Comparing IR DBI Brane Inflation to Observations Xingang Chen CTP, MIT hep-th/ ; hep-th/ ; astro-ph/ ; , 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. 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. DBI IR DBI inflation: (X.C. 04, 05) For,

S.R. DBI 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 densitySource 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 fluctuations relativistically. Relativistic (superluminal if naïve) Non-relativistic Scalars Scalars + strings (branes) Field theory regimeStringy 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 distinguish IR DBI from  CDM; but is able to give interesting constraints.

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 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:

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.