1. Primordial Non-Gaussianities and Quasi-Single Field Inflation Xingang Chen Center for Theoretical Cosmology, DAMTP, Cambridge University X.C., 1002.1416, a review on non-G; X.C., Yi Wang, 0909.0496; 0911.3380

2. CMB and WMAP (WMAP website)

3. Temperature Fluctuations (WMAP website)

4. What sources these fluctuations?

5. CMB and WMAP (WMAP website)

6. Generic Predictions of Inflationary Scenario Density perturbations that seed the large scale struture are • Primordial (seeded at super-horizon size) • Approximately scale-invaraint • Approximately Gaussian

7. Two-point Correlation Function (Power Spectrum) (WMAP5) Non-Gaussianities

8. Is this enough?

9. But we have pixels in WMAP temperature map Experimentally: Information is Compressed • Amplitude and scale-dependence of the power spectrum (2pt) • contain 1000 numbers for WMAP This compression of information is justified only if the primordial fluctuations is perfectly Gaussian. Can learn much more from the non-Gaussian components.

10. Theoretically: From Paradigm to Explicit Models • What kind of fields drive the inflation? • What are the Lagrangian for these fields? • Alternative to inflation? • Quantum gravity

11. Non-G components: Primordial Interactions • Two-point correlation Free propagation of inflaton in inflationary bkgd • Three or higher-point correlations (non-Gaussianities) Interactions of inflatons or curvatons “LHC” for Early Universe!

12. What we knew theoretically about the non-Gaussianities

13. Experimentally: Simplest inflation models predict unobservable non-G. (Maldacena, 02; Acquaviva et al, 02) • Single field • Canonical kinetic term • Always slow-roll • Bunch-Davies vacuum • Einstein gravity

14. Inflation Model Building Examples of simplest slow-roll potentials: The other conditions in the no-go theorem also needs to be satisfied.

15. Much more complicated in realistic model building ……

16. Inflation Model Building A landscape of potentials

17. Inflation Model Building Warped Calabi-Yau

18. h-Problem in slow-roll inflation: (Copeland, Liddle, Lyth, Stewart, Wands, 04) • h-Problem in DBI inflation: (X.C., 08) ? ? Inflation Model Building

19. Field range bound: (X.C., Sarangi, Tye, Xu, 06; Baumann, McAllsiter, 06) • Variation of potential: (Lyth, 97) ? : eg. higher dim Planck mass, string mass, warped scales etc.

20. Algebraic simplicity may not mean simplicity in nature.

21. Canonical kinetic term Non-canonical kinetic terms: DBI inflation, k-inflation, etc • Always slow-roll Features in potentials or Lagrangians: sharp, periodic, etc • Bunch-Davies vacuum Non-Bunch-Davies vacuum due to boundary condions, low new physics scales, etc • Single field Multi-field: turning trajectories, curvatons, inhomogeous reheating surface, etc Quasi-single field: massive isocurvatons Beyond the No-Go

22. Bispectrum is a function, with magnitude , of three momenta: Shape and Running of Bispectra (3pt) • Shape dependence: • (Shape of non-G) Fix , vary , . Squeezed Equilateral Folded Fix , , vary . • Scale dependence: • (Running of non-G)

23. Two Well-Known Shapes of Large Bispectra (3pt) For scale independent non-G, we draw the shape of Local Equilateral In squeezed limit:

24. For single field, small correlation if Physics of Large Equilateral Shape • Generated by interacting modes during their horizon exit Quantum fluctuations Interacting and exiting horizon Frozen So, the shape peaks at equilateral limit. • For example, in single field inflation with higher order derivative terms (Inflation dynamics is no longer slow-roll) (Alishahiha, Silverstein, Tong, 04; X.C., Huang, Kachru, Shiu, 06)

25. Local in position space non-local in momentum space Physics of Large Local Shape • Generated by modes after horizon exit, in multifield inflation • Isocurvature modes curvature mode • Patches that are separated by horizon evolve independently (locally) So, the shape peaks at squeezed limit. • For example, in curvaton models; (Lyth, Ungarelli, Wands, 02) multifield inflation models with turning trajectory, (very difficult to get observable nonG.) (Vernizzi, Wands, 06; Rigopoulos, Shellard, van Tent, 06)

26. What we knew experimentally about the non-Gaussianities

27. Experimental Results on Bispectra • WMAP5 Data, 08 (Yadav, Wandelt, 07) (Rudjord et.al., 09) (WMAP group, 10) ; • Large Scale Structure (Slosar et al, 08)

28. The Planck Satellite, sucessfully launched last year ; (Planck bluebook) (Smith, Zaldarriaga, 06) ;

29. 21cm: FFTT (Mao, Tegmark, McQuinn, Zaldarriaga, Zahn, 08) Other Experiments • Ground based CMB telescope: ACBAR, BICEP, ACT, …. • High-z galaxy survey: SDSS, CIP, EUCLID, LSST … • 21-cm tomography: LOFAR, MWA, FFTT, … For example:

30. Fit data to constrain for example Theoretical template Construct estimator for example Data analyses Underlying physics Different dynamics in inflation predict different non-G. Looking for Other Shapes and Runnings of Non-Gaussianities in Simple Models • Why? • So possible signals in data may not have been picked up, • if we are not using the right theoretical models. • A positive detection with one ansatz does not mean that we have found the right form.

31. Other Possible Shapes and Runnings in Simple Models with Large non-Gaussianities (X.C., Huang, Kachru, Shiu, 06; X.C., Easther, Lim, 06,08)

32. In 3pt: Peaks at folded triangle limit Other Possible Shapes and Runnings in Simple Models with Large non-Gaussianities Folded Shape: (X.C., Huang, Kachru, Shiu, 06; Meerburg, van de Schaar, Corasaniti, Jackson, 09) The Bunch-Davis vacuum: Non-Bunch-Davis vacuum: For example, a small

33. Other Possible Shapes and Runnings in Simple Models with Large non-Gaussianities Folded Shape: • Boundary conditons • “Trans-Planckian” effect • Low new physics scales

34. A feature local in time Oscillatory running in momentum space 3pt: Other Possible Shapes and Runnings in Simple Models with Large non-Gaussianities Sharp features: (X.C., Easther, Lim, 06,08) Steps or bumps in potential, a sudden turning trajectory, etc

35. Other Possible Shapes and Runnings in Simple Models with Large non-Gaussianities Sharp features: • Consistency check for glitches in power spectrum • Models (brane inflation) that are very sensitive to features

36. Other Possible Shapes and Runnings in Simple Models with Large non-Gaussianities Resonance: (X.C., Easther, Lim, 08; Flauger, Pajer, 10) Periodic features Oscillating background Resonance Modes within horizon are oscillating 3pt: Periodic-scale-invariance: Rescale all momenta by a discrete efold:

37. Other Possible Shapes and Runnings in Simple Models with Large non-Gaussianities Resonance: • Periodic features from duality cascade in brane inflation (Hailu, Tye, 06; Bean, Chen, Hailu, Tye, Xu, 08) • Periodic features from instantons in monodromy inflation (Silverstein, Westphal, 08; Flauger, Mcallister, Pajer, Westphal, Xu, 09)

38. Other Possible Shapes and Runnings in Simple Models with Large non-Gaussianities (X.C., Wang, 09)

39. Quasi-Single Field Inflation

40. One field has the mass • Others have mass (Ignored previously for den. pert.) Quasi-single field inflation (X.C., Wang, 09) Motivation for Quasi-Single Field Inflation • Fine-tuning problem in slow-roll inflation (Copeland, Liddle, Lyth, Stewart, Wands, 94) In the inflationary background, the mass of light particle is typically of order H (the Hubble parameter) E.g. C.f. is needed for slow-roll inflation • Generally, multiple light fields exist

41. A Simple Model of Quasi-Single Field Inflation • Straight trajectory: Equivalent to single field inflation • Turning trajectory: Important consequence on density perturbations. E.g. Large non-Gaussianities with novel shapes. Running power spectrum (non-constant case only). Here study the constant turn case Lagrangian in polar coordinates: slow-roll potential potential for massive field

42. Difference Between and is the main source of the large non-Gaussianities. but but etc It is scale-invariant for constant turn case.

43. Perturbation Theory • Field perturbations: • Lagrangian

44. Oscillating inside horizon Kinematic Part • Massless: Solution: Constant after horizon exit

45. Oscillating inside horizon Decay as after horizon exit. • Massive: Solution: , mass of order H E.g.

46. Oscillating inside horizon • Massive: Solution: , mass >> H E.g. Oscillating and decay after horizon exit

47. Massive: Solution: We will consider the case:

48. Interaction Part • Transfer vertex We use this transfer-vertex to compute the isocurvature-curvature conversion • Interaction vertex Source of the large non-Gaussianities

49. Perturbation Method and Feynman Diagrams Correction to 2pt 3pt To use the perturbation theory, we need These conditions are not necessary for the model building, but non-perturbative method remains a challenge.

50. In-In Formalism (Weinberg, 05) • Mixed form (X.C., Wang, 09) Introduce a cutoff . “Factorized form” for UV part to avoid spurious UV divergence; “Commutator form” for IR part to avoid spurious IR divergence. Mixed form + Wick rotation for UV part A very efficient way to numerically integrate the 3pt.