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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:

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Comparing IR DBI Brane Inflation to Observations

Xingang Chen



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

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


  • 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, …


  • 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


  • 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.



(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


Phase diagram: UV models



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

  • Potential

  • Warped space



Slow-roll inflation:

DBI inflation:

(Silverstein, Tong, 03)




: multiplicative factor

from orbifolding

: Length scale of A-throat;

: Length scale of bulk

Geometric Conditions

(Burgess,,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

  • Brane inflation is small field:




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;


Krause, Pajer, 07; …)

(Bean, Shandera, Tye, Xu, 07)

(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



Note: No comparison with data has been made.


Phase diagram: IR models

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

  • Potential


  • Warped space

  • 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.


Slow-roll inflation:

IR DBI inflation:

(X.C. 04, 05)

  • For ,

  • For ,







Geometric conditions are automatically satisfied:

  • 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:


Very easy to satisfy the condition.


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


  • 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).





Density perturbations:

1) Field theory regime

2) Hubble-expansion-induced stringy phase

  • Hubble scale < string scale:

  • Fluctuation speed < speed of light:

Phase transition at:


Density Perturbations

(X.C. 04, 05)

  • Field theory regime

  • Density perturbations:

  • Spectrum index:

Field theory regime

Stringy regime


Hubble energy

Fluctuation speed

Relativistic (superluminal if naïve)


World volume


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


  • Regional large running

For example,


Results (in IR DBI region):

  • Power spectrum

(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)


  • 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)


  • 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:

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


  • 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


Full expressions:

have to be solved numerically;

However, approximate expression for observational window:

can be obtained.

Effective parameters:

General Procedures


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 .


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


but is able to give interesting


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 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.

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:

(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 engineering the potential:

  • 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.