New Cosmological Implications New Cosmological Implications for LARGE Volume Scenariosfor LARGE Volume Scenarios

Michele CicoliMichele CicoliDAMTP, University of CambridgeDAMTP, University of Cambridge

StringPheno09, Warsaw, 16 June 2009StringPheno09, 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

Why String Inflation?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 EFTneed 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.: It is not obvious that you can get everything out of it! E.g.: Tensor ModesTensor 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

Inflation is UV sensitiveInflation is UV sensitive• Slow-roll conditionsSlow-roll conditions

are sensitive to are sensitive to dim 6 Planck suppressed operators dim 6 Planck suppressed operators !!!!!!

V=exp(K)U where K=V=exp(K)U where K=**/M/M22PP

Expand K V=(1+Expand K V=(1+**/M/M22PP)U)U

Contribution to Contribution to

problem!!!

Large Tensor ModesLarge Tensor Modes

This UV sensitivity becomes even stronger for This UV sensitivity becomes even stronger for models which predict models which predict observable gravity wavesobservable gravity waves!!!!!!

• Lyth Bound: Lyth Bound:

• Present limit (WMAP5+BAO+SN): Present limit (WMAP5+BAO+SN): r<0.2r<0.2 • Forecasts for future cosmological observations:Forecasts for future cosmological observations: PLANCK PLANCK rr~10~10-1-1

SPIDER SPIDER rr~10~10-2-2

CMBPol CMBPol rr~10~10-3-3

Trust EFT?*

NB Minf~MGUT r1/4 see GUT scale physics!!!

String Theory and 4D InflationString 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/D7Inflaton is a brane position modulus: D3/D3, D3/D7 - - NO symmetry solving the NO symmetry solving the problem problem requires fine tuning! requires fine tuning!

_

- - Inflaton is a Kaehler modulus TInflaton is a Kaehler modulus T i)i) Re(T)=volume of 4-cycles: blow-ups, fibration, VolumeRe(T)=volume of 4-cycles: blow-ups, fibration, Volume

ii)ii) Im(T)=axion aIm(T)=axion a

NaturalNatural solution of the eta problem!!! Due to the NO-SCALE structure of the potential!! 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 problem solved by shift symmetry a a+a a+

Blow-up Inflation

Small field inflationSmall field inflationNo fine-tuning! No fine-tuning!

0.960<n<0.9670.960<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)• NaturalNatural solution of the eta problem!!! Due to the NO-SCALE structure of the solution of the eta problem!!! Due to the NO-SCALE structure of the

potential!!potential!!• Swiss cheese CY with Swiss cheese CY with hh1212>h>h1111>2:>2:

• Form of the potential:Form of the potential:

Open questions Open questions

• Blow-up InflationBlow-up Inflation: flatness spoiled by loop : flatness spoiled by loop correctionscorrections

• 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!!Both solved by considering fibration moduli as inflatons!!

ForFor ~ ~ V V >>1>>1

LARGE Volume ScenariosLARGE Volume ScenariosType IIB Flux Compactifications: form of K and W - Type IIB Flux Compactifications: form of K and W - neglect string loops at this point!neglect string loops at this point!

there is a there is a non-supersymmetricnon-supersymmetric minimum at minimum at IFFIFF

i)i) h h1212 > h > h11 11 > 1 > 1 > 0 > 0

ii)ii)j j is a blow-up mode (point-like singularity) 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!

•• NNsmallsmall blow-up modes fixed by non-perturbative effects, blow-up modes fixed by non-perturbative effects, VV by by ’ corrections + W’ corrections + Wnpnp

•• There are still L=(hThere are still L=(h1111-N-Nsmallsmall-1) moduli which are sent large (e.g. fibration moduli)-1) moduli which are sent large (e.g. fibration moduli) their non-perturbative corrections are switched offtheir 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 These directions are usually lifted by string loop corrections since they turn out to be subleading with respect to respect to ’ + NP corrections ’ + NP corrections

L moduli lighter than the volume!L moduli lighter than the volume!

Extended no-scale structure explained by SUSY!Extended no-scale structure explained by SUSY!

Flat directions lifted by loopsFlat directions lifted by loops• K3 Fibration with hK3 Fibration with h1111=2: CP=2: CP44

[1,1,2,2,6][1,1,2,2,6](12)(12)

• No blow-up mode No LARGE Volume minimumNo blow-up mode No LARGE Volume minimum

• K3 Fibration with hK3 Fibration with h1111=3 =3 (explicit CY examples found also for h(explicit CY examples found also for h1111=4: MC,Collinucci,Kreuzer,Mayrhofer work in =4: MC,Collinucci,Kreuzer,Mayrhofer work in

progress)progress)

• NowNow33 is a blow-up mode LARGE Volume minimum is a blow-up mode LARGE Volume minimum

• Scalar potential without loop correctionsScalar potential without loop corrections

• Include string loop correctionsInclude string loop corrections

Fix Fix 11 at: at:

11 is a flat direction, is a flat direction, VV ~ exp( ~ exp(aa3333)!)!

Fibre Inflation 1Fibre 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 CPInflaton is a fibration modulus (volume of a K3 fiber over a CP11 base) base)• NaturalNatural solution of the eta problem!!! Due to the NO-SCALE structure of the solution of the eta problem!!! Due to the NO-SCALE structure of the

potential!!potential!!• What about string loops?What about string loops?

• L=(hL=(h1111-N-Nsmallsmall-1) flat directions lifted by loops are light:-1) flat directions lifted by loops are light:

Get Get <<1 naturally since the inflaton potential is generated only at loop level<<1 naturally since the inflaton potential is generated only at loop level

Typical large-field inflaton potential: with Typical large-field inflaton potential: with

Inflation 1Inflation 1• Fix Fix 33 and and VV at their minima and displace at their minima and displace 11 from its VEV from its VEV • Canonical normalisationCanonical normalisation

Shift by VEV:Shift by VEV:

Kaehler cone:Kaehler cone:

Fibre Inflation 2Fibre Inflation 2Base 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

Fibre Inflation 3Fibre 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:

Ne=Ne(*) Invert and get: =(Ne) and =(Ne)

NBNB Small for large Small for large No fine tuning!No fine tuning!

Fibre Inflation 4Fibre Inflation 4BUT the number of e-foldings is related to the re-heating temperatureand the inflationary scale!!

Eq. of state for prere-heating epoch:

Fix the inflationary scale by matching COBE!!

Set for matter dominance

Fibre Inflation 5Fibre Inflation 5Read off ns and r!

Detectable by CMBPol or EPIC!!

String Theory predictions inWMAP5 plots!

Two-field Cosmological Evolution 1Two-field Cosmological Evolution 1Matching COBE VV ~ 10 ~ 103-43-4 Fixed VV approximation to be checked!

Need to study the 2D problem for VV and 1!

Using

Follow the numerical evolution starting close to the second inflectionary point

Two-field Cosmological Evolution 2Two-field Cosmological Evolution 2

Get the same results for observable but more Ne due to extra motion along V V !!!!

ConclusionsConclusions• 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 KNon-perturbative effects fix only blow-up Käähler modulihler moduli• Then Then ’ effects + W’ effects + Wnpnp fix the Volume exponentially large fix the Volume exponentially large• All the other KAll the other Käähler moduli are flat directionshler moduli are flat directions• Loop corrections to V are SUB-leading w.r. to the Loop corrections to V are SUB-leading w.r. to the ’ ones due to the “extended no-scale ’ ones due to the “extended no-scale

structure”structure”• Loop corrections needed to fix the rest of KLoop corrections needed to fix the rest of Käähler moduli!hler moduli!• Most promising inflaton candidates: fibration moduli!Most promising inflaton candidates: fibration moduli!

1)1) Get inflation naturallyGet inflation naturally2)2) Dim 6 Planck suppr. op. under control due to the NO-SCALE structure!Dim 6 Planck suppr. op. under control due to the NO-SCALE structure!3)3) Get a trans-planckian field rangeGet a trans-planckian field range4)4) No tunable parameters in the inflationary potentialNo tunable parameters in the inflationary potential5)5) Inflation for all scales!! Fixed only by matching COBE!Inflation for all scales!! Fixed only by matching COBE!6)6) Correlation between r and nCorrelation between r and nss

7)7) Observable Gravity Waves: r=0.005!!!Observable Gravity Waves: r=0.005!!!

Outlook Outlook • Tension between phenomenology and cosmologyTension between phenomenology and cosmology

MMinfinf ~~ M MGUTGUT mm3/23/2 ~~ 10 101515 GeV too high!! GeV too high!!

imposeimpose mm3/23/2 ~~ 1 TeV 1 TeV M Minfinf ~ ~ 101088 GeV too low!! GeV too low!!

BUT BUT Fibre InflationFibre Inflation is present at each scale!! is present at each scale!!

Get r<<1 but possibly large non-gaussianities!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 fluctuationsvia another curvaton-like field

Lower the inflationary scale and solve the gravitino mass problem!!

String Loop Corrections to KString Loop Corrections to K

• Explicit calculation known only for unfluxed toroidal orientifolds asExplicit calculation known only for unfluxed toroidal orientifolds as

wherewhere

is due to the exchange of KK strings between D7s and D3s andis due to the exchange of KK strings between D7s and D3s and

is due to the exchange of Winding strings between intersecting D7sis due to the exchange of Winding strings between intersecting D7s

NBNB Complicated dependence on the U moduli BUT simple dependence on Complicated dependence on the U moduli BUT simple dependence on the T moduli!the T moduli!

(BHK)(BHK)

Generalisation to CY

• Generalisation to Calabi-Yau three-folds (BHP)

where either or

~ t

Conjecture for an arbitrary CY!Conjecture for an arbitrary CY!We gave a low-energy interpretation of this conjecture using

where g=-2

General formula for the 1 loop General formula for the 1 loop corrections to Vcorrections to V

NBNB Everything in terms of K Everything in terms of Kiiii and and KKWW!!!!!!

Field theory interpretation using the Colema-Weinberg potential!

SUSY is the physical explanation for the extended SUSY is the physical explanation for the extended no-scale structure!no-scale structure!

Extended No-scale StructureExtended No-scale Structure

ProofProof: Expand K: Expand K-1-1 and use homogeneity! and use homogeneity!

The loop corrections to V are subleading with respect to the The loop corrections to V are subleading with respect to the ’ ones BUT ’ ones BUT are crucial to lift the L flat directions!!!are crucial to lift the L flat directions!!!