New Cosmological Implications for LARGE Volume Scenarios

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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
arXiv0808.0691 hep-th Using previous work
contained in MC, J. Conlon, F. Quevedo
arXiv0708.1873 hep-th MC, J. Conlon, F.
Quevedo arXiv0805.1029 hep-th
Fibre Inflation
NB L. Anguelova, V. Calò, MC arXiv0904.0051
hep-th See Calòs talk
Finite-temperature effects
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Why String Inflation?
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

• 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

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
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Inflation is UV sensitive

• Slow-roll conditions
• are sensitive to dim 6 Planck suppressed
  operators !!!
• Vexp(K)U where Kff/M2P
• Expand K
  V(1ff/M2P)U
• Contribution to h

h problem!!!
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Large Tensor Modes

• This UV sensitivity becomes even stronger for
  models which predict observable gravity waves!!!
• Lyth Bound
• Present limit (WMAP5BAOSN) rlt0.2
• Forecasts for future cosmological observations
• PLANCK r10-1
• SPIDER r10-2
• CMBPol r10-3

Trust EFT?

NB MinfMGUT r1/4 see GUT scale
physics!!!
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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 ae
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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 h12gth11gt2
• Form of the potential

Small field inflation No fine-tuning!
0.960ltnlt0.967
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Open questions

• Blow-up Inflation flatness spoiled by loop
  corrections
• No detectable tensor modes since rT/Sltltlt1

For
dh V gtgt1
Both solved by considering fibration moduli as
inflatons!!
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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 gt h11 gt 1 x gt 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!

Extended no-scale structure explained by SUSY!
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Flat directions lifted by loops

• K3 Fibration with h112 CP41,1,2,2,6(12)
• No blow-up mode No LARGE Volume
  minimum
• K3 Fibration with h113
• (explicit CY examples found also for h114
  MC,Collinucci,Kreuzer,Mayrhofer work in progress)
• Now t3 is a blow-up mode LARGE Volume
  minimum

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• Scalar potential without loop corrections
• Include string loop corrections

t1 is a flat direction, V exp(a3t3)!
Fix t1 at
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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 hltlt1 naturally since the inflaton potential
  is generated only at loop level
• Typical large-field inflaton potential
  with

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Inflation 1

• Fix t3 and V at their minima and displace t1
  from its VEV
• Canonical normalisation

Kaehler cone
Shift by VEV
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Fibre Inflation 2
Base of the fibration?0
Violation of slow-roll condition h?1
Inflectionary point end of inflation jend h0,
e?1
Disagreement with experiments j ltjmax
68 CL observational upper bound
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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!
NeNe(j)
Invert and get ee(Ne) and hh(Ne)
Get Inflation at ALL scales!!!
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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
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Fibre Inflation 5
Read off ns and r!
Detectable by CMBPol or EPIC!!
String Theory predictions in WMAP5 plots!
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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
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Two-field Cosmological Evolution 2
Get the same results for observable but more Ne
due to extra motion along V !!
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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 r0.005!!!

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Outlook

• Tension between phenomenology and cosmology

Fix the inflationary scale by matching COBE!!
Minf MGUT ? m3/2 1015 GeV too high!!
impose m3/2 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 rltlt1 but possibly large non-gaussianities!
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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!
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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 gt-2
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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!
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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!!!