Making and Probing Inflation

Lev Kofman

KITPC Beijing November 6 2007

Making Inflation in String Theory

How small can be r

Gravity Waves from Preheating

Concise History of the Early Universe

Early Universe Inflation

Scale factor

time

Realization of Inflation

Inflation in the context of ever changing fundamental theory

1980

2000

1990

-inflation Old Inflation

New Inflation Chaotic inflation

Double InflationExtended inflation

DBI inflation

Super-natural Inflation

Hybrid inflation

SUGRA inflation

SUSY F-term inflation SUSY D-term

inflation

SUSY P-term inflation

Brane inflation

K-flationRoulette

Warped Brane inflation

inflation

Power-law inflation

Tachyon inflationRacetrack inflation

Assisted inflation

Family phase portrait of inflation

string theoristCY

AdS3+1 FRW

Inflation in String Theory: Cosmology with Compactification

string theoristCY

AdS3+1 FRW

Inflation in String Theory: Cosmology with Compactification

3+1 FRW

CYcosmologist

Modular Inflation.Modular Inflation. They use Kahler moduli/axion

like the fields that are a present in the KKLT stabilization.

Brane inflation.Brane inflation. The inflaton field corresponds to the distance between branes in Calabi-Yau space. Historically, this was the first class of string inflation models.

Modular Inflation.Modular Inflation. They use Kahler moduli/axion

like the fields that are a present in the KKLT stabilization.

Brane inflation.Brane inflation. The inflaton field corresponds to the distance between branes in Calabi-Yau space. Historically, this was the first class of string inflation models.

String Theory inflation models

Inflation with branes in String Theory

4-dim picture

Prototype of hybrid inflation

Inflation with branes in String Theory

4-dim picture

Prototype of hybrid inflation

throat warped geometry

Mobile brane

KKLMMT

m2 = 2H

Conformal coupling problem

Due to conformal coupling effective inflaton mass

Expected to prevent inflation

m2 = 2H

Conformal coupling problem

Due to conformal coupling effective inflaton mass

Expected to prevent inflation

Rapid-roll Inflation with conformal coupling

Scalar field non-minimally coupling with gravity

Rapid-roll inflation with conformal field

De Sitter solution

Efoldings

warping

Efoldings and mass hierarchy

Energy scale

Efoldings and mass hierarchy

solution

Kahler moduli Inflation (Conlon&Quevedo hep-th/050912)Roulette Inflation-Kahler moduli/axion

(Bond, LK, Prokushkin&Vandrevange hep-th/0612197)

String theory landscape of the Kahler moduli/axion Inflation

Ensemble of Inflationary trajectories

Lessons:

Multiple fields Inflation

Ensemble of acceleration histories (trajectories)for the same underlying theory

Prior probabilities of trajectories P(H(t))

Small amplitude of gravity waves r from inflation

Generation of gravitational waves from inflation

time

Hubble radius

end of inflation

recombination

inflationHot FRW

Initial conditions from Inflation

Baumann&Mcallister hep-th/0610285

Lyth hep-ph/9606387

Efstathiou &Mack astro-ph/0503360

.SpiderBalloon2009.9

PlanckSatellite2008.6

CMBPol 2017

Measurement of GW from CMB anisotropy polarization

0.1

0.01

< 0.34 Current limit

0.001 Ultimate limit

superheavy gravitino

A discovery or non-discovery of tensor modes A discovery or non-discovery of tensor modes would be a crucial test for string theory and particle would be a crucial test for string theory and particle

phenomenologyphenomenology

unobservable

for inflationary perturbations

KKLTKKLT

Kallosh, Linde hepth/0704.0647

Amplitude of GW and gravitino mass

Particlegenesis

time

Inflation

no entropyno temperature

BANG

Occupation number

Classical Quantum

Resonant Preheating in Chaotic Inflation

Resonant Preheating in Chaotic Inflation

preheatingexp excitation

Kolmogorovturbulence of bosons

thermalizationNon-linear

“bubbly” stage

Classical Quantum

Decay of inflatonand preheating after inflation

movie

Felder, LKhep-ph/0606256

Classical Quantum

Decay of inflatonand preheating after inflation

movie

Classical Quantum

Decay of inflatonand preheating after inflation

Evolutionof energy density

Evolution of gravitational potentiall

A. Frolov 07

Tachyonic Preheating in Hybrid Inflation

l

movie

Tachyonic Preheating

Generation of gravitational waves from random media

time

Hubble radius

end of inflation

recombination

Stochastic background of gravitational waves emitted from preheating after inflation

Emission of stochastic GW by random media

Emission of stochastic GW by random scalar fields

First order phase transitionsSecond order phase transitionsTopological defects formation

Thermal bath of scalarsTachyonic preheatingResonant preheating

No GW emission

GW generated for non-trivial dispersion relation

Random gaussian fields

Emission of GW from preheating

Numerical calculations of GW emission from Preheating

Numerical calculations of GW emission from Preheating

Analytic check

estimation

Shortcut to the answer Felder, LKhep-ph/0606256

topological effects after hybrid inflation (unstable)formation of defects results in GW emission

Application to particular hybrid model

GW from high energy inflation are targeted by CMB B-mode polarization experiments

The story of stochastic gravitational waves isCMB anisotropies of 21 century

GW from low-energy inflation are targeted by GW astronomy