Cosmology and String Theory F. Quevedo Cambridge CORFU 2005

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

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 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 ! 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 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 1986<t<1991 Geometric moduli: candidate for inflaton fields. But no potentials (V=0). Or V too steep: Or V too steep: Dilaton S, Kähler T Complex structure U Wilson lines W Candelas et al. Binetruy-Gaillard, Banks et al 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= The Brane World ADD, Horava-Witten,…

t=1998 More moduli! : D-brane inflation. But V=0 or non-calculable. t=2001 Brane/Antibrane inflation: Dvali-Tye Generically no slow roll, but… Burgess et al., Dvali et al

V Y tachyon Tachyon complex topological defects D (p-2) branes cosmic strings ! End of inflation: Open string tachyon Burgess et al. Tye et al. Copeland et al. Sen, Burgess et al.

Intersecting Brane Inflation Y: Inflaton End of inflation: tachyon Also: D3-D7 inflation Garcia-Bellido et al. Kallosh et al.

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

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

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

4D Compactifications

To fix Kähler 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.) SUSY breaking term KKLT, BKQ, SS V axionvolume

The Landscape Huge number of discrete vacua > Statistics Randall-Sundrum warping from strings! Non SUSY de Sitter Dark energy? `SM’ on D3/D7branes Soft SUSY breaking? Inflation? AD, DD, DDF, GKTT,CQ,BGHLW GKP BP CG-MQU

Populating the Landscape Classical Solutions Quantum decay (tunnel efect)

Multiverse and Eternal Inflation

Realistic Models CG-MQU, CSU

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

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

KKLT AdS Non SUSY AdS W 0 ~ W 0 < Both minima merge

Inflation and Moduli Stabilization

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

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 for Ms~ GeV 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 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 Sen, Raeymakers, Cremades-Sinha-FQ

INITIAL CONDITIONS Sen’s open string completeness conjecture t -t Pre big-bang ! ? Inflation and compactification or big-crunch/bang and decompactification ! ? and decompactification ! ?

Racetrack Inflation 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 Blanco-Pillado et al.

Improved Racetrack Blanco-Pillado et al. Douglas et al. Explicitly derived model Similar physics

Kähler Moduli Inflation Any Calabi-Yau: 21 > 11 h 21 >h 11 >2 volume τnτn V Conlon-FQ Large field inflation No fine-tuning!! 0.960<n<0.967

CONCLUSIONS Exciting times Type IIB: Several inflationary scenarios, Inflaton: Kahler modulus, brane sparation, tachyon, Wilson lines, Complex structure moduli (?). Reheating Extensions to other string theories ( Becker et al ) Initial conditions Overshooting problem,…. Open questions