New Cosmological Implications for LARGE Volume Scenarios

1. New Cosmological Implications for LARGE Volume Scenarios Michele Cicoli DAMTP, University of Cambridge StringPheno09, Warsaw, 16 June 2009 Based on: MC, C. Burgess, F. Quevedo arXiv:0808.0691 [hep-th] Using previous work contained in: MC, J. Conlon, F. Quevedo arXiv:0708.1873 [hep-th] MC, J. Conlon, F. Quevedo arXiv:0805.1029 [hep-th] Fibre Inflation NB: L. Anguelova, V. Calò, MC arXiv:0904.0051 [hep-th] SeeCalò’s talk Finite-temperature effects

2. Why String Inflation? Inflation is highly UV sensitive since you need to obtain light scalar masses need an UV complete theory to trust model building in an EFT use String Theory! String Theory has many non-trivial constraints to inflationary model building It is not obvious that you can get everything out of it! E.g.: Tensor Modes •Try to put String Theory to experimental test! •Inflation involves energy scales higher than those which can be reached by any planned terrestrial experiment more promising to probe string-related physics •The requirement of sensible embedding into String Theory can restrict the number of viable field-theoretic models •New observational data coming soon: PLANCK, EPIC, CMBPol! •Find where we are in the Landscape and how we end up there

3. Inflation is UV sensitive Slow-roll conditions are sensitive to dim 6 Planck suppressed operators !!! V=exp(K)U where K=f*f/M2P Expand K V=(1+f*f/M2P)U Contribution to h h problem!!!

4. Large Tensor Modes This UV sensitivity becomes even stronger for models which predict observable gravity waves!!! Lyth Bound: Present limit (WMAP5+BAO+SN): r<0.2 Forecasts for future cosmological observations: PLANCK r~10-1 SPIDER r~10-2 CMBPol r~10-3 Trust EFT? * NB Minf~MGUT r1/4 see GUT scale physics!!!

5. String Theory and 4D Inflation Focus on slow-roll inflation Two general classes of string inflation Open String Inflaton Closed String Inflaton _ - Inflaton is a brane position modulus: D3/D3, D3/D7 - NO symmetry solving the h problem  requires fine tuning! - Inflaton is a Kaehler modulus T i)Re(T)=volume of 4-cycles: blow-ups, fibration, Volume Natural solution of the eta problem!!! Due to the NO-SCALE structure of the potential!! dim 6 Planck suppressed operators under control !!! probably related to symmetries of the higher-dimensional theory! ii)Im(T)=axion a h problem solved by shift symmetry a a+e

6. Blow-up Inflation • Type IIB CY flux compactifications: LARGE Volume Scenarios • Inflaton is a blow-up mode (volume of a small 4-cycle) • Natural solution of the eta problem!!! Due to the NO-SCALE structure of the potential!! • Swiss cheese CY with h12>h11>2: • Form of the potential: Small field inflation No fine-tuning! 0.960<n<0.967

7. Open questions Blow-up Inflation: flatness spoiled by loop corrections No detectable tensor modes since r=T/S<<<1 For dh ~ V >>1 Both solved by considering fibration moduli as inflatons!!

8. LARGE Volume Scenarios Type IIB Flux Compactifications: form of K and W - neglect string loops at this point! there is a non-supersymmetric minimum at IFF i) h12 > h11 > 1 x > 0 ii) tj is a blow-up mode (point-like singularity) non-perturbative superpotential guaranteed since the cycle is rigid! • Nsmall blow-up modes fixed by non-perturbative effects, V by a’ corrections + Wnp • There are still L=(h11-Nsmall-1) moduli which are sent large (e.g. fibration moduli) their non-perturbative corrections are switched off • Get L flat directions! • These directions are usually lifted by string loop corrections since they turn out to be subleading with respect to a’ + NP corrections L moduli lighter than the volume! Extended no-scale structure explained by SUSY!

9. Flat directions lifted by loops K3 Fibration with h11=2: CP4[1,1,2,2,6](12) No blow-up mode No LARGE Volume minimum K3 Fibration with h11=3 (explicit CY examples found also for h11=4: MC,Collinucci,Kreuzer,Mayrhofer work in progress) Now t3 is a blow-up mode LARGE Volume minimum

10. Scalar potential without loop corrections Include string loop corrections t1 is a flat direction, V ~ exp(a3t3)! Fix t1 at:

11. Fibre Inflation 1 Type IIB CY flux compactifications: LARGE Volume Scenarios Inflaton is a fibration modulus (volume of a K3 fiber over a CP1 base) Natural solution of the eta problem!!! Due to the NO-SCALE structure of the potential!! What about string loops? L=(h11-Nsmall-1) flat directions lifted by loops are light: Get h<<1 naturally since the inflaton potential is generated only at loop level Typical large-field inflaton potential: with

12. Inflation 1 Fix t3 and Vat their minima and displace t1 from its VEV Canonical normalisation Kaehler cone: Shift by VEV:

13. Fibre Inflation 2 Base of the fibration→0 Violation of slow-roll condition: h1 Inflectionary point: end of inflation jend : h=0, e1 Disagreement with experiments j*<jmax: 68% CL observational upper bound

14. Fibre Inflation 3 Form of the potential in the inflationary regime: All the adjustable parameters enter only in the prefactor!! Very predictive scenario!!! NB Small for large j No fine tuning! Ne=Ne(j*) Invert and get: e=e(Ne) and h=h(Ne) Get Inflation at ALL scales!!!

15. Fibre Inflation 4 BUT the number of e-foldings is related to the re-heating temperature and the inflationary scale!! Eq. of state for pre re-heating epoch: Fix the inflationary scale by matching COBE!! Set for matter dominance

16. Fibre Inflation 5 Readoff ns and r! Detectable by CMBPol or EPIC!! String Theory predictions in WMAP5 plots!

17. Two-field Cosmological Evolution 1 Matching COBE Fixed V approximation to be checked! V ~ 103-4 Need to study the 2D problem for V and t1! Using Follow the numerical evolution starting close to the second inflectionary point

18. Two-field Cosmological Evolution 2 Get the same results for observable but more Ne due to extra motion along V !!

19. Conclusions LARGE Volume Scenarios very appealing (natural moduli stabilisation, EFT under control, generate hierarchies) Non-perturbative effects fix only blow-up Kähler moduli Then a’ effects + Wnp fix the Volume exponentially large All the other Kähler moduli are flat directions Loop corrections to V are SUB-leading w.r. to the a’ ones due to the “extended no-scale structure” Loop corrections needed to fix the rest of Kähler moduli! Most promising inflaton candidates: fibration moduli! Get inflation naturally Dim 6 Planck suppr. op. under control due to the NO-SCALE structure! Get a trans-planckian field range No tunable parameters in the inflationary potential Inflation for all scales!! Fixed only by matching COBE! Correlation between r and ns Observable Gravity Waves: r=0.005!!!

20. Outlook Tension between phenomenology and cosmology Fix the inflationary scale by matching COBE!! Minf~ MGUT m3/2~ 1015 GeV too high!! imposem3/2~ 1 TeV  Minf~ 108 GeV too low!! BUT Fibre Inflation is present at each scale!! If you let the inflaton just drive inflation and generate the density fluctuations via another curvaton-like field Lower the inflationary scale and solve the gravitino mass problem!! Get r<<1 but possibly large non-gaussianities!

21. String Loop Corrections to K Explicit calculation known only for unfluxed toroidal orientifolds as where is due to the exchange of KK strings between D7s and D3s and is due to the exchange of Winding strings between intersecting D7s (BHK) NB Complicated dependence on the U moduli BUT simple dependence on the T moduli!

22. Generalisation to CY • Generalisation to Calabi-Yau three-folds (BHP) where either or ~ t Conjecture for an arbitrary CY! We gave a low-energy interpretation of this conjecture using where g=t-2

23. General formula for the 1 loop corrections to V NB Everything in terms of Kii and dKW!!! Field theory interpretation using the Colema-Weinberg potential! SUSY is the physical explanation for the extended no-scale structure!

24. Extended No-scale Structure Proof: Expand K-1 and use homogeneity! The loop corrections to V are subleading with respect to the a’ ones BUT are crucial to lift the L flat directions!!!