Comparing IR DBI Brane Inflation to Observations

1. 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.

2. 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, …

3. 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

4. Outline • Properties of brane inflation: Phase diagrams • Analytical and numerical properties of IR DBI • Comparison with data

5. 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

6. A-throat Phase diagram: UV models Firouzjahi,Tye,05 Shandera,Tye,06 (KKLMMT, 03; Silverstein, Tong, Alishahiha,03,04; ) • Potential • Warped space

7. S.R. S.R. Slow-roll inflation:

8. DBI inflation: (Silverstein, Tong, 03) S.R. S.R. DBI

9. : 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

10. Clean separation b.t. Slow-roll and DBI: • Brane inflation is small field: S.R. S.R. DBI

11. 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)

12. 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.

13. B-throat Phase diagram: IR models (X.C., 04,05; Bean, X.C., Peiris, Xu, 07) • Potential , • Warped space

14. 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.

15. S.R. Slow-roll inflation:

16. IR DBI inflation: (X.C. 04, 05) • For , • For , S.R. DBI DBI

17. S.R. DBI DBI Geometric conditions are automatically satisfied:

18. 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

19. 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.

20. 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

21. Outline • Properties of brane inflation: Phase diagrams • Analytical and numerical properties of IR DBI • Comparison with data

22. Two attractor solutions: • IR DBI inflation: • Non-relativistic roll, typically fast roll: Brane Dynamics (X.C.04,05; Bean,X.C.,Peiris,Xu,07)

23. : 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

24. 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:

25. 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.

26. Spectral index • Regional large running For example, if Results (in IR DBI region): • Power spectrum

27. 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

28. 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)

29. 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.

30. 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)

31. Outline • Properties of brane inflation: Phase diagrams • Analytical and numerical properties of IR DBI • Comparison with data

32. 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:

33. 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:

34. 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

35. 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

36. 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:

37. 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.

38. The results Data cannot distinguish IR DBI from LCDM; but is able to give interesting constraints.

39. 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:

40. 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.

41. 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.

42. Reconstructed Power Spectrum Dashed lines: 1) Single-field slow-roll; 2) Empirical power law ansatz. (Peiris, Easther, 06)

43. 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:

44. 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:

45. 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

46. 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.