1. Inflationary observables: what can we learn about fundamental physics? Paolo Creminelli (ICTP, Trieste) Alessandria, 15 th December 2006

2. V Friction is dominant To have ~ dS space the potential must be very flat: Slow-roll inflation This gives a period of inflation: Curvature, inhomogeneities and relics are diluted away. For we have a completely smooth Universe. For we have quantum fluctuations of all the light degrees of freedom. Inflaton itself (scalar perturbations) and graviton (tensor modes). The study of perturbations gives information about this early cosmological era.

3. WMAP3: + other experiments at shorter scale: CMB+LSS+Lyman Clear evidence of coherence and ~ scale invariance: modes are already there out of Hubble scale, with ~ scale invariant spectrum Polarization: E-modes (already detected) + B-modes (smoking gun of GW contribution) Data on quantum fluctuations during inflation

4. Inflationary observables 1. Tilt of the spectrum. Very recently: (Do not take too seriously: wait!) Experimental evidence of deviation from dS! In most models: 2. Tensor modes. Contribution of spin-2 modes in the CMB map. 3. Non-gaussianities. It describes the interaction among (scalar) modes. Now: r < 0.5 Planck (2009?): r < 0.05 Future (?): r < 0.01 Now: NG < 10 -3 Very close to a free field! Future: NG < 10 -5

5. What are the implication of a GW signal? Lyth’s bound. We need ~ 60 e-folds of inflation Observation of GWs implies (in model indep. way): How difficult is this? Typical simple example: One expects: Why should V remains flat over such a large range? Cfr. Hybrid Models: Something abrupt at the end of inflation No observable gravitational waves

6. Toy model in field theory Take a PNGB, approximate shift symmetry: To inflate: How can I get f >> M P ? Gravity will give terms violating the symmetry: Arkani-Hamed, Cheng, P.C., Randall etal 2003 Abelian gauge field in 5d, compactified on S 1 R AMAM Cannot write down a gauge invariant potential for A 5. Charge matter will induce a non-local potential for the Wilson line:

7. No problem in having f >> M P I can make f as large as I want making g 4 small: weak coupling limit! For R >> M s no problem with quantum gravity corrections: gauge symmetry + locality. Extra dimensions help! Working out the details we get all the predictions: detectable GWs! ~ The effective field theorist is not afraid of trans-Planckian VEV … and the string theorist? Taylor expanding…

8. f >> M P in string theory? Banks, Dine, Fox, Gorbatov, hep-th/0303252 In all known examples, we cannot get f >> M P Example: Type I on a 6-torus Wilson line: Naively we can go to a radius R << M s -1. T-dual picture: Wilson line is the distance between D8-branes in type I’ R’ But in this 1-d geometry I have a linear growth of the dilaton: Easy? Strong coupling for: Same thing in higher codimension + for large g dualize to heterotic: NO WAY!

9. GWs in the swampland? Arkani-Hamed, Motl, Nicolis, Vafa, hep-th/0601001 Conjecture: we cannot take the limit g --> 0. There must be a distinction between a global and a gauge symmetry! If for an extremal BH. There must be states: In D=5: Looking at magnetically charged BH: So that: requires It seems that inflationary models with detectable GWs cannot be embedded in string theory No sign of this in EFT

10. N-flation Dimopoulos, Kachru, McGreevy, Wacker, hep-th/0507205 If we cannot get parametrically for a single field, can we gain if we a large number of fields N? E.g, we can have a large number of axions: Pythagoras saves the day. Effective displacement: Problem: to have a large N you would need a large compactification space, cannot take N large keeping M P fixed Hard to make a parametric separation, but on some compactification one can get observable GWs Bottom line: GWs are surely not generic. If observed they would force to look at very specific corners of the landscape

11. Non-Gaussianity: any correlation among modes?

12. Slow-roll = weak coupling V Friction is dominant To have ~ dS space the potential must be very flat: Maldacena, JHEP 0305:013,2003, Acquaviva etal Nucl.Phys.B667:119-148,2003 The inflaton is extremely weakly coupled. Leading NG from gravity. Completely model independent as it comes from gravity Unobservable (?). To see any deviation you need > 10 12 data. WMAP ~ 2 x 10 6

13. Smoking gun for “new physics” Any modification enhances NG –Modify inflaton Lagrangian. Higher derivative terms, ghost inflation, DBI inflation… –Additional light fields during inflation. Curvaton, variable decay width… Potential wealth of information Any signal would be a clear signal of something non-minimal Translation invariance: Scale invariance: F contains information about the source of NG Note. We are only considering primordial NGs. Neglect non-linear relation with observables. Good until primordial NG > 10 -5. see P.C. + Zaldarriaga, Phys.Rev.D70:083532,2004 Bartolo, Matarrese and Riotto, JCAP 0606:024,2006

14. Higher derivative terms Potential terms are strongly constrained by slow-roll. Impose shift symmetry: P.C. JCAP 0310:003,2003 Most relevant operator: Change inflaton dynamics and thus density perturbations 3 point function: In EFT regime NG < 10 -5 Difficult to observe We get large NG only if h. d. terms are important also for the classical dynamics One can explicitly calculate the induced 3pf:

15. Alishahiha, Silverstein and Tong, Phys.Rev.D70:123505,2004 DBI inflation Example where higher derivative corrections are important AdS A probe D3 brane moves towards IR of AdS. Geometrically there is a speed limit The dual description of this limit is encoded in h.d. operators. DBI action: The scalar is moving towards the origin of the moduli space. H.d. operators come integrating out states becoming massless at the origin. It helps inflation slowing down the scalar (potential?) Generic in any warped brane model of inflation (reconstruct the shape of the throat?) 3pf can be as large as you like Generic 3pf for any model with: Conformal invariance (see e.g. S. Kecskemeti etal, hep-th/0605189) S. Kachru etal. hep-th/0605045

16. Perturbations generated by a second field Parallel Universes: NG is generated by inefficiency: RHN neutrinos will not be completely dominant. To match 10 -5 we need larger fluctuations and thus larger NGs In general: NG > 10 -5, but model dependent. Possible isocurvature contributions. Every light scalar is perturbed during inflation. Its perturbations may become relevant in various ways: Curvaton Variable inflaton decay 2 field inflation Perturbation of parameters relevant for cosmo evolution Example: variable decay of right-handed neutrinos with L.Boubekeur, hep-ph/0602052 The RHN goes out of equilibrium and decay in ≠ way in ≠ regions of the Universe

17. The shape of non-Gaussianities Babich, P.C., Zaldarriaga, JCAP 0408:009,2004 LOCAL DISTRIBUTION Typical for NG produced outside the horizon. 2 field models, curvaton, variable decay… EQUILATERAL DISTRIBUTIONS Derivative interactions irrelevant after crossing. Correlation among modes of comparable. F is quite complicated in the various models. But in general Quite similar in different models

18. Shape comparison The NG signal is concentrated on different configurations. They can be easily distinguished (once NG is detected!) They need a dedicated analysis

19. Analysis of WMAP 3yr data WMAP alone gives almost all we know about NG. Large data sample + simple. Not completely straightforward! It scales like N pixels 5/2 ~ 10 16 for WMAP!!! Too much… But if F is “factorizable” the computation time scales as N pixels 3/2 ~ 10 9. Doable! Use a fact. shape with equilateral properties New: tilt in the 3yr analysis! P.C., Senatore, Zaldarriaga, Tegmark, astro-ph/0610600

20. No detection :( WMAP data (after foreground template corrections) are compatible with Gaussianity We have the best limits on NG for the two shapes -36 < f NL local < 100 at 95% C.L. -256 < f NL equil. < 332 at 95% C.L. Reduction of noise + change in cosmo. parameters (e.g. optical depth) Slight (20%) improvement wrt to WMAP3 analysis for the local shape. Limits on equil. shape are not weaker: different normalization. In models: c s > 0.028 at 95% C.L.

21. Conclusions Cosmology is converging to its own Standard Model Compelling but not particularly constraining for fundamental physics There is some room for future data to change the simplest picture 1.Gravitational waves: 2.Non-Gaussianities: non-minimal models ruled out 3.Something more exotic. Who thought ?