Open Problems in Inflationary Cosmology

Open Problems in Inﬂationary Cosmology

Daniel Baumann Institute for Advanced Study

Benasque, February 2011 -34 10 sec. Was inﬂation the primordial origin of all structure in the universe? ? 380,000 yrs.

Eva Silverstein

Anthony Lewis 13.7 billion yrs.

Volker Springel

Licia Verde How can inﬂation become part of the standard history of the universe with the same level of conﬁdence as BBN ? Outline

Observations Theory

1. Current Observations 2. Status “What do we really know?” “What is Inﬂation?”

4. Future Observations 3. Problems “How can we learn more?” “Physics thrives in crisis” Steven Weinberg Current Observations The homogeneous universe is well- described by a ﬂat FRW background.

0.0181 < Ω < 0.0071 − k

WMAP The homogeneous universe is well- described by a ﬂat FRW background.

(Primordial) density ﬂuctuations are: • small

∆T 4 10− T ∼

COBE The homogeneous universe is well- described by a ﬂat FRW background.

(Primordial) density ﬂuctuations are: • small • scale-invariant

n 1 P (k) k s− s ∝ ns(k)

CMB LRG

Peiris and Verde (2010) k The homogeneous universe is well- described by a ﬂat FRW background.

(Primordial) density ﬂuctuations are: • small • scale-invariant • Gaussian

fNL =0 fNL = 500

1% non-Gaussianity The homogeneous universe is well- described by a ﬂat FRW background.

(Primordial) density ﬂuctuations are: • small • scale-invariant • Gaussian • adiabatic

Multipole moment WMAP The homogeneous universe is well- described by a ﬂat FRW background.

(Primordial) density ﬂuctuations are: • small • scale-invariant • Gaussian • adiabatic • superhorizon

θ > 1◦ TE ! " cross-correlation temperature-polarization angular scales WMAP Multipole moment Inﬂation is an elegant explanation for the data: Guth (1980) ﬂat homogeneous

adiabatic

Gaussian

scale-invariant superhorizon

Multipole moment isotropic Theory Inflation We need a definition: H˙ H2 − " where ds2 = dt2 + a(t)2d!x 2 − a˙ H = a Inflation H˙ H2 − " There exist many different microscopic realizations of inflation, BUT only a few distinct mechanisms (effective theories) Inflation H˙ H2 approximate− time-translation" symmetry Inflation H˙ H2 inflation has to −end, so symmetry" is spontaneously broken

fluctuations in the ‘clock’ Goldstone boson δφ π δt ∼ ˙ δa ∼ φ ζ = Hπ ∼ a curvature perturbations Inflation H˙ H2 tests of minimal− inflation" = tests of (pseudo)-Goldstone

ﬂuctuations are predicted to be: nearly massless • scale-invariant m2 H˙ π = | | 1 • Gaussian H2 H2 ! • adiabatic • superhorizon Inﬂation H˙ H2 − " implies a shrinking Hubble sphere

d 1 (aH)− < 0 dt comoving scales 1 (aH)− ζ˙ =0 Pζ (k) C! sub-horizon super-horizon ∆T 1 k− ζˆ transfer projection function zero-point ﬂuctuations exit re-entry

CMB today time inﬂation reheating hot big bang Inverse Problem predicted observed comoving scales 1 (aH)− ζ˙ =0 Pζ (k) C! sub-horizon super-horizon ∆T 1 k− ζˆ transfer projection function zero-point ﬂuctuations exit re-entry

CMB today time inflation reheating hot big bang Classic Predictions scalar fluctuations tensor fluctuations

H4 H2 Pζ P ∼ M 2 H˙ h 2 pl ∼ Mpl

power spectra teach us about: H(t) Cheung et al. Senatore et al. Non-Gaussianity in the effective theory of inﬂation

quasi-dS Goldstone curvature perturbation H(t) π ζ = Hπ

2 22 2 Lorentz symmetry 2 π˙ ccss (∂iπ) L ∝ speed− of sound non-linearly realized 1 2 (1) 3 symmetry 3 2 π˙ (∂iπ) + O 2 π˙ L ∝ ccs cs Cheung et al. Senatore et al. Non-Gaussianity in the effective theory of inﬂation

1 2 (1) 3 3 2 π˙ (∂iπ) + O 22 π˙ L ∝ cs css 1 large interactions from small sound speed: • fNL 2 ∼ cs • two distinct shapes:

equilateral orthogonal +

214

• vanishing squeezed limit: =0 Maldacena Senatore and Zaldarriaga Multi-Field Inﬂation φ2

• natural from the top-down? • new phenomenology? - isocurvature ﬂuctuations - squeezed non-Gaussianity - new consistency conditions

reheating surface φ1 What is the “theory space” of multi-field inflation? Challenges WhatWhat is theis the physics physics of ofinflation? inflation? How did inflation start? • singularity - inflation is past-geodesically incomplete. before Initial Conditions - is there really a horizon problem in QG? • patch problem • overshoot problem • eternal inflation? • measure problem

What is the physics of inﬂation? during Lagrangian • UV-sensitivity: - eta problem - gravitational waves - non-Gaussianity • naturalness / ﬁne-tuning

after Reheating How did inflation end? • observational signatures? WhatWhat is theis the physics physics of ofinflation? inflation? How did inflation start? • singularity - inflation is past-geodesically incomplete. before Initial Conditions - is there really a horizon problem in QG? • patch problem • overshoot problem • eternal inflation? • measure problem

What is the physics of inﬂation? during Lagrangian • UV-sensitivity: - eta problem - gravitational waves - non-Gaussianity • naturalness / ﬁne-tuning

after Reheating How did inﬂation end? • observational signatures? So far we have discussed ﬂuctuations around a given quasi-de Sitter background H(t)

but we haven’t said how this background arises in the ﬁrst place. Problem 1: Why is the inﬂaton so light ? The Eta Problem

2 2 slow-roll inﬂation: V (φ)=MplH M 2 V 2 ε = pl ! 1 2 V ! ! " 2 V !! η = Mpl 1 V ! scalar ﬁeld φ

Why is the inﬂaton so light ? m2 η φ 1 ≈ H2 " The Eta Problem like the Higgs hierachy problem

m2 Λ2 H2 φ ∼ uv ! The Eta Problem

like the Higgs hierachy problem

m2 H2 φ ∼ supersymmetry ameliorates the problem, but doesn’t solve it. need ﬁne-tuning or additional symmetry (1 part in 100) (easy to assume, hard to explain) The Eta Problem mφ H Mpl ? energy low-energy Λ UV-completion effective ﬁeld theory e.g. string theory

integrate out massive particles or parameterize our ignorance

slow-roll potential high-energy corrections

δ(φ) V0(φ) + O δ 4 ΛΛ − !δ In inﬂation, even Planck-suppressed interactions cannot be ignored ! The Eta Problem

Inﬂation is sensitive to dimension-6 Planck-suppressed operators

φ2 ∆V = V0 2 ∆η =1 Mpl

Can we forbid corrections with a symmetry ? The Eta Problem 2 shift symmetry φ V φ φ + const. 0 2 → Λ

spontaneous breaking of global symmetries

Many models implement this solution in supergravity.

φ The Eta Problem BUT: How does the symmetry arise from the top-down? What is the UV-completion? The Eta Problem BUT: “Quantum gravity breaks global symmetries.”

Conﬁrmed by many examples in string theory. charge in Banks et al. (1999) Seiberg and Banks (2010) More generally: Black hole evaporation breaks global symmetries e.g. Kallosh et al. (1995)

charge out = ???

Planck-suppressed operators reintroduce the eta problem ! The Eta Problem

“Quantum gravity breaks global symmetries.” protecting the inﬂation from this is the real challenge:

1. compute the symmetry breaking effects in string theory see Eva Silverstein’s talk

2. find a sufficiently powerful symmetry in field theory e.g. “Inflating with Baryons” DB and Daniel Green Every model of inflation has to address the eta problem.

Some classes of models have observational signatures that dramatically enhance the UV sensitivity:

Gravitational Waves Non-Gaussianity Problem 2: Is large ‘r’ UV-completable ? Gravitational Waves CMB Polarization

E-mode

B-mode

measures: H

Mpl energy scale of inﬂation Gravitational Waves CMB Polarization

E-mode

B-mode

observable if: Pt tensor-to-scalar ratio: r 0.01 ≡ Ps ! gravity waves density ﬂuctuations Gravitational Waves

The Lyth Bound ∆φ r 1/2

Mpl ≈ 0.01 ! "Lyth (1996) φend φCMB ∆φ observable gravitational waves super-Planckian ﬁeld variation r 0.01 ∆φ M ! ! pl

This makes an effective ﬁeld theorist nervous and a string theorist curious! Gravitational Waves observable gravitational waves n 4 φ ∆φ M Λ ∆V = φ cn ! pl ! Λ n " # an inﬁnite series of! corrections, of arbitrarily high dimension, can become important Hence, we expect:

... while we need:

few M × pl Gravitational Waves

φ n ∆V = φ4 c n Λ n ! " #

What is the UV-completion of large-ﬁeld inﬂation?

Opportunity for String Inﬂation! see Eva Silverstein’s talk Problem 3:

Is small ‘cs’ UV-completable ? Non-Gaussianity

measures: inflaton interactions (going beyond free-fields) Non-Gaussianity slow-roll inflation =(∂φ)2 V (φ) small self-interactions Gaussian fluctuations L − + higher-derivative corrections ∞ (∂φ)2n ∆ = c L n Λ2n n=2 !

non-Gaussian ﬂuctuations c 1 s !

observable if and only if: (∂φ)2 Λ4 UV completion ? ∼ see DBI inﬂation breakdown of the derivative expansion ! Non-Gaussianity Can also see the problem in the effective theory of the Goldstone ﬂuctuations: DB and Daniel Green (to appear)

slow-roll small cs strong coupling

2 2 M H˙ symmetry breaking M H˙ cs pl| | pl| |

2 ˙ 5 strong coupling Mpl H cs | | new physics ? H4 Hubble scale H4 “Why should I care about UV-completion?” Future Observations 1. Gravitational Waves

2. Non-Gaussianity 3. Multi-Field Inflation Can we falsify inflation? Can we falsify inflation ? Can we falsify ...

the paradigm? single-ﬁeld? multi-ﬁeld?

4 local 2 Ω > ζ 10− f > 1 τNL > (fNL) k ∼ NL ?

H˙ n =2 > 0 nt =8csr nt > 8r t H2 | | ! | |

superhorizon vector modes ? ? ? Conclusions φ2 V0 2 Mpl eta problem

Inﬂation is sensitive to Planck-scale physics!

gravitational waves non-Gaussianity 2 4 ∆φ Mpl (∂φ) M ! ∼ pl inflatoninflaton massmass WhatWhat is theis the physics physics of ofinflation? inflation? How did inflation start? • singularity - inflation is past-geodesically incomplete. before Initial Conditions - is there really a horizon problem in QG? • patch problem • overshoot problem • eternal inflation? • measure problem

What is the physics of inﬂation? during Lagrangian • UV-sensitivity: - eta problem - gravitational waves - non-Gaussianity ? • naturalness / ﬁne-tuning

after Reheating How did inﬂation end? • observational signatures? The End