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] NB: L. Anguelova, V. Calò, MC arXiv:0904.0051 [hep-th] See Calò’s talk Fibre Inflation Finite-temperature effects

2. Why String Inflation? Inflation is highly UV sensitive since you need to obtain light scalar massesInflation is highly UV sensitive since you need to obtain light scalar masses need an UV complete theory to trust model building in an EFT need an UV complete theory to trust model building in an EFT use String Theory! use String Theory! String Theory has many non-trivial constraints to inflationary model buildingString 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 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 conditionsSlow-roll conditions are sensitive to dim 6 Planck suppressed operators !!! V=exp(K)U where K=  *  /M 2 P Expand K V=(1+  *  /M 2 P )U Contribution to  Contribution to   problem!!!

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

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

6. Blow-up Inflation Small field inflation No fine-tuning! 0.960<n<0.967 Type IIB CY flux compactifications: LARGE Volume ScenariosType IIB CY flux compactifications: LARGE Volume Scenarios Inflaton is a blow-up mode (volume of a small 4-cycle)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!!Natural solution of the eta problem!!! Due to the NO-SCALE structure of the potential!! Swiss cheese CY with h 12 >h 11 >2:Swiss cheese CY with h 12 >h 11 >2: Form of the potential:Form of the potential:

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

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 there is a non-supersymmetric minimum at IFF i) h 12 > h 11 > 1  > 0 ii)  j is a blow-up mode (point-like singularity) non-perturbative superpotential guaranteed since the cycle is rigid! non-perturbative superpotential guaranteed since the cycle is rigid! N small blow-up modes fixed by non-perturbative effects, V by  ’ corrections + W np N small blow-up modes fixed by non-perturbative effects, V by  ’ corrections + W np There are still L=(h 11 -N small -1) moduli which are sent large (e.g. fibration moduli) There are still L=(h 11 -N small -1) moduli which are sent large (e.g. fibration moduli) their non-perturbative corrections are switched off their non-perturbative corrections are switched off Get L flat directions! Get L flat directions! These directions are usually lifted by string loop corrections since they turn out to be subleading with respect to  ’ + NP corrections These directions are usually lifted by string loop corrections since they turn out to be subleading with respect to  ’ + NP corrections L moduli lighter than the volume! L moduli lighter than the volume! Extended no-scale structure explained by SUSY!

9. Flat directions lifted by loops K3 Fibration with h 11 =2: CP 4 [1,1,2,2,6] (12)K3 Fibration with h 11 =2: CP 4 [1,1,2,2,6] (12) No blow-up mode No LARGE Volume minimumNo blow-up mode No LARGE Volume minimum K3 Fibration with h 11 =3K3 Fibration with h 11 =3 (explicit CY examples found also for h 11 =4: MC,Collinucci,Kreuzer,Mayrhofer work in progress) (explicit CY examples found also for h 11 =4: MC,Collinucci,Kreuzer,Mayrhofer work in progress) Now  3 is a blow-up mode LARGE Volume minimumNow  3 is a blow-up mode LARGE Volume minimum

10. Scalar potential without loop correctionsScalar potential without loop corrections Include string loop correctionsInclude string loop corrections Fix  1 at:  1 is a flat direction, V ~ exp( a 3  3 )!

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

12. Inflation 1 Fix  3 and V at their minima and displace  1 from its VEVFix  3 and V at their minima and displace  1 from its VEV Canonical normalisationCanonical normalisation Shift by VEV: Kaehler cone:

13. Fibre Inflation 2 Base of the fibration→0 Inflectionary point: end of inflation  end :  =0,   1 Disagreement with experiments  *  max : 68% CL observational upper bound Violation of slow-roll condition:   1

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

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!! Setfor matter dominance

16. Fibre Inflation 5 Read off n s and r! Detectable by CMBPol or EPIC!! String Theory predictions in WMAP5 plots!

17. Two-field Cosmological Evolution 1 Matching COBE V ~ 10 3-4 V Fixed V approximation to be checked! V Need to study the 2D problem for V and  1 ! Using Follow the numerical evolution starting close to the second inflectionary point

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

19. Conclusions LARGE Volume Scenarios very appealingLARGE Volume Scenarios very appealing (natural moduli stabilisation, EFT under control, generate hierarchies) (natural moduli stabilisation, EFT under control, generate hierarchies) Non-perturbative effects fix only blow-up Kähler moduliNon-perturbative effects fix only blow-up Kähler moduli Then  ’ effects + W np fix the Volume exponentially largeThen  ’ effects + W np fix the Volume exponentially large All the other Kähler moduli are flat directionsAll the other Kähler moduli are flat directions Loop corrections to V are SUB-leading w.r. to the  ’ ones due to the “extended no-scale structure”Loop corrections to V are SUB-leading w.r. to the  ’ ones due to the “extended no-scale structure” Loop corrections needed to fix the rest of Kähler moduli!Loop corrections needed to fix the rest of Kähler moduli! Most promising inflaton candidates: fibration moduli!Most promising inflaton candidates: fibration moduli! 1)Get inflation naturally 2)Dim 6 Planck suppr. op. under control due to the NO-SCALE structure! 3)Get a trans-planckian field range 4)No tunable parameters in the inflationary potential 5)Inflation for all scales!! Fixed only by matching COBE! 6)Correlation between r and n s 7)Observable Gravity Waves: r=0.005!!!

20. Outlook Tension between phenomenology and cosmologyTension between phenomenology and cosmology M inf ~ M GUT  m 3/2 ~ 10 15 GeV too high!! impose m 3/2 ~ 1 TeV  M inf ~ 10 8 GeV too low!! BUT Fibre Inflation is present at each scale!! Get r<<1 but possibly large non-gaussianities! Fix the inflationary scale by matching COBE!! 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!!

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

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=  -2

23. General formula for the 1 loop corrections to V NB Everything in terms of K ii and  K W !!! 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  ’ ones BUT are crucial to lift the L flat directions!!!