Cosmology and String Theory

F. Quevedo Cambridge CORFU 2005

OUTLINE String Cosmology before 2003 FQ hepth/0210292 The KKLT Scenario and the String Landscape Inflation and Moduli Stabilization

STRING COSMOLOGY String theory is fundamental then it should have important implications in early universe Quantum gravity Big bang or before Experimental tests of the theory?

OBSERVATIONAL CHALLENGES

CMB Anisotropies

EXPERIMENTAL EVIDENCE FOR Λ>0 Ω = Ω Λ + Ω M + Ω K = 1 Ω = ρ/ρ c relative energy density K = -1,0,1 open, flat, closed universe Ω Λ ~ 0.7, Ω M ~ 0.3, Ω k ~ 0

PROBLEM

Do not understand the theory in time dependent backgrounds !!!

Effective Field Theories

General Aspects Branderberger-Vafa Scenario ((S 1 ) 9 x time) T-duality Minimal distance !

Winding modes D=4 (since 2+2=4)!

Pre Big-Bang Cosmology Gasperini, Veneziano,… t=0 singularity + strong coupling

String Theory and 4D Inflation

MOTIVATION Inflation: very successful but only scenarios in search of a theory String theory: fundamental theory but lacks experimental tests.

Is it possible to `derive’ inflation from string theory?

Need to compute scalar potential from String theory satisfying slow-roll conditions: Number of e-folds N>60 Density perturbations

HISTORY t<1986 Calabi-Yau String Compactifications: Many free moduli (size and shape of extra dimensions) from g mn , B mn , φ, A m I Candelas et al.

Dilaton S, K ähler T Complex structure U Wilson lines W 1986

Binetruy-Gaillard, Banks et al Or V too steep: Brustein-Steinhardt

New Problems: Overshooting (natural to end up in runaway) Cosmological Moduli Problem (moduli overclose the universe or ruin nucleosynthesis) Brustein-Steinhardt Coughlan et al.

Banks et al.

De Carlos et al.

t=1995-1998 The Brane World ADD, Horava Witten,…

t=1998 More moduli! : D-brane inflation. But V=0 or non-calculable.

Dvali-Tye t=2001 Brane/Antibrane inflation: Burgess et al., Dvali et al Generically no slow roll, but…

End of inflation: Open string tachyon Burgess et al.

V tachyon Y Tachyon complex topological defects D (p-2) branes cosmic strings !

Sen, Burgess et al.

Tye et al. Copeland et al.

Intersecting Brane Inflation Garcia-Bellido et al.

Y: Inflaton End of inflation: tachyon Also: D3-D7 inflation Kallosh et al.

Ekpyrotic/Cyclic Scenario Horava Witten 11D a(0)=0 weak coupling (bounce?) But: singularity? Potential by hand,…

Outstanding Problem Moduli Stabilization A Solution: turn-on fluxes …GKP, KKLT, … t> 2003 KKLT Scenario

KKLT Scenario Type IIB String on Calabi-Yau orientifold …GKP, KKLT, … Turn on Fluxes ∫ a F 3 = n a Superpotential ∫ b H 3 = m b Size of cycle a = U a W = ∫ G 3 Λ Ω, G 3 = F 3 –iS H 3 Scalar Potential: V= e K |D a W| 2 Minimum D a W = 0 Fixes U a and S T moduli unfixed: No-Scale models GKP

4D Compactifications

To fix K ähler moduli: Non-perturbative D7 effects Fluxes Non-perturbative Volume SUSY AdS minimum (W 0 << 1)

Lifting to de Sitter (add anti D3 branes, D-terms, etc.) KKLT, BKQ, SS SUSY breaking term V axion volume

The Landscape Huge number of discrete vacua >10 500 Statistics AD, DD, DDF, GKTT,CQ,BGHLW Randall-Sundrum warping from strings!

GKP Non SUSY de Sitter Dark energy?

BP `SM’ on D3/D7branes CG-MQU Soft SUSY breaking?

Inflation?

Populating the Landscape Classical Solutions Quantum decay (tunnel efect)

Multiverse and Eternal Inflation

Realistic Models CG-MQU, CSU

Exponentially Large Volumes BBCQ, CQS At least two K ähler moduli (h 21 >h 11 >1) Perturbative corrections to K Example : Exponentially large !

Non SUSY AdS W 0 ~1-10 String scale: Ms 2 =Mp 2 /

V

W 0 ~10 -10 KKLT AdS Non SUSY AdS Both minima merge W 0 <10 -11

Inflation and Moduli Stabilization

Brane-Antibrane Inflation KKLMMT, HKP, KTW, FT, BCSQ, … φ inflaton field φ D3 Brane

Slow-roll (large field) inflation possible.

Need 1/1000 fine tuning of parameters to get 60-efoldings ( η-problem) N~60, δ H ~10 -5 Ms~ 10 15 GeV for n s ~1.05

Burgess, Cline, Stoica, FQ Needs at least two throats !

Also: D3-D7 on K3xT2 DBI in the sky Kallosh et al.

Silverstein-Tong, Chen

Warped Tachyonic Inflation Sen, Raeymakers, Cremades-Sinha-FQ A,B depend on warping (fluxes) and E&M fields on non BPS brane. If A,B~1 no slow-roll AB large slow-roll No fine-tuning! But need large fluxes

INITIAL CONDITIONS Sen’s open string completeness conjecture t -t Pre big-bang ! ?

Inflation and compactification or big-crunch/bang and decompactification ! ?

Racetrack Inflation Blanco-Pillado et al.

Topological eternal inflation !

Slow roll if 1/1000 fine tuning, N~60, δ H ~10 -5 for Ms~10 15 GeV n s ~ 0.95

Improved Racetrack Blanco-Pillado et al.

Douglas et al.

Explicitly derived model Similar physics

K ähler Moduli Inflation Any Calabi-Yau: h 21 >h 11 >2 Conlon-FQ Large field inflation No fine-tuning!!

0.960

V volume τ n

CONCLUSIONS Exciting times Type IIB: Several inflationary scenarios, Inflaton: Kahler modulus, brane sparation, tachyon, Wilson lines , Complex structure moduli (?).

Open questions Reheating Extensions to other string theories ( Becker et al ) Initial conditions Overshooting problem,….