Phenomenological Phenomenological Classification of Inflationary Classification of Inflationary

PotentialsPotentials

Katie Mack (Princeton University)

with George Efstathiou (Cambridge University)

Efstathiou & Mack, JCAP 05, 008 (2005)astro-ph/0503360

The Lyth Bound RevisitedThe Lyth Bound Revisited

Katie Mack (Princeton University)

with George Efstathiou (Cambridge University)

Efstathiou & Mack, JCAP 05, 008 (2005)astro-ph/0503360

Outline

• Current status of inflation

• What the observations can tell us

• Linking observations to fundamental theory (Lyth Bound)

• Phenomenological approach

• Implications for future theoretical work

The inflationary paradigm today

• Inflation is successful offers solution to

horizon problemflatness problem

general predictions have been upheldflat universegaussian and adiabatic metric fluctuationsnearly scale-independent spectrum

…but which inflation theory are we talking about?

The inflationary paradigm today

• Inflation is successful offers solution to

horizon problemflatness problem

general predictions have been upheldflat universegaussian and adiabatic metric fluctuationsnearly scale-independent spectrum

…but which inflation theory are we talking about?

S-dimensional assisted inflation assisted brane inflationanomoly-induced inflationassisted inflationassisted chaotic inflationboundary inflationbrane inflationbrane-assisted inflationbrane gas inflationbrane-antibrane inflationbraneworld inflationBrans-Dicke chaotic inflationBrans-Dicke inflationbulky brane inflationchaotic inflationchaotic hybrid inflationchaotic new inflationD-brane inflationD-term inflationdilaton-driven inflationdilaton-driven brane inflationdouble inflationdouble D-term inflation

dual inflation dynamical inflationdynamical SUSY inflationeternal inflationextended inflationextended open inflationextended warm inflationextra dimensional inflationF-term inflationF-term hybrid inflationfalse-vacuum inflationfalse-vacuum chaotic inflationfast-roll inflationfirst-order inflationgauged inflationHagedorn inflationhigher-curvature inflationhybrid inflationhyperextended inflationinduced gravity inflationintermediate inflationinverted hybrid inflationisocurvature inflation......................

@ Paul Shellard

• Tensor modesTensor modes– produced by gravitational waves– no contribution from density perturbations

• Detection would…– confirm prediction of primordial gravitational waves in

inflation– give the energy scale of inflation

the good news

“…we cannot yet distinguish between broad classes of inflationary theories that have different physical motivations.” –Peiris et al. (2003)

WMAP alone WMAP+2dF+Lyα

the bad news

Seljak et al., 2004 (astro-ph/0407372)

B-Mode Polarization

Current upper limits

r = 0.36

Beyond WMAP

• Currently proposed experiments (ground and balloon-borne) can reach r=0.01 at ~3σ level

• Space-based, with improved foreground knowledge, could get to r~10-3 at ~3σ

(Verde, Peiris & Jimenez, astro-ph/0506036)

You may ask…What about gravitational wave detectors?

Of the planned experiments, only Big Bang Observer (next generation after LISA) has any chance of detecting primordial

GWs

Linking observation to physics

• Future experiments may detect primordial gravitational waves, but what would this tell us about inflation itself?

• Goal: Find a way to link the observables to the fundamental physics without assuming a particular model

Phenomenological Approach

• Produce a set of inflationary models to be as general as possible

• Require only:– single field– inflation sustained long enough to solve

horizon problem (~ 55 e-foldings)

• Calculate r and Δφ, compare with Lyth Bound

The Lyth BoundDavid Lyth (1996) suggests rough relation:

for ΔN ~ 4 (CMB multipoles ~2 to ~100)

Considering the full course of inflation, with at least 50-60 e-folds, Δφ could exceed this by an order of magnitude

If slow-roll parameter

is monotonically increasing, a stronger condition is required:

The Lyth Bound

General expectation:

large r => large Δφ

High values of r require changes in the field value of order mPl

Monte Carlo Reconstruction Results (106 models)

But in the real world…

• Can improve the scatter by comparing with observables

• From Seljak et al. 2004, astro-ph/0407372

n run

0.92 < ns < 1.06-0.04 < nrun < 0.03

Remaining models

• Now have tighter empirical relationship between r and Δφ

Δφ/mPl ~ 6 r1/4

(for r > ~ 10-3)

What have we learned?

• To obtain a large value of r, you need a large variation in the scalar field

• For r ~ 10-3, need Δφ of order unity

If any conceivable CMB polarization experiment is to detect tensor modes,

Δφ must be large

Implications for inflationLarge field variations cannot be described by low-energy

effective field theory, where the potential is written as:

with . This is invalid for .

Does that mean we need new physics?Not necessarily… quantum gravity corrections may still be

small as long as V < mpl4

But we will need a new way to talk about such models.

The bottom line

Future CMB polarization experiments can only probe high field inflation models (e.g.,

chaotic inflation)

Understanding the physics of such models is important if such experiments are to tell us anything useful about the mechanism

behind inflation

NN=50 N=0

t=t_i t t=t_end

initialparameters

NN=50 N=0

t=t_i t t=t_end

initialparameters

NN=50 N=0

t=t_i t t=t_end

x

initialparameters

NN=50 N=0

t=t_i t t=t_end

x

observables

initialparameters

NN=50 N=0

t=t_i t t=t_end

observables

x

initialparameters

parameters at epsilon = 1

NN=50 N=0

t=t_i t t=t_end

observables

x

initialparameters

parameters at epsilon = 1

NN=50 N=0

t=t_i t t=t_end

x

observables

x

initialparameters

parameters at epsilon = 1

NN=50 N=0

t=t_i t t=t_end

x

observables

observables

x

initialparameters

parameters at epsilon = 1

parameters at N=50

V 50 e-foldings before end of

inflation

end of inflation

Single-field inflation

• Scalar field φ rolling down potential V(φ)

• Slow rolling of inflaton field causes inflation

• Some commonly considered models: V ~ φ2

V ~ φ4

Mechanics of inflation

Equations of Motion: • Change in Hubble Parameter depends on change in scalar field (“speed of roll”)

• In slow-roll inflation, take H ~ constant, slow roll of inflaton

• Expand Hubble Parameter in power series

• Use slow-roll parameters to represent this expansion

acceleration

Condition for inflation:

Satisfied when:

E mode and B mode polarization

E modes (no curl) B modes (no divergence)

WMAP vs. Planck

TE TE

E E

Planck projected B-mode measurement

B-mode: r = 0.1, = 0.17

Other experiments

Clover

QUIET

None of these experiments likely to probe below r ~10-2

Cooray, astro-ph/0503118

r = 0.13

r = 5 * 10-4

r = 10-5

Limits on future gravitational

wave experiments