Inflation and Branes

Bottom-up approach to inflation: reconstruction of acceleration trajectories

Top-down approach to inflation:seeks to embed it in fundamental theory

Lev Kofman, CITA

Nearly Normal Galaxies August 8, 2005, Santa Cruz

Early Universe Inflation

Scale factor

time

Realization of Inflation

Particlegenesis

time

Inflation

no entropyno temperature

BANG

Classical Quantum

Decay of inflatonand preheating after inflation

movieFelder, LK, Linde, 01,05

Classical Quantum

Decay of inflatonand preheating after inflation

inflationHot FRW

Initial conditions from Inflation

4 dimensional Inflation predicts

No classical inhomogeneities from the past

Scale free gaussian fluctuations of all light scalars

No vector perturbations

Scalar (almost scale free gaussian) metric perturbations

Tensor (scale free gaussian) metric perturbations

Creation of all SM particles in preheating/thermalization

Òtot =1

Cö÷úû = 0

î ÿk(t)eik~x~

Aö =0

Ð ! Ðk(t)eik~x~

hik ! hk(t)eik~x~eij

Treh

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-flationN-flation

Warped Brane inflation

inflation

Power-law inflation

Tachyon inflationRacetrack inflation

Assisted inflation

Search for inflaton with branes in extra dimensions

4-dim picture

Dvali,Tye 98

Compactification of inner dimensions with branes

Old string theory

New phenomenology

Strongly warped 5d geometry

ds2 = A2(y)(à dt2+dx~2) +gabdyadyb

Randal, Sundrum 99

New ideas about 4d gravity

New interactions with SM particles

New ideas about mass hierarchy

New ideas about cosmological constant

New ideas about Inflation

Stabilization of Inner dimensionsand moduli in string theory

dS4 â M

ds2 = A2(y)(à dt2+e2Htdx~2) +gabdyadyb

Realization of String Theory Inflation

on the ground of KKLT throat warped geometry

Hybrid inflationwith inflaton fluctuationsMobile brane

Mobile brane

modulated fluctuations

Conformal coupling problem

Chaotic inflation

scalar field associated with angular position at

KKLMMT03

Mukohyama, LK 05

Kallosh etal 02

Open strings

between branes are unstable

End point of inflation

BANG

SM particles

Closed strings

Unstable KK modes

Long-living KK modesrelated to inner isometries

LK, Yi 05

string theoristCY

AdS3+1 FRW

Fluctuations in Cosmology with Compactification

string theoristCY

AdS3+1 FRW

3+1 FRW

Fluctuations in Cosmology with Compactification

CYcosmologist

string theorist

Practical cosmologist

CY

AdS

CY +fluctuations

3+1 FRW

3+1 FRW

3+1 FRW +fluctuations

Fluctuations in Cosmology with Compactification

CYcosmologist

Modulated Fluctuations

Hà1

x~

t

Light field at inflation

Inflation radiation

LK03, Dvali etal03

4 dim Inflation in 10dim String Theory predicts

All what 4 dim inflation predicts

Scale free gaussian fluctuations of many light scalars

Creation of non-SM particles (KK modes) in reheating/thermalization

î ÿk(t)eik~x~

TK K

Short-wavelength gravitational radiation

Modulated cosmological fluctuations

String theory Cosmic strings

Scanning Inflation R.Bond, C.Contaldi,A.Frolov, L.KofmanT.SouradeepP.Vandrevange

Bottom-up

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-flationN-flation

Warped Brane inflation

inflation

Power-law inflation

Tachyon inflationRacetrack inflation

Assisted inflation

Ensemble of Inflationary trajectories

Chebyshev decomposition

Space of models opens wide

H(N) P(k)

ns;nt; r;dn=dlnk;As; :::

ï ;ñ:::

Observational constraints on trajectories

Markov Chain Monte Carlo

Degeneracy of the Potential Reconstruction

Reconstruction of Inflationary Trajectory

Cosmic Numerology: CMBall + LSS, stable & consistent pre-WMAP1 & post-WMAP1 (BCP03), Jun03 data (BCLP04), CMBall+CBIpol04, CMBall+Boom03+LSS

Jul’21 05, CMBall Jul05

LSS=2dF, SDSS (weak lensing, cluster abundances); also HST, SN1a

As = 22 +- 3 x 10-10

ns = .95 +- .02 (.97 +- .02 with tensor) (+- .004 PL1)

At / As < 0.36 95% CL (+- .02 PL2.5+Spider)

dns /dln k = -.07 +- .04 to -.05 +- .03 (+- .005 P1)

-.002 +- .01 (+Lya McDonald etal 04)

(Aiso / As < 0.3 large scale, < 3 small scale niso = 1.1+-.6)

The Parameters of Cosmic Structur Formation