Probing Inﬂation with CMB Polarizationcmbpol.uchicago.edu/workshops/path2009/depot/presentation-50.pdf · Probing Inﬂation with CMB Polarization Daniel Baumann High Energy Theory

Probing Inflation with CMB Polarization

Daniel Baumann

High Energy Theory GroupHarvard University

Chicago, July 2009

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

Daniel Baumann


Chicago, July 2009

the organizers

“I don’t know!”

Daniel Baumann


Chicago, July 2009

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

Daniel Baumann


Chicago, July 2009

Based on

CMBPol Mission Concept Study: Probing Inflation with CMB PolarizationDaniel 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-modes2. 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

InflationThe 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= !!

6(1 + 3w) > 0 " w < !1

3

a

a= (H2 + H) > 0 ! H =

!!

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 of primordial fluctuations

horizonH!1

‣ stretches microscopic scales to superhorizon sizes

‣ correlates spatial regions over apparently acausal distances

time

The Shrinking Hubble SphereThe comoving “horizon” shrinks during inflation

and grows after inflation

today

time

comoving scales

inflation reheating hot big bang

(aH)!1

(aH)!1 ! a12 (1+3w)

w > !13

w < !13

“Goodbye and Hello-again”

horizon exit horizon re-entry

sub-horizonsuper-horizon

sub-horizon

large-scale correlations can be set up causally!

today

time

comoving scales


(aH)!1

k!1

Conditions for Inflation

w < !13

" 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 DynamicsParameterize the decay of the inflationary energy by a scalar field Lagrangian

A flat potential drives acceleration

slow-roll conditions

! !M2

pl

2

!V !

V

"2

! !M2pl

V !!

V

!, |"| < 1Linde (1982)

Albrecht and Steinhardt (1982)

L =12(!")2 ! V (")

“clock”

inflation

end of inflation

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

reheating

!"

Zeta in the Sky

reheating

!"

!

!"

!T

inflaton fluctuations

curvature perturbationson uniform density hypersurfaces

density perturbations

CMB anisotropies

Zeta in the Sky

• gauge-invariant

• freeze on super-horizon scales!

curvature perturbationson uniform density hypersurfaces

ds2 = dt2 ! a2(t) e2!(t,x) dx2

Zeta in the Sky

!!k!k!" = (2")3 #(k + k!) P!(k)

two-point correlation function !!(x)!(x!)"

power spectrum

curvature perturbationon uniform density hypersurfaces

ds2 = dt2 ! a2(t) e2!(t,x) dx2

evaluated at horizon crossing

DB: TASI Lectures on Inflation (2009)

today

time

comoving scales


(aH)!1

k!1

The Inverse Problem


sub-horizon

today

time

comoving scales

zero-point fluctuations


(aH)!1

!kk!1

The Inverse Problem


sub-horizon

todayhorizon exit

time

comoving scales



(aH)!1

!!k!k!"

!kk!1

The Inverse Problem


super-horzionsub-horizon

todayhorizon exit

time

comoving scales



(aH)!1

!!k!k!"! # 0

!kk!1

The Inverse Problem

observed

predicted by inflation



transfer function

CMBrecombination today

projection

horizon exit

time

comoving scales

horizon re-entry



(aH)!1

C!!T!!k!k!"! # 0

!kk!1

The Inverse Problem

predicted by inflation



transfer function

CMBrecombination today

projection

horizon exit

time

comoving scales

horizon re-entry



(aH)!1

C!!T!!k!k!"! # 0

!kk!1

The Inverse Problemobserved

Prediction from Inflation

!2s !

k3

2!2P!(k) =

!H

2!

"2 !H

"

"2

!" !"! #de Sitter fluctuations conversion

Scalar Fluctuations

evaluated at horizon crossing k = aH


!2s !

k3

2!2P!(k) =

!H

2!

"2 !H

"

"2

Scalar Fluctuations

!2s = Ask

ns!1

scale-dependence

ns ! 1 = 2! ! 6"e.g. slow-roll inflation

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

H(t)


!2s !

k3

2!2P!(k) =

!H

2!

"2 !H

"

"2

Scalar Fluctuations

Different shapes for the inflationary potential

lead to slightly different predictions!

reheating 2!f0

Observations

Observational EvidenceFlatnessInflation predicts WMAP sees1

!k = 0 (±10!5) !0.0181 < !k < 0.0071

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

Observational EvidenceScalar FluctuationsInflation predicts WMAP seespercent-level deviations from ns = 1

ns = 0.963+0.014!0.015

2.5! ns = 1away from

Observational EvidenceScalar FluctuationsInflation predicts WMAP sees

Gaussian and Adiabatic Fluctuations

Gaussian and Adiabatic Fluctuations

Observational EvidenceScalar FluctuationsInflation predicts WMAP sees

Correlations of Superhorizon Fluctuations

Correlations of Superhorizon Fluctuations at Recombination

Multipole moment

(!+

1)C

TE

!/2

"[µ

K2]

tem

pera

ture

-pol

ariz

atio

n cr

oss-

corr

elat

ion

! > 1!

Fingerprints of the Early UniverseWe have only just begun to probe the fluctuations

created by inflation:

The next decade of experiments will be tremendously exciting!

Tensor Fluctuationsgravitational waves

not yet detected

Scalar Fluctuationsdensity 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!(!")2, (!#)2,!", . . .

"! V (", #)


• minimal models: single-field slow-roll

L =12(!")2 ! V (")

Gaussian fluctuations

all information in power spectra

ScalarsAs

ns

!s

shapeV !

V,

V !!

V,

V !!!

V

Tensors At

scale!

V



• 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


information beyond the power spectra bispectrum, trispectum, etc.


What do different parameter regimes for observables teach us

about high-energy physics?

e.g.r > 0.01 f local

NL > 1large tensors large non-Gaussianity


(this talk) (the coffee break)

Primordial Gravitational Waves

Tensors

Besides scalar fluctuations inflation produces tensor fluctuations:

ds2 = dt2 ! a2(t)(1 + hij)dxidxj

gravitational wavesmassless gravitons

de Sitter fluctuations of any light field

robust prediction of inflation!

!2t (k) =

8M2

pl

!H

2!

"2

TensorsThe tensor-to-scalar ratio

r ! !2t

!2s

is model-dependent because scalars are!

!2s (k) =

!H

2!

"2 !H

"

"2

strong model-dependence!

TensorsThe tensor-to-scalar ratio

r ! !2t

!2s

is model-dependent because scalars are!

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

In contrast,

!2t ! 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 TheoremB-modes are only created by gravitational

waves (tensor modes not scalar modes!)

E < 0

E > 0

B < 0

B > 0

! hijtensorsscalars

Seljak and Zaldarriaga, Kamionkowski et al.

The B-mode Theorem


! 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 operation or in planning.

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

Komatsu et al. (2008)WMAP 5 yrs.

r < 0.22tensor-to-scalar ratio


Superhorizon B-modes

1 23 4

2

1

1

2

-

-

CB(!) [mK2]

! [!]

DB and Zaldarriaga

superhorizon at recombination

unambiguous signature of inflation!

like the TE test for superhorizon scalarsSpergel and Zaldarriaga

B-modes as a Probe of High-Energy Physics

Energy Scale of InflationTensors 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 > 0.01It is hard to overstate the importance of such a result for the high-energy physics community which currently only has two indirect clues about physics at that scale:

1. Apparent Unification of Gauge Couplings2. Lower Bound on the Proton Lifetime

Tensors measure the energy scale of inflation

The Lyth Bound

!2t (k) =

8M2

pl

!H

2!

"2

dNe ! Hdt = d ln a

tensor-to-scalar ratio

where

!2s (k) =

!H

2!

"2 !H

"

"2

tensors scalars

r ! !2t

!2s

= 8!

d!

dNe

1Mpl

"2

The Lyth Boundtensor-to-scalar ratio

!!

Mpl!

! r

0.01

"1/2

field evolution over 60 e-foldsr ! !2t

!2s

= 8!

d!

dNe

1Mpl

"2

The Lyth Bound

!!

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

!!!Mpl

The Lyth Bound

i.e. we require a smooth potential over a range !!!Mpl

few !Mpl

But, in an effective field theory with cutoff

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

!

! < Mpl

EMpl

Ms

Msusy

MX

MY

MKK

H

m!

!

low-energy EFT

UV-completione.g. string theory

Effective Field Theory

Effective Field Theory EMpl

Ms

Msusy

MX

MY

MKK

H

m!

!

low-energy EFT


• integrate out heavy fields M > !If we know the complete theory:

V (!, ") ! Ve!(!)


Ms

Msusy

MX

MY

MKK

H

m!

!

low-energy EFT


• integrate out heavy fields M > !

• low-energy effective potential receives (computable) corrections

If we know the complete theory:

!V =O!

M !!4


Ms

Msusy

MX

MY

MKK

H

m!

!

low-energy EFT


• integrate out heavy fields M > !

• parameterize our ignorance about the UV, i.e. add all corrections consistent with symmetries.

Wilson

!V =!

!

O!

"!!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

observable gravitational waves


1. No Shift Symmetry in the UV

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

!

Ve!(!) =12m2!2 +

14"!4 +

!!

p=1

"p!4

"!

!

#2p

Effective Field Theory with Cutoff ! < Mpl


If the action is invariant under

! ! ! + const.

then the dangerous corrections are forbidden by symmetry

2. Shift Symmetry in the UV

Ve!(!) =12m2!2 +

14"!4 +

!!

p=1

"p!4

"!

!

#2p


! ! ! + const.

Ve!(!) =12m2!2

few !Mpl

e.g.

2. Shift Symmetry in the UV

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

Large-Field Inflation2. 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!!!Mpl

Primordial B-modes undetectable

• The Patch Problem

homogeneous patch

L > H!1

physical horizonH!1For 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!1/2Since

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

Small-Field!!!Mpl



• The Overshoot Problem

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

! ! V 1/2

overshoot

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

Small-Field!!!Mpl




• “Fine-Tuned” PotentialsBoyle, Steinhardt and Turok (2005)

!end !cmb

" = 1 " ! 1

For single-field models the transition

within 60 e-folds requires “fine-tuned” potentials!

r = 16 ! ! 1 " ! = 1

Small-Field!!!Mpl




• “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!!!Mpl





Large-FieldPrimordial B-modes detectable!

!!!Mpl

• Potentials are “Simple” Functions

e.g.V (!) =

12m2!2

but are corrections under control?

Small-Field!!!Mpl






!!!Mpl

• Attractor Solutions


Small-Field!!!Mpl






!!!Mpl

• Improved Initial Conditions



Small-Field!!!Mpl






!!!Mpl




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!!!Mpl






!!!Mpl

My prediction:

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




Conclusions


The Wagner Principle

50%


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

Documents

Probing Inﬂation with CMB Polarizationcmbpol.uchicago.edu/workshops/path2009/depot/presentation-50.pdf · Probing Inﬂation with CMB Polarization Daniel Baumann High Energy Theory