B-modes and the Nature of Inflation Daniel Baumann Cambridge - PowerPoint PPT Presentation

B-modes and the Nature of Inflation Daniel Baumann Cambridge University with Daniel Green and Rafael Porto STRINGS 2014

Data-Driven Cosmology Primordial density perturbations are: • superhorizon • scale-invariant • Gaussian • adiabatic Planck ? Have primordial gravitational waves been detected? BICEP2

What does this teach us about the UV-completion of inflation?

In e ff ective field theory , we parameterize the e ff ects of the UV-completion by higher-dimension operators. In this talk, I will consider the leading higher-derivative corrections to the slow-roll action: 2( ∂φ ) 2 − V ( φ ) − ( ∂φ ) 4 L = − 1 + · · · Λ 4 Λ

In e ff ective field theory , we parameterize the e ff ects of the UV-completion by higher-dimension operators. In this talk, I will consider the leading higher-derivative corrections to the slow-roll action: 2( ∂φ ) 2 − V ( φ ) − ( ∂φ ) 4 L = − 1 + · · · Λ 4 Λ This induces a non-trivial speed of sound for the inflaton fluctuations: L = − 1 � � ( ∂ t δφ ) 2 − c 2 c 2 s ( ∂ i δφ ) + · · · 2 s I will discuss what the data from Planck and BICEP teaches us about this important class of deformations of slow-roll inflation.

Higgs vs. Technicolor perturbative non-perturbative or ? can’t be described by small corrections to slow-roll inflation

Effective Theory of Inflation Cheung et al. Goldstone boson π ( t, x ) of broken time translations graviton h ij ( t, x ) H ( t ) The Goldstone and the graviton are massless, so their quantum fluctuations are amplified during inflation.

Effective Theory of Inflation Cheung et al. Goldstone boson π ( t, x ) graviton � � g ij = a 2 ( t ) (1 + 2 ζ ( t, x )) δ ij + 2 h ij ( t, x ) ζ ( t, x ) h ij ( t, x ) temperature anisotropies B-mode polarization

Slow-Roll Inflation Slow-roll inflation corresponds to nearly free Goldstone bosons with relativistic dispersion relation: � π 2 − ( ∂ i π ) 2 � pl | ˙ L π = M 2 H | ˙

Slow-Roll Inflation Slow-roll inflation corresponds to nearly free Goldstone bosons with relativistic dispersion relation: symmetry breaking scale � π 2 − ( ∂ i π ) 2 � pl | ˙ L π = M 2 H | ˙ quantum gravity scale

Slow-Roll Inflation (quantum gravity) background (symmetry breaking) Goldstone fluctuations (freeze-out) superhorizon

Slow-Roll Inflation (quantum gravity) background (symmetry breaking) Goldstone fluctuations (freeze-out) superhorizon

Slow-Roll Inflation (quantum gravity) background (symmetry breaking) Goldstone fluctuations (freeze-out) superhorizon

Beyond Slow-Roll Deviations from slow-roll inflation are parameterized by higher- order self-interactions and/or a non-trivial dispersion relation.

Beyond Slow-Roll Deviations from slow-roll inflation are parameterized by higher- order self-interactions and/or a non-trivial dispersion relation. A well-motivated possibility is a non-trivial sound speed :

Beyond Slow-Roll Deviations from slow-roll inflation are parameterized by higher- order self-interactions and/or a non-trivial dispersion relation. A well-motivated possibility is a non-trivial sound speed : non-linearly realized symmetry allows power spectrum measurements to constrain the interacting theory.

Beyond Slow-Roll symmetry breaking scale Writing gives strong coupling scale

Unitarity Bound 2-to-2 Goldstone scattering violates unitarity when DB and Green DB, Green and Porto

Beyond Slow-Roll (quantum gravity) background (symmetry breaking) strongly coupled (unitarity bound) Goldstone fluctuations (freeze-out) superhorizon

Beyond Slow-Roll (quantum gravity) background (symmetry breaking) strongly coupled (unitarity bound) Goldstone fluctuations (freeze-out) non-Gaussianity f NL ∝ 1 superhorizon c 2 s

A Theoretical Threshold Λ u = f π non-perturbative perturbative superluminal

A Theoretical Threshold non-perturbative perturbative ruled out by Planck superluminal

A New Bound on the Sound Speed DB, Daniel Green and Rafael Porto see also: Creminelli et al. [arXiv:0404.1065] D’Amico and Kleban [arXiv:0404.6478]

A small sound speed enhances the scalar power spectrum and suppresses the tensor-to-scalar ratio:

A small sound speed enhances the scalar power spectrum and suppresses the tensor-to-scalar ratio: BICEP2 then implies a lower bound on the sound speed: Creminelli et al. 16 ε > 0 . 01 r D’Amico and Kleban c s = ε

Naively, the bound weakens for large . But, for new e ff ects kick in: 1. scale-invariance of the scalars is in danger 2. tensors and scalars freeze at di ff erent times scalars tensors

scalars tensors This leads to an extra suppression in the tensor-to-scalar ratio: � H t � 2 r = 16 ε c s H s

Summing Large Logs At next-to-leading order in slow-roll, one finds: This is large in the regime of interest.

Summing Large Logs At next-to-leading order in slow-roll, one finds: This is large in the regime of interest. we can solve the evolution exactly: For DB, Green and Porto

A New Bound on the Sound Speed 0 . 22 0.20 0 . 18 0.15 0 . 14 c s r 0.10 0 . 10 0 . 06 0.05 0 . 02 0.02 0.05 0.1 0.2 0.5 1.0 ε 1 ε DB, Green and Porto

A New Bound on the Sound Speed 0 . 25 0 . 14 0 . 21 0 . 12 0 . 17 c s r 0 . 10 0 . 13 0 . 08 0 . 09 0 . 06 0 . 05 0.02 0.05 0.1 0.2 0.5 1.0 ε 1 ε DB, Green and Porto

Summing Large Logs Extending to and , we find: tensors scalars DB, Green and Porto

Expected Degeneracies Our bound would weaken if large is possible. ε But this has to be consistent n s − 1 = − 2 ε − η − s with the scalar spectrum: α s = − 2 εη

Expected Degeneracies Our bound would weaken if large is possible. ε But this has to be consistent n s − 1 = − 2 ε − η − s with the scalar spectrum: α s = − 2 εη Taking this into account strengthens the bound: I. II. strengthens the bound

Data Analysis * A joint likelihood analysis of Planck and BICEP2 gives: c s > 0 . 25 excluded by Planck * warning: no foreground subtraction CosmoMC

A New Bound on the Sound Speed π ( ∂ i π ) 2 | f ˙ | < 4 NL 0 . 25 non- ruled out by Planck + BICEP2 perturbative perturbative

Conclusions • If the BICEP2 result survives, then c s > 0 . 25 almost reaching the unitarity threshold ( c s ) � = 0 . 47 . threshold • This corresponds to | f ˙ π ( ∂ i π ) 2 BICEP2 , two orders of | < 3 . 3 4 NL magnitude stronger than the Planck-only bound. Planck • This does not rule out large equilateral non-Gaussianity from other operators in the EFT of inflation: π c (˜ ∂ i π c ) 2 π 3 = − ˙ − ˙ with Λ � Λ c s , L (3) e.g. c Λ 2 Λ 2 is radiatively stable! π c s • Order-one equilateral non-Gaussianity remains a well-motivated experimental target.

“If you build it they will come.” Thank you for your attention!

Robustness of the Bound δ 1 = 0 1.0 δ 1 6 = 0 δ 1 6 = 0 , Λ CDM δ 1 6 = 0 , { ε 3 , δ 2 } P 0.5 0.1 0.02 0.05 0.1 0.2 0.5 1.0 c s