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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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slide1
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.

slide2
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, …
slide3
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

slide4
Outline
  • Properties of brane inflation: Phase diagrams
  • Analytical and numerical properties of IR DBI
  • Comparison with data
slide5
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
slide6
A-throat

Phase diagram: UV models

Firouzjahi,Tye,05

Shandera,Tye,06

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

  • Potential
  • Warped space
slide7
S.R.

S.R.

Slow-roll inflation:

slide8
DBI inflation:

(Silverstein, Tong, 03)

S.R.

S.R.

DBI

slide9
: 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
slide10
Clean separation b.t. Slow-roll and DBI:
  • Brane inflation is small field:

S.R.

S.R.

DBI

slide11
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)

slide12
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.

slide13
B-throat

Phase diagram: IR models

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

  • Potential

,

  • Warped space
slide14
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.
slide15
S.R.

Slow-roll inflation:

slide16
IR DBI inflation:

(X.C. 04, 05)

  • For ,
  • For ,

S.R.

DBI

DBI

slide17
S.R.

DBI

DBI

Geometric conditions are automatically satisfied:

slide18
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

slide19
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.

slide20
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

slide21
Outline
  • Properties of brane inflation: Phase diagrams
  • Analytical and numerical properties of IR DBI
  • Comparison with data
slide22
Two attractor solutions:
  • IR DBI inflation:
  • Non-relativistic roll, typically fast roll:

Brane Dynamics

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

slide23
: 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

slide24
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:
slide25
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.

slide26
Spectral index
  • Regional large running

For example,

if

Results (in IR DBI region):

  • Power spectrum
slide27
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

slide28
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)

slide29
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.

slide30
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)

slide31
Outline
  • Properties of brane inflation: Phase diagrams
  • Analytical and numerical properties of IR DBI
  • Comparison with data
slide32
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:
slide33
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:
slide34
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

slide35
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

slide36
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:

slide37
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.

slide38
The results

Data cannot distinguish

IR DBI from LCDM;

but is able to give interesting

constraints.

slide39
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:

slide40
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.
slide41
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.

slide42
Reconstructed Power Spectrum

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

(Peiris, Easther, 06)

slide43
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:
slide44
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:

slide45
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

slide46
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.

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