Fibre Inflation High-Fibre models from regular potentials String Pheno Workshop: CERN 2008 C.P. Burgess with M. Cicoli and F.Quevedo

Fibre Inflation

High-Fibre models

from regular potentials

String Pheno Workshop: CERN 2008

C.P. Burgess with M. Cicoli and F.Quevedo

String Phenomenology Workshop CERN 2008

Outline

• String inflation• Why build models only a mother could love?• Gravity waves and stringy signals?

• Fibre Inflation and the LVS• Inflating with moduli

• Inflationary Observables• Correlations between r and ns; gravity waves;…


String Inflation

• What might one hope to learn?• about strings• about inflation


String Inflation


String Theory: a theory in search of observational tests

Inflation: successful phenomenology seeking an underlying theory


String Inflation


… Rocky Kolb


String Inflation


Difficult to identify where we live within the string landscape. Seek ‘modules’ encoding low-energy features: standard model; dark energy; inflation; …


String Inflation


Inflation provides a good description of primordial fluctuations as seen in the CMB: a rare observational window on physics at high energies?

Wish to know from string theory:

How hard is it to get flat enough potentials?

Does embedding into string theory carryobservational implications?

How does reheating work?

etc…


String Inflation


WMAP

Seek: stringy inflationary signatures

Because inflation is found in 4D effective theory, predictions tend to follow 4D mechanisms

r

0.6

0.2

ns


String Inflation


WMAP

Seek: stringy inflationary signatures

Could hope that string inflation provides only a subset of the possible 4D inflationary possibilities.

r

0.6

0.2

ns


String Inflation


WMAP

Small-field models

Hybrid models

Large-field models

r

0.6

0.2

ns


String Inflation


WMAP

Small-field models

Hybrid models

Large-field models

r

0.6

0.2

ns


String Inflation


WMAP

Small-field models

Hybrid models

Large-field models

r

0.6

0.2

ns


String Inflation


Linde & KalloshBaumann & McAllister

r

0.6

0.2

ns Strings: small tensor amplitude?


String Inflation


Lyth

r

0.6

0.2

ns Strings: small tensor amplitude?

2

2

816

peff MNr

2

2

2 8e

peff NHdt

HMrN

Appears difficult to obtain large p


Emerging Picture

• Mechanisms

• Robustness

• Mind broadening First attempts to get large field range:

Type IIA: brane motion wrapped on a twisted torus.

Type IIB: aperiodic Bmn fields

Silverstein & WestphalMcAllister, Silverstein & Westphal


Emerging Picture

• Mechanisms

• Robustness

• Mind broadening First attempts to get large field range:

Type IIA: brane motion wrapped on a twisted torus.

Type IIB:aperiodic Bmn fields

Silverstein & WestphalMcAllister, Silverstein & Westphal

Within the domain of low-energy effective theory?

2sM


Fibre Inflation

• The Large Volume Scenario

• Inflation in the LVS


Fibre Inflation



Searches over the years for accelerating cosmologies in 4D and extraD supergravities lead instead to strong no-go results.

Leading order in gs and a’ often give no-scale models for moduli (eg Kahler moduli in Type IIB).

The flat potentials of no-scale models tend lie on the boundary of the no-go results; eg:

Covi, Gomez-Reino, Gross, Louis, Palma & Scrucca

22/3

2 /1

3/22)(

mHnfR i

(n=3 for no-scale models)


Fibre Inflation



Searches over the years for accelerating cosmologies in 4D and extraD supergravities lead instead to strong no-go results.

Leading order in gs and ’ often give no-scale models for moduli (eg Kahler moduli in Type IIB).

The flat potentials of no-scale models tend lie on the boundary of the no-go results

Suggests looking for inflation starting with no-scale moduli but including subleading gs and ’ terms.


Fibre Inflation



In 4D string loops and ’ corrections are suppressed (in Einstein frame) by powers of 6D volume, V-1/3.

Becker, Becker, Haack & Louis

33

21

1mn

mn

s

RgRggg

VgRgg

s2/3

1

2/32ln2

sgVK


Fibre Inflation



Given several Kahler moduli, b » s , correction to K together with superpotential W = W0 + A ea s can stabilize V at a very large volume minimum

Balasubramanian, Berglund, Conlon & Quevedo

sss gg

13/2

2/3

ss gaas eWeWV /

00

3/2 Essentially any large volume is possible for a small

range of s.


Fibre Inflation



Potential has naturally weak dependence on any other large moduli b » i » s with V ~ V(b , i ).

If

then

up to 1/V and exp[-ai] and exp[-a b] terms

Conlon & Quevedo

3

20

202

ˆ

V

We

V

We

VU ss asas

saAeWW 0


Fibre Inflation



Potential has naturally weak dependence on any other large moduli b » i » s with V ~ V(b , i ).

If

then

up to 1/V and exp[-ai] and exp[-a b] terms

Conlon & Quevedo

3

20

202

ˆ

V

W

V

We

VU sas s

saAeWW 0


Fibre Inflation



Kahler modulus inflation: inflaton potential obtained by keeping terms that are of order exp[-ai]

Slow roll naturally arises when i is displaced to large values from its minimum.

Conlon & Quevedo

3

20

202

ˆ

V

We

V

We

VU ii aiai

2/14/3 Vi


Fibre Inflation



Fibre inflation: inflaton potential dominated by subleading 1/V ~ exp[-a s] corrections rather than by exp[-a i] corrections.

Such corrections arise in the leading string loops, since Utree ~ V-3 while Uloop ~ V-10/3.

It turns out that such loops can also compete with the exp[-a i] terms and so can ruin slow roll of Kahler Modulus Inflation.

Cicoli, Conlon & QuevedoCicoli, CB & Quevedo


Fibre Inflation



String loop potential: explicit 1-loop contributions have only been computed on orbifolded tori. Most of the potential’s complication lies in its dependence on the complex structure moduli.

Dependence on Kahler moduli can be inferred using educated guesses based on kinds of loops that enter (KK tree exchange, loops of winding states, etc).

Berg, Haack & PajerCicoli, Conlon & Quevedo

2/12/11 VK


Fibre Inflation



String loop potential: explicit 1-loop contributions have only been computed on orbifolded tori. Most of the potential’s complication lies in its dependence on the complex structure moduli.

Dependence on Kahler moduli can be inferred using educated guesses based on kinds of loops that enter (KK tree exchange, loops of winding states, etc).


2/12/11 VK

Potentially dangerous terms drop from the potential!


Fibre Inflation



Kahler Modulus dependence of string loops:

KK tree exchange

Loop of winding states


i

jiji

i KK

i taCVm

CVK 1

21

i

jij

i

i W

i

ta

CV

m

CVK ~

~~1

21


Fibre Inflation



Kahler Modulus dependence of string loops:

KK tree exchange

Loop of winding states


i

jiji

i KK

i taCVm

CVK 1

21

i

jij

i

i W

i

ta

CV

m

CVK ~

~~1

21

2-cycle transverse to D7

2-cycle of intersecting D7s


Fibre Inflation



A Specific Model: Choose a Calabi-Yau that is a K3 fibration plus a blow-up modulus, with 2 » 1 » 3

take leading corrections to W:

add leading ’ and string loop corrections to K:

Cicoli, CB & Quevedo

2/33121

23

2221 cttbtatV

30

aAeWW

2/1112

2

2/111

2/11

12/1

3

1 ~ˆln2

CCCC

VVK


Fibre Inflation



Potential at leading order:

stabilizes 3 ~ gs-1 and V ~ exp[a3]

Potential at next-to-leading order:

acquire potential in 1 ~ exp[2 /3]

Natural slow roll once › 1, but boundary at ‹ 6.

3/43/3/10

43 eeV

CU


Fibre Inflation








3/43/3/10

43 eeV

CU


Fibre Inflation








3/43/3/10

43 eeV

CU

only one free parameter!


Fibre Inflation



Higher loops?

likely to introduce singularity at boundary ~ 6

guess:

for O(1) coefficients, ratio of 2-loop to 1-loop terms is negligible when ‹ 5.9

21

12 t

KK loop

loop


Fibre Inflation



Higher loops?

likely to introduce singularity at boundary ~ 6

for O(1) coefficients, ratio of 2-loop to 1-loop terms is negligible when ‹ 5.9

Cicoli, CB & Quevedo


Inflationary Observables

• Robust features

• More model dependent results



• Robust features


Slow roll parameters depend only on Ne



• Robust features


Correlates r and ns like for large-field models.



• Robust features


Correlates r and ns like for large-field models.

Central value



• Robust features


Getting large enough scalar perturbations requires volumes of order V ~ few thousand

Never get much more than 50-60 e-foldings, so might expect to see imprints of onset of inflation at horizone exit.

Slowness of roll does not require tuning of parameters in the potential, but does require initial conditions relatively near to the edge of the Kahler cone


Summary

• Systematic large volume expansions seem able to provide slow roll regimes with less tuning than most inflationary scenarios.

• Fibre inflation models can allow trans-Planckian excursions of the inflaton, and so can accommodate observably large r


Many thanks to the Organizers!!

• Angel Uranga• The TH administrative staff (Nanie, Nadje & Jean)

• Ignatio Antoniadis

• Elias Kiritsis

• Fernando Quevedo

• Herman Verlinde


fin

Documents

Fibre Inflation High-Fibre models from regular potentials String Pheno Workshop: CERN 2008 C.P. Burgess with M. Cicoli and F.Quevedo