourced by

¨ a > 0

a nearly constant energy density and negative pressure ¨ a a = −ρ 6(1 + 3w) > 0 ⇔ w < −1 3 ¨ a a = (H2 + ˙ H) > 0 ⇔ H = ρ 3 ≈ const.

Inflation

Guth (1980)

A period of accelerated expansion solves the horizon and flatness problems

= 0

= 0

i.e. explains why the universe is so large and old!

creates a nearly scale-invariant spectrum

• f primordial fluctuations

horizon

H−1

• stretches microscopic scales to

superhorizon sizes

• correlates spatial regions over

apparently acausal distances

time

The Shrinking Hubble Sphere

The comoving “horizon” shrinks during inflation and grows after inflation

today

time comoving scales

inflation

reheating

hot big bang

(aH)−1

(aH)−1 ∝ a

1 2 (1+3w)

w > −1 3 w < −1 3

“Goodbye and Hello-again”

horizon exit horizon re-entry

sub-horizon

super-horizon

sub-horizon

large-scale correlations can be set up causally!

today

time comoving scales

inflation

reheating

hot big bang

(aH)−1

k−1

Conditions for Inflation

w < −1 3 ⇔ d(aH)−1 dt < 0 ⇔ ¨ a > 0

negative pressure shrinking comoving horizon accelerated expansion

crucial for the generation of perturbations at the heart of the solution of the horizon and flatness problems

and

What is the Physics of the Inflationary Expansion?

We don’t know!

This is why we are here!

Classical Dynamics

Parameterize the decay of the inflationary energy by a scalar field Lagrangian

A flat potential drives acceleration

slow-roll conditions

ǫ ≡ M 2

pl

2 V ′ V 2 η ≡ M 2

pl

V ′′ V

ǫ, |η| < 1

Linde (1982) Albrecht and Steinhardt (1982)

L = 1 2(∂φ)2 − V (φ)

“clock” inflation end of inflation

Quantum Dynamics

Quantum fluctuations lead to a local time delay in the end of inflation and density fluctuations after reheating

reheating

δρ

Zeta in the Sky

reheating

δφ

ζ

δρ ∆T

inflaton fluctuations curvature perturbations

• n uniform density hypersurfaces

density perturbations CMB anisotropies

Zeta in the Sky

• gauge-invariant
• freeze on super-horizon scales!

curvature perturbations

• n uniform density hypersurfaces

ds2 = dt2 − a2(t) e2ζ(t,x) dx2

Zeta in the Sky

ζkζk′ = (2π)3 δ(k + k′) Pζ(k)

two-point correlation function

ζ(x)ζ(x′)

power spectrum curvature perturbation

• n uniform density hypersurfaces

ds2 = dt2 − a2(t) e2ζ(t,x) dx2

evaluated at horizon crossing

DB: TASI Lectures on Inflation (2009)

today

time comoving scales

inflation

reheating

hot big bang

(aH)−1

k−1

The Inverse Problem

DB: TASI Lectures on Inflation (2009)

sub-horizon

today

time comoving scales

zero-point fluctuations

inflation

reheating

hot big bang

(aH)−1 ˆ ζk

k−1

The Inverse Problem

DB: TASI Lectures on Inflation (2009)

sub-horizon

today

horizon exit

time comoving scales

zero-point fluctuations

inflation

reheating

hot big bang

(aH)−1

ζkζk

ˆ ζk

k−1

The Inverse Problem

DB: TASI Lectures on Inflation (2009)

super-horzion

sub-horizon

today

horizon exit

time comoving scales

zero-point fluctuations

inflation

reheating

hot big bang

(aH)−1

ζkζk

˙ ζ ≈ 0

ˆ ζk

k−1

The Inverse Problem

• bserved

predicted by inflation

DB: TASI Lectures on Inflation (2009)

super-horzion

sub-horizon

transfer function

CMB recombination

today

projection

horizon exit

time comoving scales

horizon re-entry zero-point fluctuations

inflation

reheating

hot big bang

(aH)−1

C ∆T

ζkζk

˙ ζ ≈ 0

ˆ ζk

k−1

The Inverse Problem

predicted by inflation

DB: TASI Lectures on Inflation (2009)

super-horzion

sub-horizon

transfer function

CMB recombination

today

projection

horizon exit

time comoving scales

horizon re-entry zero-point fluctuations

inflation

reheating

hot big bang

(aH)−1

C ∆T

ζkζk

˙ ζ ≈ 0

ˆ ζk

k−1

The Inverse Problem

• bserved

Prediction from Inflation

∆2

s ≡ k3

2π2 Pζ(k) = H 2π 2 H ˙ φ 2

δφ

δφ → ζ

de Sitter fluctuations conversion

Scalar Fluctuations

evaluated at horizon crossing k = aH

Prediction from Inflation

∆2

s ≡ k3

2π2 Pζ(k) = H 2π 2 H ˙ φ 2

Scalar Fluctuations

∆2

s = Askns−1

scale-dependence

ns − 1 = 2η − 6ǫ

e.g. slow-roll inflation

how the power is distributed over the scales is determined by the expansion history during inflation

H(t)

Prediction from Inflation

∆2

s ≡ k3

2π2 Pζ(k) = H 2π 2 H ˙ φ 2

Scalar Fluctuations

Different shapes for the inflationary potential lead to slightly different predictions!

reheating

2πf

Observations

Observational Evidence

Flatness

Inflation predicts WMAP sees1 Ωk = 0 (±10−5) −0.0181 < Ωk < 0.0071

1WMAP 5yrs.+BAO: 95% C.L.

Observational Evidence

Scalar Fluctuations

Inflation predicts WMAP sees

percent-level deviations from ns = 1

ns = 0.963+0.014

−0.015

2.5σ ns = 1

away from

Observational Evidence

Scalar Fluctuations

Inflation predicts WMAP sees

Gaussian and Adiabatic Fluctuations Gaussian and Adiabatic Fluctuations

Observational Evidence

Scalar Fluctuations

Inflation predicts WMAP sees

Correlations of Superhorizon Fluctuations

Correlations of Superhorizon Fluctuations at Recombination

Multipole moment

(ℓ + 1)CT E

ℓ

/2π [µK2]

temperature-polarization cross-correlation

θ > 1◦

Fingerprints of the Early Universe

We have only just begun to probe the fluctuations created by inflation: The next decade of experiments will be tremendously exciting!

Tensor Fluctuations

gravitational waves

not yet detected

Scalar Fluctuations

density fluctuations

detected

• hints of scale-dependence
• first constraints on Gaussianity and Adiabaticity
• superhorizon nature confirmed

Part 2: THE FUTURE

How can we probe the Physical Origin of Inflation?

How do we constrain the Inflationary Action?

“like in all of physics we ultimately want to know the action”

• field content
• potential, kinetic terms
• interactions
• symmetries
• couplings to gravity
• etc.

L = f

• (∂φ)2, (∂ψ)2, φ, . . .
• − V (φ, ψ)

How do we constrain the Inflationary Action?

• minimal models: single-field slow-roll

L = 1 2(∂φ)2 − V (φ)

Gaussian fluctuations all information in power spectra

Scalars

As ns αs

shape

V ′ V , V ′′ V , V ′′′ V

Tensors At scale!

V

“like in all of physics we ultimately want to know the action”

How do we constrain the Inflationary Action?

• minimal models: single-field slow-roll
• non-minimal models:
• non-minimal coupling to gravity
• multiple fields
• higher-derivative interactions

fluctuations can be non-Gaussian and non-adiabatic

“like in all of physics we ultimately want to know the action”

information beyond the power spectra bispectrum, trispectum, etc.

How do we constrain the Inflationary Action?

What do different parameter regimes for observables teach us about high-energy physics?

e.g.

r > 0.01 f local

NL

> 1

large tensors large non-Gaussianity

“like in all of physics we ultimately want to know the action” (this talk) (the coffee break)

Primordial Gravitational Waves

Tensors

Besides scalar fluctuations inflation produces tensor fluctuations:

ds2 = dt2 − a2(t)(1 + hij)dxidxj

gravitational waves

massless gravitons de Sitter fluctuations of any light field

robust prediction of inflation!

∆2

t(k) =

8 M 2

pl

H 2π 2

Tensors

The tensor-to-scalar ratio

r ≡ ∆2

t

∆2

s is model-dependent because scalars are!

∆2

s(k) =

H 2π 2 H ˙ φ 2

strong model-dependence!

Tensors

The tensor-to-scalar ratio

r ≡ ∆2

t

∆2

s is model-dependent because scalars are!

The prediction for tensors is simple and the same in all models!

In contrast,

∆2

t ∝ H2

Detecting Tensors via B-modes

E- and B-modes

E-mode

• Polarization is a rank-2 tensor field.
• One can decompose it into a divergence-like E-mode

and a vorticity-like B-mode.

B-mode

The B-mode Theorem

B-modes are only created by gravitational waves (tensor modes not scalar modes!)

E < 0 E > 0 B < 0 B > 0

ζ hij

tensors scalars

Seljak and Zaldarriaga, Kamionkowski et al.

The B-mode Theorem

Seljak and Zaldarriaga, Kamionkowski et al.

ζ hij

Challinor

B-modes are only created by gravitational waves (tensor modes not scalar modes!)

The B-mode Theorem

So far only upper-limits, but many experiments now in

• peration or in planning.

Detection of primordial B-modes is often considered a smoking gun of inflation.

Komatsu et al. (2008)

WMAP 5 yrs. r < 0.22

tensor-to-scalar ratio

Seljak and Zaldarriaga, Kamionkowski et al.

Superhorizon B-modes

1 2 3 4 2 1 1 2

• C

˜ B(θ) [mK2]

θ [◦]

DB and Zaldarriaga

superhorizon at recombination

unambiguous signature of inflation!

like the TE test for superhorizon scalars

Spergel and Zaldarriaga

B-modes as a Probe of High-Energy Physics

Energy Scale of Inflation

Tensors measure the energy scale of inflation

Einf ≡ V 1/4 = 1016GeV r 0.01 1/4

Single most important data point about inflation!

If we observe tensors it proves that inflation occurred at the GUT-scale!

r > 0.01

Energy Scale of Inflation

Einf ≡ V 1/4 = 1016GeV r 0.01 1/4

Single most important data point about inflation!

r > 0.01

It is hard to overstate the importance of such a result for the high-energy physics community which currently

• nly has two indirect clues about physics at that scale:
• 1. Apparent Unification of Gauge Couplings
• 2. Lower Bound on the Proton Lifetime

Tensors measure the energy scale of inflation

The Lyth Bound

∆2

t(k) =

8 M 2

pl

H 2π 2

dNe ≡ Hdt = d ln a

tensor-to-scalar ratio

where

∆2

s(k) =

H 2π 2 H ˙ φ 2

tensors scalars

r ≡ ∆2

t

∆2

s

= 8 dφ dNe 1 Mpl 2

The Lyth Bound

tensor-to-scalar ratio

∆φ Mpl ≈ r 0.01 1/2

field evolution over 60 e-folds

r ≡ ∆2

t

∆2

s

= 8 dφ dNe 1 Mpl 2

The Lyth Bound

∆φ Mpl ≈ r 0.01 1/2

If we observe tensors it proves that the inflaton field moved over a super-Planckian distance!

r > 0.01

∆φ ≫ Mpl

The Lyth Bound

i.e. we require a smooth potential

• ver a range ∆φ ≫ Mpl

few × Mpl

But, in an effective field theory with cutoff we generically don’t expect a smooth potential over a super-Planckian range

Λ

Λ < Mpl

E

Mpl

Ms Msusy MX MY MKK

H mφ

Λ

low-energy EFT UV-completion

e.g. string theory

Effective Field Theory

Effective Field Theory

E

Mpl

Ms Msusy MX MY MKK

H mφ

Λ

low-energy EFT UV-completion

e.g. string theory

• integrate out heavy fields M > Λ

If we know the complete theory:

V (φ, ψ) → Veff(φ)

Effective Field Theory

E

Mpl

Ms Msusy MX MY MKK

H mφ

Λ

low-energy EFT UV-completion

e.g. string theory

• integrate out heavy fields M > Λ
• low-energy effective potential

receives (computable) corrections

If we know the complete theory:

∆V = Oδ M δ−4

Effective Field Theory

E

Mpl

Ms Msusy MX MY MKK

H mφ

Λ

low-energy EFT UV-completion

e.g. string theory

• integrate out heavy fields M > Λ
• parameterize our ignorance about the UV,

i.e. add all corrections consistent with symmetries.

Wilson

∆V =

• δ

Oδ Λδ−4

If we know the complete theory:

• low-energy effective potential

receives (computable) corrections

Typically, we don’t know the complete theory:

Large-Field Inflation

UV sensitivity of inflation is especially strong in any model with

• bservable gravitational waves

Large-Field Inflation

• 1. No Shift Symmetry in the UV

we generically don’t expect a smooth potential over a super-Planckian range

Λ

Veff(φ) = 1 2m2φ2 + 1 4λφ4 +

∞

• p=1

λpφ4 φ Λ 2p Effective Field Theory with Cutoff Λ < Mpl

Large-Field Inflation

If the action is invariant under

φ → φ + const.

then the dangerous corrections are forbidden by symmetry

• 2. Shift Symmetry in the UV

Veff(φ) = 1 2m2φ2 + 1 4λφ4 +

∞

• p=1

λpφ4 φ Λ 2p

Large-Field Inflation

φ → φ + const. Veff(φ) = 1 2m2φ2

few × Mpl

e.g.

• 2. Shift Symmetry in the UV

With such a shift symmetry chaotic inflation is “technically natural”

Large-Field Inflation

• 2. Shift Symmetry in the UV

Seeing B-modes would show that the inflaton field respected a shift symmetry up to the Planck scale! We know fields with that property:

axions1

1 The first controlled large-field models using axions have recently been constructed

in string theory.

Large-Field vs. Small-Field

Small-Field

∆φ ≪ Mpl

Primordial B-modes undetectable

• The Patch Problem

homogeneous patch

L > H−1

physical horizon

H−1

For inflation to start the inflaton field has to be homogeneous over a distance that is a few times the horizon size at that time!

H−1 ∝ r−1/2

Since this seems to be a bigger problem for small-field (low-r) models.

Small-Field

∆φ ≪ Mpl

Primordial B-modes undetectable

• The Patch Problem
• The Overshoot Problem

For inflation to start the field has to reach the flat part of the potential with small speed.

˙ φ ∼ V 1/2

• vershoot

This problem is worse for small- field (low-r) models.

Small-Field

∆φ ≪ Mpl

Primordial B-modes undetectable

• The Patch Problem
• The Overshoot Problem
• “Fine-Tuned” Potentials

Boyle, Steinhardt and Turok (2005)

φend φcmb

= 1 1

For single-field models the transition within 60 e-folds requires “fine-tuned” potentials!

r = 16 ǫ ≪ 1 ⇒ ǫ = 1

Small-Field

∆φ ≪ Mpl

Primordial B-modes undetectable

• The Patch Problem
• The Overshoot Problem
• “Fine-Tuned” Potentials

These qualitative fine-tuning problems of small- field inflation are hard to quantify! Typically, the arguments run into the ill- understood measure problem!

Small-Field

∆φ ≪ Mpl

Primordial B-modes undetectable

• The Patch Problem
• The Overshoot Problem
• “Fine-Tuned” Potentials

Large-Field

Primordial B-modes detectable!

∆φ ≫ Mpl

• Potentials are “Simple”

Functions

e.g. V (φ) = 1 2m2φ2

but are corrections under control?

Small-Field

∆φ ≪ Mpl

Primordial B-modes undetectable

• The Patch Problem
• The Overshoot Problem
• “Fine-Tuned” Potentials

Large-Field

Primordial B-modes detectable!

∆φ ≫ Mpl

• Attractor Solutions
• Potentials are “Simple” Functions

Small-Field

∆φ ≪ Mpl

Primordial B-modes undetectable

• The Patch Problem
• The Overshoot Problem
• “Fine-Tuned” Potentials

Large-Field

Primordial B-modes detectable!

∆φ ≫ Mpl

• Improved Initial Conditions
• Potentials are “Simple” Functions
• Attractor Solutions

Small-Field

∆φ ≪ Mpl

Primordial B-modes undetectable

• The Patch Problem
• The Overshoot Problem
• “Fine-Tuned” Potentials

Large-Field

Primordial B-modes detectable!

∆φ ≫ Mpl

• Potentials are “Simple” Functions
• Attractor Solutions
• Improved Initial Conditions

A convincing argument that the tensor amplitude has to be large does NOT exist! HOWEVER, there is also no convincing argument that it has to be small!

Small-Field

∆φ ≪ Mpl

Primordial B-modes undetectable

• The Patch Problem
• The Overshoot Problem
• “Fine-Tuned” Potentials

Large-Field

Primordial B-modes detectable!

∆φ ≫ Mpl

My prediction: Before we (theorists) come up with such an argument, YOU will have DETECTED B-modes!

• Potentials are “Simple” Functions
• Attractor Solutions
• Improved Initial Conditions

Conclusions

“How likely is it that B-modes exist at the r=0.01 level?”

The Wagner Principle

50%

“How likely is it that B-modes exist at the r=0.01 level?”

The Wagner Principle

50%

If something can either happen or not happen the chances are 50-50.

black holes at the LHC destroying the Earth?

Walter Wagner

More seriously:

i.e. flatness and homogeneity of the universe and a primordial spectrum of nearly scale-invariant, Gaussian and adiabatic scalar fluctuations. Inflation has been remarkably successful at explaining all current observations However, in some sense this may be viewed as a “postdiction” (debatable)

(We knew the universe was homogeneous and had small density fluctuations)

i.e. flatness and homogeneity of the universe and a primordial spectrum of nearly scale-invariant, Gaussian and adiabatic scalar fluctuations. Tensor modes are a robust prediction of inflation. Seeing their B-mode signature would be a remarkable achievement. It would teach us a great deal about the physics of inflation and rule out all alternative theories. Inflation has been remarkably successful at explaining all current observations

A B-mode detection would teach us a great deal about the physics of inflation:

• 1. Inflation occured!
• 2. It happened near the GUT-scale!
• 3. The inflaton field moved over a super-Planckian

distance! 3’. Its potential was controlled by a shift symmetry.

i.e. the inflaton was something like an axion

Thank you for your attention!

There is more to be learnt from Scalars!

Non-Gaussianity and Non-Adiabaticity probe further details of the inflationary action: field content, interactions, symmetries, ... I didn’t have time to describe this, but see: CMBPol Mission Concept Study: Probing Inflation with CMB Polarization

White Paper of the Inflation Working Group

arXiv: 0811.3919