Transcript LARGE Volume Scenarios

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]
Fibre Inflation
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]
Finite-temperature effects
See Calò’s talk
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
Inflation is UV sensitive
•
Slow-roll conditions
are sensitive to dim 6 Planck suppressed operators !!!
V=exp(K)U where K=f*f/M2P
V=(1+f*f/M2P)U
Expand K
Contribution to h
h problem!!!
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
*
NB Minf~MGUT r1/4
Trust EFT?
see GUT scale physics!!!
String Theory and 4D Inflation
• Focus on slow-roll inflation
• Two general classes of string inflation
• Open String Inflaton
_
- Inflaton is a brane position modulus: D3/D3, D3/D7
- NO symmetry solving the h problem  requires fine tuning!
• Closed String Inflaton
- 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
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
Open questions
• Blow-up Inflation: flatness spoiled by loop
corrections
For
dh ~ V >>1
• No detectable tensor modes since r=T/S<<<1
Both solved by considering fibration moduli as inflatons!!
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
i) h12 > h11 > 1
IFF
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
Extended no-scale structure explained by SUSY!
L moduli lighter than the volume!
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
• Scalar potential without loop corrections
t1 is a flat direction, V ~
exp(a3t3)!
• Include string loop corrections
Fix t1 at:
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
Inflation 1
• Fix t3 and V at their minima and displace t1 from its VEV
• Canonical normalisation
Kaehler cone:
Shift by VEV:
Fibre Inflation 2
Base of the fibration→0
Violation of slow-roll
condition: h1
Inflectionary point: end
of inflation jend : h=0, Disagreement with experiments j* <jmax:
e1
68% CL observational upper bound
Fibre Inflation 3
Form of the potential in the inflationary regime:
All the adjustable parameters enter only in the prefactor!!
Very predictive scenario!!!
Ne=Ne(j*
)
NB Small for large j
No fine tuning!
Invert and get:
Get Inflation at ALL scales!!!
e=e(Ne)
and
h=h(Ne)
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
Fibre Inflation 5
Read off ns and r!
Detectable by CMBPol
or EPIC!!
String Theory predictions in
WMAP5 plots!
Two-field Cosmological Evolution 1
Matching COBE
V ~ 103-4
Fixed V approximation to be checked!
Need to study the 2D problem for V and t1!
Using
Follow the numerical evolution starting close to the second inflectionary point
Two-field Cosmological Evolution 2
Get the same
results for
observable but
more Ne due to
extra motion
along V !!
Conclusions
•
•
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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!
1)
2)
3)
4)
5)
6)
7)
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!!!
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•
•
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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 r<<1 but possibly large non-gaussianities!
String Loop Corrections to K
• Explicit calculation known only for unfluxed toroidal orientifolds as
(BHK)
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
NB Complicated dependence on the U moduli BUT simple dependence on
the T moduli!
Generalisation to CY
• Generalisation to Calabi-Yau three-folds (BHP)
where either
~t
or
Conjecture for an arbitrary CY!
We gave a low-energy interpretation of this conjecture using
where g=t-2
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!
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!!!