Update on Update on String String CosmologyCosmology

Update on Update on String String CosmologyCosmology

Renata Kallosh

Renata Kallosh

Stanford, March 8, 2008

Outline

• Dark Energy and the Landscape of String Theory : Type IIA, Type IIB, Heterotic string theories

• Brane Inflation and Modular inflation

• What can fundamental physics learn from future detection or non-detection of

• B-modes from cosmic strings

• B-modes from inflation

• LHC: Tension between string cosmology and a TeV gravitino

Space of M/String Theory vacuaSpace of M/String Theory vacua

• Moduli Stabilization by fluxes and non-perturbative corrections in non-critical and type IIB superstring theory de Sitter vacua, models of inflation

• Until recently problems in type IIA superstring theory

• Heterotic string theory?

Type IIA string theory

• Stabilization of all moduli is possibble in a class of models in massive IIA. In these models there is the infinite number of AdS vacua, Lambda<0 DeWolfe, Giryavets, Kachru,Taylor, 2005

• Cannot be uplifted to de Sitter vacua, Lambda>0, no-go theorem RK , M. Soroush, 2006

• In these models inflation is not possible, no-go theorem Hertzberg, Kachru, Taylor, Tegmark, 2007

• New type IIA models: extra dimensions with negative curvature, inflation with gravity waves, Silverstein, Westphal

• Cosmology as a selection principle?

1998 CC > 0 CC ~ 10-120

SUPERSTRING THEORY: many AdS vacua with CC < 0 and Minkowski vacua with CC = 0, but no de Sitter vacua with CC > 0

2001-2003

Existence of Dark Energy is a real issue, supported not only by supernovae. It describes 70% of everything.Fundamental Physics has to explain it.

First constructions of metastable de Sitter vacua in String Theory

• It is possible to stabilize internal dimensions, and to obtain an accelerating universe. Eventually, our part of the universe will decay, but it will take a very long time

• Vacuum stabilization can be achieved in 10100 - 101000

different ways. This means that the value of CC ~ 10-120 in Planck units may not be impossible in the context of stringy landscape with anthropic reasoning

• W = - 1, CC=const, is in agreement with the data so far

100 150 200 250 300 350 400

0.2

0.4

0.6

0.8

1

1.2

V

Metastable dS minimumMetastable dS minimum

V is the potential as the function of the volume of extra dimensions, described by

What if CC=const will be definitely ruled out observationally as the explanation of Dark Energy?

• Most likely, it will not happen earlier than in 10 years from now (???)

• It may be difficult to explain it, as we will have to explain not only the

height of the potential 10-120 but also the slope ~ 10-120

Allen at al

We focus on string theory (supergravity) models of inflation

• Generic class of inflationary models in talks of

• Lyth, Wise, Weinberg,…, Sasaki, …:

“Give me 2 fields and I will give you any level of non-gaussianity, any ns and any r=T/S which will agree with future experiments”

“Give me a place to stand on, and I will move the earth.”

Thanks to Navin Sivanandam

Stringy inflation modelson WMAP5

Bevis, Hindmarsh, Kunz, Urrestilla

January 2008

WMAP3-based

10% of cosmic strings

For this model cosmic strings have to be detected!

B-modes from gravity waves from inflation

B-modes from cosmic strings

Pogosian, Wyman February 2008

Spergel: cosmic strings should be “eye-visible”

Inflation in string theory

To produce a sensible cosmology in string theory it was necessary to stabilize all moduli but the inflaton. In 4d theory such moduli (scalar fields) have a runaway behavior. In string theory and supergravity they often have physical and geometrical meaning as volumes of extra dimensions and various cycles in topologically non-trivial extra dimensions. The inflaton can also be related to a distance between branes.

If scalars have a geometric meaning in extra dimensions, what is their range in four-dimensional Planck units? In view of the Lyth bound on tensor to scalar fluctuation ratio r=T/S

What has string theory to say on limits on r=T/S ?

WMAP5+…

Cosmic strings ?, VilenkinCopeland, Myers, Polchinski

Seeing cosmic strings on the sky would be a window of string theory into the real world

Brane Inflation in string theoryBrane Inflation in string theoryBrane Inflation in string theoryBrane Inflation in string theory

KKLMMT brane-anti-brane inflation

Hybrid D3/D7 brane inflation

(Stringy D-term inflation)

Dirac-Born-Infeld inflation

Two-throat model

Modular Inflation models

Kahler modular inflationRoulette inflation

Racetrack inflation

Cosmology, string theory and effective supergravity

Generic potential of N=1 supergravity depends on a number of complex scalar fields which have a geometric meaning of coordinates in Kähler geometry

+ D-terms

Kähler potential and the Superpotential

the first working model of the moduli inflation Blanco-Pilado, Burgess, Cline, Escoda, Gomes-Reino, Kallosh, Linde, Quevedo

Superpotential:

Kähler potential:

Racetrack Inflation, Racetrack Inflation, KKLTKKLT Racetrack Inflation, Racetrack Inflation, KKLTKKLT

KKLT Uplifting term:KKLT Uplifting term:

Rescaling (same slow-roll etc)Rescaling (same slow-roll etc)

nnss=0.95=0.95

No grav. wavesNo grav. waves

No cosmic stringsNo cosmic strings

Spectral index as a function of the number of e-foldings(minus the total number of e-foldings)

Racetrack InflationRacetrack Inflation

Update on KKLMMT brane inflation model:recent detailed studies of quantum corrections

eta-problem

quantum corrections do not remove terms, but add other terms to the potential. With fine-tuning one can find an inflection point and slow-roll inflation

Baumann, Dymarsky, Klebanov , Maldacena, McAllister… 2007

Princeton group

Accidental Inflation Linde, WesphalPhenomenology?

Cosmic strings, no GW

Update on D3/D7 brane inflation

Work in Progress: Haack, RK, Krause, Linde, Luest, Zagermann

The model is controlled by special geometry of N=2 supergravity

The reason for the recent update was the observation by Hindmarsh et al than one can fit the data with ns=1 assuming the presence of light cosmic strings. (Summer Trieste workshop)

This is in amazing agreement with the prediction from 2003 by RK and Lindethat in D-term inflation one can have light cosmic strings for very small gauge couplings under condition that ns=1

In usual regime of D-term inflation ns ~ 0.98

D3/D7 InflationD3/D7 Inflation D3/D7 InflationD3/D7 InflationDasgupta, Herdeiro, Hirano, RK, 2001Dasgupta, Herdeiro, Hirano, RK, 2001 This is a stringy version of hybrid D-term

Inflation

D3 is moving

The mass of D3-D7 strings (hypers) is split due to the presence of the anti-self-dual flux on D7

Inflaton TrenchInflaton Trench

SHIFT SYMMETRY, slightly broken by quantum SHIFT SYMMETRY, slightly broken by quantum correctionscorrections

The motion of branes does not destabilize the volumeThe motion of branes does not destabilize the volume

Hsu,RK,Prokushkin;Hsu,RK,Prokushkin;Firouzjahi,TyeFirouzjahi,Tye

In F-theory compactifications on K3 x K3 one of the attractive K3

must be a Kummer surface to describe an orientifold in IIB, the

second attractive K3 can be regular.

Type IIB string theory on K3 x orientifold

Aspinwall, RK

Tripathy, Trivedi; Ferrara, Trigiante et al

Bergshoeff, RK, Kashani-Poor, Sorokin,Tomasiello

All moduli stabilized

How long is de Sitter valley in D3/D7 brane inflation model?

Long thin pillow

A D3-brane and a D7-brane are placed on a rectangular, but ``asymmetrical'' (non-square) torus. The D3-brane (white circle) can travel at most the distance L1 along the lower edge of the rectangle before it hits the D7-brane. This corresponds to the larger of the two topologically non-trivial circles (right figure) on the torus (red dashed lines). Making the torus very thin and long can thus yield, at least kinematically, a large field range.

Enhancement factor, depends on the choice of fluxes

K3 x

Pillow with 4 fixed points

What controls the breaking of shift symmetry in D3/D7 model on

K3 x

If these corrections are small, we derive the model with ns = 1, 10% of cosmic strings. If confirmed by data, we have a clear link to string theory.

What if tensor modes are detected?Current bound: r = T/S < 0.2 from WMAP5+…

What this would mean for the fundamental physics, string theory and supergravity?

All relatively well developed brane inflation models and

modular inflation models in string theory predict a non

detectable level of tensor modes.

New models, or new versions of known models, may lead to different results

see Eva’s talk for the first example

Axion Valley Model: The first realization of `natural

inflation’ (pNGb) in Supergravity Shift symmetric quadratic Kähler potential

KKLT-type superpotential

The potential after the KKLT-type uplifting

has a minimum at some value of the radial variable x0. The radial direction is very steep. At this minimum the potential is that of natural inflation (pNGb)

RK, Soroush, Sivanandam, 2007

Axion Valley Potential

Sharp minimum in radial direction x,very shallow minimum for the axion

The potential shows the periodic structure for

pNGb potential is the slice at the bottom of the valley

There are models of inflation in supergravity which predict tensor modes with

• They have approximately shift-symmetric quadratic Kähler potentials

In string theory the computableKähler potentials in known cases of Calabi-Yau compactification have shift symmetry

However, they are logarithmic, not quadratic

• These models predict undetectably small tensor modes in inflation.

RK, Soroush, Sivanandam

KKLT, C111=1

Simplest example of KKLT potential

One modulus

Axion is as steep as the radial modulus, there is no axion valley.

No detectable GW in models with stringy logarithmic Kähler potentials

At fixed T and

Hodge-Kahler manifold

Will this string theory model provide the axion valley potential predicting GW ???

Less studied corners of the stringy landscape

T. Grimm, N = 1 orientifold compactification with O3/O7 planes. R-R 2-forms

The relevant moduli originate from hypermultiplets in both cases

In the context of inflation in string theory and supergravity, the detection (or non-detection) of the tensor modes from

inflation is of crucial importance!

At the present level of understanding there seems to be a unique way to read the features of the geometry of extra dimensions from the sky.

No detection: Calabi-Yau 3-folds logarithmic Kähler potentials prediction, well studied corner of the stringy landscape

Detection: shift symmetric nearly quadratic Kähler potentials in effective supergravity. String theory?...

Spaces of negative curvature of extra dimensions

Additional problem: For most of the models based on the KKLT moduli stabilization,

R.K., Linde 2003

Summary When we learned that our universe is accelerating, it was a

creative crisis, which forced us to reconsider many issues in string theory, including the issue of moduli stabilization and metastable vacua.

If tensor modes are detected, it may provide us with hints about the geometry of extra dimensions from the sky. Before the experiments will reach the level

we may have more string theory models to test.

If cosmic strings detected, it will give us an importantselection principle for string theory confronting the data