Comparing IR DBI Brane Inflation to Observations

Xingang Chen

CTP, MIT

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

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

陈新刚

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 CDM model: Running of spectral index, Large non-Gaussianities, Tensor modes, Cosmic strings, …

Observational signatures Specific stringy dynamics

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

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

• Warped compactification (Gidding, Kachru, Polchinski, 01;Klebanov, Strassler, 00; Verlinde, 99; Randall, Sundrum, 99)

• 6 dimensional bulk

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

Phase diagram: UV models

• Potential

• Warped space

A-throat

(KKLMMT, 03; Silverstein, Tong, Alishahiha,03,04; )Firouzjahi,Tye,05 Shandera,Tye,06

S.R.

S.R.

Slow-roll inflation:

S.R. DBI

S.R.

DBI inflation: (Silverstein, Tong, 03)

Geometric Conditions

• Planck mass: integration over compact space

• Throats glued to the bulk

: multiplicative factor from orbifolding

• Maximum separation between branes

: Length scale of A-throat; : Length scale of bulk

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

S.R. DBI

S.R.

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

• Brane inflation is small field:

• 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.

(Bean, Shandera, Tye, Xu, 07) (Berg, Haack, Kors, 04; Baumann et al, 06; Burgess,Cline,Dasgupta,Firouzjahi,06; Krause, Pajer, 07; …)

But inconsistent within GKP-type warped compactification--- no UV DBI inflation due to probe brane backreactions

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

• DBI region: STA model (Silverstein, Tong, Alishahiha, 03,04)

Large non-Gaussianity:

Tensor mode:

Antibrane tension cannot drive inflation

So need

Excessive probe brane backreaction

Requirement:

But:

Note: No comparison with data has been made.

Phase diagram: IR models

• Potential

• Warped space

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

B-throat

,

• 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:

S.R.

DBIDBI

IR DBI inflation: (X.C. 04, 05)

• For ,

• For ,

S.R.

DBIDBI

Geometric conditions are automatically satisfied:

Main Difference Between UV and IR DBI Model

• 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.

B-throat warp factor is smaller than

Flux induced warp factor is exponentially small:

(Giddings,Kachru,Polchinski,01)

Very easy to satisfy the condition.

Condition for IR DBI inflation:

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

• Probe brane back-reaction; (Silverstein,Tong,03; X.C.,04)

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

• Back-reaction from expanding background.

Easy to satisfy in IR DBI model.

Throat is cut off at

Maximum number of DBI e-folds:

Back-reaction from Expanding Background

• From the point of view of closed string creation

Closed string density Source of the bkgd (N branes)

(X.C.,05)

• From the point of view of open string fluctuations

Transverse scalar fluctuations on the source branes: (X.C., Tye, 06)

Outline

• Properties of brane inflation: Phase diagrams

• Analytical and numerical properties of IR DBI

• Comparison with data

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

Two attractor solutions:

• IR DBI inflation:

• Non-relativistic roll, typically fast roll:

(1)(2)(3)(4)

2) Hubble-expansion-induced stringy phase1) Field theory regime

Density perturbations:

1) : 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).

• Stringy phase transition:

Hubble scale < string scale:

Fluctuation speed < speed of light:

Density Perturbations

Density perturbations:

Spectrum index:

(X.C. 04, 05)

• Field theory regime

Phase transition at:

if

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 fluctuationsrelativistically.

Relativistic (superluminal if naïve)Non-relativistic

Scalars Scalars + strings (branes)

Field theory regime Stringy regime

Fluctuation speed

Hubble energy

E-fold

World volume

Results (in IR DBI region):

Power spectrum

Spectral index

Regional large running

For example, if

Large non-Gaussianity

• 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:

(Babich, Creminelli, Zaldarriaga, 04)

Shape: dependence on the shape of momenta triangle

Running: dependence on the size of momenta triangle(X.C. 05)

Local shape (Slow-roll inflation)

In the absence of sharp features (X.C., Easther, Lim, 06),running is weak, shape has two categories:

Equilateral shape (DBI inflation)

• DBI inflation:

• IR DBI inflation

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

(X.C. 05)

• UV DBI inflation (STA model)

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.

Small Tensor Mode

Lyth Bound:

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

is tiny in IR DBI inflation

• Tensor to scalar ratio:

(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:

Observables

• Amplitude of power spectrum:

• Scale dependence of power spectrum:Spectrum index and its running

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

• Non-Gaussianity bound:

• Several consistency conditions, for example:

Scale – e-fold relation:

Geometric constraint:

Number of inflaton branes

Implementing Markov Chain Monte Carlo

Goal: Compare to data directly from microscopic parameters,using Bayes’ theorem:

: parameters; : data.

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:

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

1) Extract isolated expression for a small window

in terms of smaller number of parameters

Full expressions:

have to be solved numerically;

However, approximate expression for observational window:

can be obtained.

Effective parameters:

E.g.

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:

These parameters will have simple likelihood surface.

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 .

The results

Data cannot distinguishIR DBI from CDM;but is able to give interestingconstraints.

Summary of MCMC Results

Microscopic parameters:

• 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

• Number of inflaton branes:

• B-throat charge:

Flux number , small number of inflatons is ruled out.

• A-throat minimum warp factor:

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

Secondary derived parameters:

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

• 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 largerunning 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:

Observational predictions:

• Large, but regional, running of spectral index:

In future experiments, Planck is expected to reach .(Planck bluebook)

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)

• Large non-Gaussianities:

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)

Distinguishing IR DBI and other models

• Slow-roll potential with mild features

Usual slow-roll gives negligible running of spectral index:

To distinguish, use the non-Gaussianity:

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

adding mild features, such as periodic ripples.

Helps to sustain the inflation Generating large running of spectral index

varies between

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

• Non-Bunch-Davies vaccum (Martin, Brandenberger, 00; ……)

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

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

Conclusions

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

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

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

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

String theory making testable predictions with distinctive signatures;Probing string theory using cosmological observations.