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Comparing IR DBI Brane Inflation to Observations

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Comparing IR DBI Brane Inflation to Observations

Xingang Chen

陈新刚

CTP, MIT

hep-th/0408084; hep-th/0501184; astro-ph/0507053;

0710.1812, with Rachel Bean, Hiranya Peiris, Jiajun Xu.

Motivation

- Large number of ongoing and forthcoming experiments:
- WMAP, SDSS, SNLS, ACBAR, Planck, ACT, Spider, ...

- Specifying inflation model and probing underlying
- fundamental theory such as string theory

- Signatures beyond the vanilla LCDM model:
- Running of spectral index, Large non-Gaussianities,
- Tensor modes, Cosmic strings, …

Approach

- Scan parameter space with minimum requirement:
- Enough inflationary e-folds.

- Look for observational signatures in all parameter space
- and compare with data.

- Probing string theory through dynamics of our own vacuum

Observational signatures Specific stringy dynamics

Outline

- Properties of brane inflation: Phase diagrams

- Analytical and numerical properties of IR DBI

- Comparison with data

Brane Inflation in

Warped Compactification

- Brane inflation(Dvali, Tye, 98; )
- Brane position as inflaton;
- Brane annihilation or collision as ending.

Burgess,Majumdar,Nolte,Quevedo,

Rejesh,Zhang;Dvali,Shafi,Solganik,01

(Gidding, Kachru, Polchinski, 01;

Klebanov, Strassler, 00; Verlinde, 99;

Randall, Sundrum, 99)

- Warped compactification

- 6 dimensional bulk
- Warped space generated by
- point-like (6d) sources

A-throat

Phase diagram: UV models

Firouzjahi,Tye,05

Shandera,Tye,06

(KKLMMT, 03; Silverstein, Tong, Alishahiha,03,04; )

- Potential

- Warped space

S.R.

S.R.

Slow-roll inflation:

DBI inflation:

(Silverstein, Tong, 03)

S.R.

S.R.

DBI

: multiplicative factor

from orbifolding

: Length scale of A-throat;

: Length scale of bulk

Geometric Conditions

(Burgess, et.al.,01; X.C,05; X.C.,Sarangi,Tye,Xu,06; Baumann,McAllister,07)

- Planck mass: integration over compact space

- Throats glued to the bulk

- Maximum separation between branes

- Clean separation b.t. Slow-roll and DBI:

- Brane inflation is small field:

S.R.

S.R.

DBI

- Slow-roll region: KKLMMT model, 03

Shape of the potential may be adjusted to fit the spectral index;

In the absence of sharp feature,

Non-Gaussianity and running spectral index are unobservable;

Tensor mode is too small to be observed.

(Berg, Haack, Kors, 04;

Baumann et al, 06;

Burgess,Cline,Dasgupta,Firouzjahi,06;

Krause, Pajer, 07; …)

(Bean, Shandera, Tye, Xu, 07)

- DBI region: STA model

(Silverstein, Tong, Alishahiha, 03,04)

Large non-Gaussianity:

Tensor mode:

But inconsistent within GKP-type warped compactification

--- no UV DBI inflation due to probe brane backreactions

(Bean, X.C., Peiris, Xu, 07)

- Antibrane tension cannot drive inflation

So need

- Excessive probe brane backreaction

Requirement:

But:

Note: No comparison with data has been made.

B-throat

Phase diagram: IR models

(X.C., 04,05; Bean, X.C., Peiris, Xu, 07)

- Potential

,

- Warped space

- Multi-throat brane inflation(X.C. 04)

- Antibrane-flux annihilation (Kachru, Pearson, Verlinde, 01)
- Generate branes as candidate inflatons
- Exit B-throat, roll through bulk, settle down in another throat
- Enough warping: DBI inflation; Flat potential: slow-roll inflation.

S.R.

Slow-roll inflation:

IR DBI inflation:

(X.C. 04, 05)

- For ,

- For ,

S.R.

DBI

DBI

S.R.

DBI

DBI

Geometric conditions are automatically satisfied:

- UV DBI

- Antibrane tension cannot drive inflation,
since it is warped down by the same A-throat warp factor.

An extra, steep, potential is needed to raise the inflationary energy:

with a large m :

- IR DBI

- Speed-limit and antibrane tension are independent of each other:
Speed-limit: B-throat; Inflationary energy: A-throat.

Flexible shape of brane moduli potential:

: over ten orders of magnitude.

Main Difference Between UV and IR DBI Model

B-throat warp factor is smaller than

- Non-trivial condition:
Various back-reactions that chop off the IR end of throat

- Probe brane back-reaction;

(Silverstein,Tong,03; X.C.,04)

Easy to satisfy in IR DBI model.

- Back-reaction from expanding background.

(X.C.,05; X.C.,Tye,06)

Condition for IR DBI inflation:

- Flux induced warp factor is exponentially small:

(Giddings,Kachru,Polchinski,01)

Very easy to satisfy the condition.

- From the point of view of closed string creation

(X.C.,05)

Closed string density

Source of the bkgd (N branes)

- From the point of view of open string fluctuations

(X.C., Tye, 06)

Transverse scalar fluctuations on the source branes:

Throat is cut off at

Maximum number of DBI e-folds:

Back-reaction from Expanding Background

Outline

- Properties of brane inflation: Phase diagrams

- Analytical and numerical properties of IR DBI

- Comparison with data

Two attractor solutions:

- IR DBI inflation:

- Non-relativistic roll, typically fast roll:

Brane Dynamics

(X.C.04,05; Bean,X.C.,Peiris,Xu,07)

- : Field theory applies;
- 2) : Open string creation
- (Stringy quantum fluctuations);
- 3) : Closed string creation starts;
- 4) : Closed strings smooth out background
- (de Sitter back-reaction cuts off the throat).

(4)

(3)

(2)

(1)

Density perturbations:

1) Field theory regime

2) Hubble-expansion-induced stringy phase

- Stringy phase transition:

- Hubble scale < string scale:
- Fluctuation speed < speed of light:

Phase transition at:

if

Density Perturbations

(X.C. 04, 05)

- Field theory regime

- Density perturbations:

- Spectrum index:

Field theory regime

Stringy regime

E-fold

Hubble energy

Fluctuation speed

Relativistic (superluminal if naïve)

Non-relativistic

World volume

Scalars

Scalars + strings (branes)

Estimate the Transition Behavior

(Bean, X.C., Peiris, Xu, 07)

- Model: Brane transverse fluctuations:
- Random-walk within the horizon, speed given by H;
- Frozen outside of the horizon.

We generalize the behavior of brane transverse fluctuations

relativistically.

- Spectral index

- Regional large running

For example,

if

Results (in IR DBI region):

- Power spectrum

- Non-Gaussianities in general single field inflation
- are characterized by 5 parameters:

(X.C., Huang, Kachru, Shiu, 06)

c.f. slow-roll inflation, 2 parameters:

(Maldacena, 02; Seery, Lidsey, 05)

- Leading Non-Gaussianities:

Large non-Gaussianity

In the absence of sharp features (X.C., Easther, Lim, 06),

running is weak, shape has two categories:

Equilateral shape (DBI inflation)

Local shape (Slow-roll inflation)

Shape: dependence on the shape of momenta triangle

(Babich, Creminelli, Zaldarriaga, 04)

Running: dependence on the size of momenta triangle

(X.C. 05)

- DBI inflation:

(Alishahiha,Silverstein,Tong,04;X.C.,Huang,Kachru,Shiu,06)

- UV DBI inflation (STA model)

- IR DBI inflation

(X.C. 05)

- Different requirements on microscopic parameters.

Geometric conditions have no effect on IR DBI.

- In IR DBI, the large non-G can be small enough to satisfy current bound.

Negative running:

Non-G tends to be the smallest in the entire DBI inflation trajectory.

is tiny in IR DBI inflation

Small Tensor Mode

- Tensor to scalar ratio:

Lyth Bound:

(Lyth,96; Baumann,Mcallister,06; Lidsey,Huston,07)

(Bean, X.C., Peiris, Xu, 07)

Outline

- Properties of brane inflation: Phase diagrams

- Analytical and numerical properties of IR DBI

- Comparison with data

Microscopic Parameters

- Shape of inflaton brane moduli potential:

- Charge of the B-throat:

- Number of inflaton branes:

- Fundamental string scale:

- A-throat warp factor and number of antibranes:

- Scale dependence of power spectrum:

Spectrum index and its running

- Non-Gaussianity bound:

- Several consistency conditions, for example:

DBI e-folds and scale of the transient large running of

- Scale – e-fold relation:

- Geometric constraint:

- Number of inflaton branes

Observables

- Amplitude of power spectrum:

Goal: Compare to data directly from microscopic parameters,

using Bayes’ theorem:

: data.

: parameters;

Possible obstacles: Nonlinear and non-transparent relation

between microscopic parameters and observables

Non-Gaussian posterior distributions, curved likelihood surface, etc.

Difficult to search the likelihood surface efficiently

Solution: Reparameterization:

Implementing Markov Chain Monte Carlo

E.g.

Full expressions:

have to be solved numerically;

However, approximate expression for observational window:

can be obtained.

Effective parameters:

General Procedures

(Bean,X.C.,Hiranya,Xu,07)

1) Extract isolated expression for a small window

in terms of smaller number of parameters

2) Run a trial MCMC with the effective parameters ,

to ensure that these parameters have simple likelihood surface.

3) Express (approximately) in terms of microscopic parameters ,

which provides guidance to the reparameterization .

E.g.

Using the efold – scale relation:

We approximate:

The reparameterization:

4) Run the full MCMC with .

Analytical approximation dropped, observables calculated numerically.

5) Transform the likelihood surface of to the space of the original

parameters .

Re-weighted to impose any desired priors on .

These parameters will have simple likelihood surface.

The results

Data cannot distinguish

IR DBI from LCDM;

but is able to give interesting

constraints.

- Shape of moduli potential:

Data picks out O(1) value from 10 orders of magnitude that allows IR DBI.

- Fundamental string scale:

Intermediate string scale, intermediate large volume compactification

- B-throat charge:

- Number of inflaton branes:

Flux number , small number of inflatons is ruled out.

- A-throat minimum warp factor:

A-throat tends to be short; tunneling reheating is possible.

Summary of MCMC Results

Microscopic parameters:

- The stringy phase transition:

The stringy phase transition happens at the largest scales in the sky;

but its impact extends to shorter scales, generating transient large

running of .

- Inflation scale:

This gives a tiny tensor to scalar ratio:

- Cosmic string tension:

is tension of D-string left over in A-throat after brane annihilation;

F-string tension:

Secondary derived parameters:

- Inflationary phases: the last e-folds come from
- non-relativistic fast-roll inflation.

- Large, but regional, running of spectral index:

In future experiments, Planck is expected to reach .

(Planck bluebook)

Observational predictions:

Better theoretical understanding and experimental measurement

may lead to finer structures.

Reconstructed Power Spectrum

Dashed lines: 1) Single-field slow-roll; 2) Empirical power law ansatz.

(Peiris, Easther, 06)

In future experiments: on CMB scales, Planck can achieve ;

on LSS scales, high-z galaxy surveys can reach similar or better resolutions.

(Smith, Zaldarriaga, 06; Sefusatti, Komatsu, 07)

- Large non-Gaussianities:

However, large running of can be achieved by engineering the potential:

adding mild features, such as periodic ripples.

(Bean, X.C., Peiris, Xu, 07)

- Helps to sustain the inflation
- Generating large running of spectral index

varies between

To distinguish, use the non-Gaussianity:

Distinguishing IR DBI and other models

- Slow-roll potential with mild features

Usual slow-roll gives negligible running of spectral index:

- Non-Bunch-Davies vaccum

(Martin, Brandenberger, 00; ……)

Generalize slow-roll results

to case with arbitrary speed of sound

(Danielsson, 02; Polarski, Starobinsky, 95)

(Bean, X.C., Peiris, Xu, 07)

Running spectral index:

- Slow-roll with non-BD: have much smaller , or have frequent oscillations
- IR DBI with non-BD: frequent oscillations

- Main difference:
- Non-BD case: new physics energy scale M >> Hubble parameter H,
so field theory apply

- Phase transition in IR DBI: new physics (stringy) scale is
comparable or larger than Hubble parameter H

Conclusions

- Multi-throat brane inflation and IR DBI:
- Phase diagram of brane inflation;
- Comparision with UV models.

- Warp compactification:
- Speed-limit: DBI inflation;
- Warped string scale: stringy phase transition.

- Comparing to data:
- Current data gives interesting constraints to microscopic parameters.

- Observational predictions:
- Regional large running of spectral index; Large non-Gaussianities.

String theory making testable predictions with distinctive signatures;

Probing string theory using cosmological observations.