Tachyon Mediated Non-Gaussianity. Louis Leblond Texas A&M - - PowerPoint PPT Presentation

Tachyon Mediated Non-Gaussianity.

Louis Leblond Texas A&M Cosmo 08 University of Wisconsin-Madison

arXiv:0805.1229 hep-th/0610321

Bhaskar Dutta, Jason Kumar, L.L. L.L. and Sarah Shandera

Louis Leblond, Cosmo 08, Madison

Non-Gaussianity in the CMB

Gaussianity is a consequence of the slow-rolling conditions (from which the inflaton behaves like a free field). Detectable NG can be generated by going beyond the standard single field slow-roll approximation. non-standard kinetic term (e.g. DBI) Multi-fields (this talk, present a string theory motivated D-term inflation with NG from multi-fields)

WMAP5 −9 < f N L < 111

Silverstein & Tong

ζ( x, t) = ζGauss + 3 5fNL(ζ2

Gauss − ζ2 Gauss)

Louis Leblond, Cosmo 08, Madison

Tachyon Mediated Non-Gaussianity

In Hybrid inflation

Visible Hidden T

many string theory models are of this type

φ ζ

, Curvature

Louis Leblond, Cosmo 08, Madison

A Quick History

In multi-fields inflation, curvature ( )is NOT constant after horizon exit and NG can be generated in its evolution. In general, one needs to integrate these effects over the whole trajectory but in many systems, the effects can all be located at the end simplifying the analysis. Curvaton: a new field starts dominating the energy density well after the end of inflation. Modulated Reheating: Reheating starts everywhere in sync, but the final temperature is modulated. Modulated End: The onset of reheating is modulated but then proceed everywhere the same.

Bernardeau & Uzan Bernardeau, Kofman, Uzan

Linde & Mukhanov Lyth & Wands Moroi & Takahashi

Dvali, Gruzinov & Zaldarriaga

Lyth Alabidi & Lyth

ζ

Louis Leblond, Cosmo 08, Madison

A Quick History

In multi-fields inflation, curvature ( )is NOT constant after horizon exit and NG can be generated in its evolution. In general, one needs to integrate these effects over the whole trajectory but in many systems, the effects can all be located at the end simplifying the analysis. Curvaton: a new field starts dominating the energy density well after the end of inflation. Modulated Reheating: Reheating starts everywhere in sync, but the final temperature is modulated. Modulated End: The onset of reheating is modulated but then proceed everywhere the same.

Bernardeau & Uzan Bernardeau, Kofman, Uzan

Linde & Mukhanov Lyth & Wands Moroi & Takahashi

Dvali, Gruzinov & Zaldarriaga

Lyth Alabidi & Lyth

ζ

Louis Leblond, Cosmo 08, Madison

Basic Idea

Couple Hybrid inflation (2 fields) to an extra field. (Here Tachyon = Waterfall field) There is no direct coupling between and . They couple only through the T which is very massive during inflation. Inflation ends at a critical value of the inflaton for which the mass of the tachyon is zero.

V = Vinf(φ) + Vhid(χ) + Vmess(φ, χ, T)]

φ χ

φc(χ)

modulated by quantum fluctuation

• f the hidden field

Horizon exit C Inflation ends B A t

ζ = δN

N = φc(χ)

φ∗

H ˙ φ dφ

δN = −H ˙ φ δφ

• ∗

+ H ˙ φ ∂φc ∂χ δχ

• φc

+1 2 H ˙ φ ∂2φc ∂χ2

• δχ2− < δχ2 >
• φc

+ · · ·

Louis Leblond, Cosmo 08, Madison

From field perturbations to curvature.

delta N formalism

The new field only change the end

• f inflation

* = horizon exit

“transfer function”

γ ≡ ∂φc ∂χ

• φc

Usual contribution

Note sign difference

Sasaki & Stewart

κ ∼ e−ηχNe

Louis Leblond, Cosmo 08, Madison

The 2-pt function

Pζ

2 =

H2

∗

8π2M 2

pl

1 ǫ∗ + γ2κ2 ǫf

• include a “damping”

ηχ ∼ 0.01 Ne ∼ 55

κ ∼ 0.6 most models must have

γ < 1

counter example: hilltop potential which flattens out at the end

Alabidi and Lyth

In most models, the potential is steeper at the end than at horizon exit (could argue it is unnatural to have it the other way around)

In brane inflation, inflation ends with a tachyon. Coulombic potential is too steep while the DBI regime does better. Most recent analysis found no effects.

Lyth & Riotto L.L. & Shandera Chen, Gong, Shiu

f int

NL ∼ NeMpγ3κ6

H2 ǫ2

∗

ǫ3/2

f

V,χχχ

F( k1, k2, k3) ∼ −NeH2V,χχχκ6 k3

i

k3

i

< δχ3 > < δζ3 >

Louis Leblond, Cosmo 08, Madison

The intrinsic contribution to fNL

Bernardeau, Brunier

T φ ζ

,

χ

Falk, Rangarajan, Srednicki, ’93 Zaldarriaga Lyth, Malik Seery

Barnaby, Cline

In most model the contribution to the 2-pt will be negligible but the 3- pt function can be significant. Because, the hidden field is NOT the inflaton, its potential can be steeper and it can be strongly interacting.

Louis Leblond, Cosmo 08, Madison

The Non-linear Contribution

From the non-linear piece in the delta N, we will get a non-zero 3-pt curvature even for gaussian

χ

δN = −H ˙ φ δφ

• ∗

+ H ˙ φ ∂φc ∂χ δχ

• φc

+1 2 H ˙ φ ∂2φc ∂χ2

• δχ2− < δχ2 >
• φc

+ · · ·

β ≡

• f int

NL

f loc

NL

• = 1

3 γ γ,χ V,χχχ H2 Neκ The ratio of these two contributions

γ ∼ χ β ∼ ηχNeκ2

This is always smaller than 1 but one can still have a significant fraction of NG in intrinsic

Louis Leblond, Cosmo 08, Madison

The Non-linear Contribution

From the non-linear piece in the delta N, we will get a non-zero 3-pt curvature even for gaussian

χ

β ≡

• f int

NL

f loc

NL

• = 1

3 γ γ,χ V,χχχ H2 Neκ The ratio of these two contributions

γ ∼ χ β ∼ ηχNeκ2

This is always smaller than 1 but one can still have a significant fraction of NG in intrinsic

Louis Leblond, Cosmo 08, Madison

The Non-linear Contribution

From the non-linear piece in the delta N, we will get a non-zero 3-pt curvature even for gaussian

χ

f loc

NL ∼ −∂γ

∂χγ2κ4Mp ǫ2

∗

ǫ3/2

f

β ≡

• f int

NL

f loc

NL

• = 1

3 γ γ,χ V,χχχ H2 Neκ The ratio of these two contributions

γ ∼ χ β ∼ ηχNeκ2

This is always smaller than 1 but one can still have a significant fraction of NG in intrinsic

W = λφTϕ1 + λNGχTϕ2

Louis Leblond, Cosmo 08, Madison

IBM-flation

Can realize D-term inflation, using open string between branes (strings are in vector- like rep) Using gauge invariance one can “brane engineered” flat direction by forbidding dimension 6 operators for example. and large NG mediated by the tachyon can get a regime with cosmic strings

S

+

• a

b c

ns ∼ 1

Dutta, Kumar, L.L

Battye, Garbrecht, Moss Bevis, Hindmarsh, Kunz, Urestilla

φ

T

ϕ1

W = λφTϕ1 + λNGχTϕ2

Louis Leblond, Cosmo 08, Madison

IBM-flation

Can realize D-term inflation, using open string between branes (strings are in vector- like rep) Using gauge invariance one can “brane engineered” flat direction by forbidding dimension 6 operators for example. and large NG mediated by the tachyon can get a regime with cosmic strings

S

+

• a

b c

ns ∼ 1

Dutta, Kumar, L.L

Battye, Garbrecht, Moss Bevis, Hindmarsh, Kunz, Urestilla

φ

T

ϕ1

ϕ2 χ

Louis Leblond, Cosmo 08, Madison

Detailed example

The tachyon mass depends on both and

φ

χ

m2

T = −g2ξ + λ2φ2 + (λ2 NG − qg2 2)χ2

γ ≈ χ f int

NL ∼ −8 ,

ns ∼ 1.002 , f loc

NL ∼ 45 ,

Gµ ∼ 7 × 10−7 .

so the non-linear contribution dominate

a point in parameter space

Louis Leblond, Cosmo 08, Madison

Conclusion

One can generate observable NG at the end of hybrid inflation with a rich structure. Many models fails because the potential is too steep at the

• end. D-term inflation in the regime of flat spectrum can lead

to observable NG. The NG has the local shape and both sign can be obtained. One can write a string theory motivated model with such

• features. Another, more detailed but similar models will be

presented here. A new look into multi-field DBI?

Haack, Kallosh, Krause, Linde, Lust, Zagermann

L.L. & Shandera Huang, Shiu & Underwood Langlois, Renaux-Patel, Steer, Tanaka