C AN WE CONSTRAIN MODELS FROM THE STRING THEORY BY N ON - GAUSSIANITY ? APCTP-IEU Focus Program Cosmology and Fundamental Physics June 11, 2011 Kyung Kiu.

CAN WE CONSTRAIN MOD-ELS FROM THE STRING THEORY BY NON-GAUSSIAN-ITY ?

APCTP-IEU Focus Program

Cosmology and Fundamental Physics

June 11, 2011

Kyung Kiu Kim (IEU)

With Chanju Kim and Frederico Arroja

OUTLINE

Motivation Large volume scenario Non-gaussianity in Multi-field Inflation (C. Pe-

terson and M. Tegmark) Possible way to produce large Non-gaussian-

ity in some model from Large volume sce-nario

Evolution of non-gaussianity with the adia-baticity assumption.

Summary

MOTIVATION

I’m in the IEU. I would like to know whether my main tool,

string theory, can explain our universe or not.

The string theory is a consistent theory and has good properties mathematically.

So many string theorists hope that string theory plays a role of TOE.

But the string theory looks so far from obser-vations or experiments, because the energy scale is so high (gravity scale).

MOTIVATION

In cosmology, the inflation model was pro-posed and gives good agreement or fitting to observations.

It provides many nice explanations for our universe.

If it is the right model for our universe and the sting theory is the theory of the universe, then the string theory should contain the in-flation model.

Recently, Human beings paid really big money for taking photos and we are waiting for the results.

MOTIVATION

One of the results is the non-gaussianity of the universe.

This could give very important information for our early universe.

If we assume the string theory explains the inflation, we need to calculate the non-gaus-sianity in string theory models and compare it to the observation.

THE MODELS FROM THE STRING THEORY

Since we don’t want inconsistency in string theory, there is many obstacles and difficul-ties in construction of models in string theory.

The models for non-gaussianity in string the-ory- The large volume scenarios from flux com-pactification(eta problem)- DBI inflation models(movement of D brane, Fred’s talk)- Axion monodromy models(eta problem)- ….

We are devoted to the large volume scenar-ios.

THE LARGE VOLUME SCENARIO

String theory is defined in 10 dimensional spacetime.

One of way to obtain 4 dimensional model is compactifiying 6 dimension in type IIB string theory.

This gives a 4 dimensional N=1 Supergravity action.


However, the supergravity has a fine tuning problem, eta problem.

Without fine-tuning, we cannot produce small eta during the inflation.

In order to solve the problem, we may take some assumption.

The resulting scenario is the large volume scenarios.


Details of the construction can be found in the Prof. Nam’s talk.

I gives a very short introduction here. N=1 SUGRA action given by the Kahler poten-

tial K and the holomorphic superpotential W. V_uplift is effect of the supersymmetry-break-

ing from other sectors of the theory.( We know physical origin.)


From flux compactification of Type IIB string theory, These K and W are given by


4 cycle volume + i (axionic part-ner)

Origin was known(instanton or gaugino con-densation,…).


Dimensionless classical volume

D_i is a harmonic 2 form in M. t^i is an area of 2 cycle in M

THE LARGE VOLUME SCENARIO Because of G_3, complex structure moduli

and axion have string scale masses and they are decoupled.

The low energy theory

Taking large volume scenario,

Alpha and lambda are from the intersection number.


The model is up to

with


In order to make the metric canonical, one can introduce

then the metric on field space becomes canonical type.


One may introduce a simple model(an example in 1010.3261)

Two light fields play role of inflatons.

The model is boiled down to

NON-GAUSSIANITY IN MULTI FIELD IN-FLATION

Single field slow roll inflation model which has canonical kinetic term gives small non-gaussianity.

Easiest way to avoid small non-gaussianity is introducing multi-field which could produce large Non-gaussianity.

In string theory, many fields situations are very common because there are many scalar fields.

As we explained, after flux compactification, it is very natural to obtain many scalar field with canonical type of kinetic term.


The local type non-gaussianity has been given by WMAP data.

The Planck will give more exact value of NG. For simplicity and insight, we first consider

two field case with delta N formalism(Ki-young’s talk).

Starting with action

NON-GAUSSIANITY IN MULTI FIELD IN-FLATION(C PETERSON AND M TEGMARK)

The number of e-folds N is given by

We can express time derivative with e-folds numbers

The background eom becomes


With the slow-roll parameters

The field velocity

Define some vectors


Slow-roll approximation in this convention

and

This means low field-speed and slowly chang-ing speed.


We have many fields, one may choose an-other direction and take slowly changing limit

Slow turn limit

In the SRST limit, the evolution equation is

The speed-up rate and turn-rate are approx-imated by

Give by potential V


The hessian

The perturbation equation in Fourier space.

In SRST limit


The evolution of is approximated by

The curvature mode and the iso-curvature mode

This evolution is expressed by a transfer ma-trix


Alpha and beta are given by in SRST limit

Related to two point function

Three kinds of spectrum (curvature, cross and iso-curvature )


The curvature spectral index

where, tensor spectral index was used

The gradient of N

Correlation angle


Curvature iso-curvature correlation

Tensor to scalar ratio

f_NL and power spectrum in the delta N for-malism

then


One can find

f_NL becomes simpler form

With a little algebra


Most important term is

Condition for large f_NL1. The total amount of sourcing of curvature modes by iso-curvature modes (TRS) must be extremely sensitive to a change in the initial conditions perpendicular to the inflaton trajectory. In other words, two neighboring trajectories must experience dramatically different amounts of sourcing.2. The total amount of sourcing must be non-zero. Usually, the amount of sourcing must also be moderate, to avoid having


Fine tuning for Non-gaussianity 1 vs 100

POSSIBLE WAY TO PRODUCE LARGE NON-GAUSSIANITY IN SOME MODEL FROM LARGE VOLUME SCENARIO

One model from string flux compactification.

EVOLUTION OF NON-GAUSSIANITY WITH THE ADIABATICITY ASSUMPTION

1011.4934 (J. Meyers and N. Sivanandam) The adiabaticity assumption

The non-gaussianity is decreasing exponen-tially.

EVOLUTION OF NON-GAUSSIANITY WITH THE ADIABATICITY ASSUMPTION

If the adiabaticity assumption is considered, we cannot expect local type large non-gaus-sianity.

So it could be difficult to produce large NG in all the multi field case.

However, this assumption is not so strong.

SUMMARY

Flux compactification of type IIB string theory can give multi-field inflation model(Large volume scenario).

In the multi- field case, the large NG requires fine tuning in the field trajectories.

In the string theory, we can generate the model which can produce large NG.

With the adiabaticity assumption, large NG is very difficult produce.

In order to constrain string theory models, we have to understand how the fine-tuning con-strains the parameter space of the models.

C AN WE CONSTRAIN MODELS FROM THE STRING THEORY BY N ON - GAUSSIANITY ? APCTP-IEU Focus Program Cosmology and Fundamental Physics June 11, 2011 Kyung Kiu.

Documents

large nongaussianity

string theory models

large volume scenarios

action slide

large volume s cenario

consistent theory

sting theory

summary slide