primordial avec les perturbations cosmologiques *

Transcription

1 Tests de l Univers primordial avec les perturbations cosmologiques * Filippo Vernizzi Batz-sur-Mer, 16 octobre, 2008 * Soustitré en anglais

2 What is the initial condition?

3 Standard single field inflation Vacuum energy of an overdamped homogeneous scalar field && a & φ + 3 & φ + V' φ = a ( ) 0 V ( ) φ φ Slow-roll: Expansion rate >> spacetime variation:

4 Cosmic acceleration H 1 t time a() t

5 Cosmic acceleration H 1 t time a( t)

6 Hubble exit H 1 t time a( t)

7 End of inflation H 1 t time a( t)

8 In the limit h = 0 we are left with nothing!

9 Scalar field fluctuations Perturbations: Amplification of vacuum quantum fluctuations by an external classical field, the expansion of the Universe: Field fluctuations imprint curvature perturbations (time delay in the expansion):

10 Cosmic acceleration H 1 t time a() t

11 Cosmic acceleration H 1 t time a( t)

12 Hubble exit H 1 t time a( t)

13 End of inflation H 1 t time a( t)

14 Standard evolution: deceleration H 1 t time a( t)

15 Hubble re-entry entry H 1 a( t) t time

16 Hubble re-entry entry H 1 t time

17 Cosmic Microwave Background Radiation distribution or curvature perts distribution when the Universe was 1090 times smaller than today T ~ δt ζ ~ 10 5 WMAP5

18 Power spectrum C l Scale-invariant spectrum Hydrodynamical oscillations of the plasma Nolta et al. 08

19 Deviation from n S =0 The power spectrum slowly varies during inflation: we expect a deviation from an exact scale invariant spectrum

20 Blue spectrum n S >0

21 Red spectrum n S <0

22 Gravity waves Scalar fluctuations (curvature): Tensor fluctuations (free gravity): Inflation produces also gravity waves Some models predict the observable amount (r > 0.01), some much less At the moment r < 0.2 (95% CL) The strongest smoking-gun of inflation: polarization

23 Testing inflationary models Scalar fluctuations (curvature): Tensor fluctuations (free gravity): Ratio tensor to scalar flucs Komatsu et al. 08 Tilt

24 Wait a minute Who tells us that the inflaton is a scalar field with standard action? Who tells us that the inflaton is responsible of the perturbations? Komatsu et al. 08 These constraints can be very misleading!

25 Non-Gaussianities Potential source of information in the mode coupling in this map: Happy families are all alike; every unhappy family is unhappy in its own way. Tolstoy, Pisma Zh.Eksp.Teor.Fiz.Ann.Karen WMAP5

26 What do we measure? Information in the amplitude and shape: Local non-gaussianity (squeezed state): r r 2 G NL G ( x) = ζ ( x) f ζ ( x) ζ + r k r 2 k r 1 k r 3 or equilateral one: k r 1 k r k r 2 3 Babich, Creminelli, Zaldarriaga 04

27 How much non-gaussian? Experimentally: CMB still gives the best constraints so far (but LSS will be important in the future) Current constraints: local 9 < f < 111 ( l max NL = equil 151 < f < 253 ( l max NL = 500) 700) Komatsu et al. 08

28 We look for a correlator: How do we compute it? Not a scattering amplitude: Vacuum of the interacting theory It is an equal time correlator Maldacena 02; Weinberg 05 ( in-in or Schwinger-Keldysh formalism) We measure quantum correlation functions in the sky!

29 Standard slow-roll inflation Slow-roll implies weak coupling: η H ~ V''' V' 4 H V''' H ~ O ε, η 10 ( 2 2 ) 5 V'''' ( 3 3 ) ( 5 10 ) 2 ~ O ε,η The inflaton is an extremely weakly coupled field! Mixing with gravity leads to stronger signal, but still small Expanding gravity + scalar field action at 3 rd -order: Maldacena 02 ζ k r 2 ζ k r 3 ζ k r 1

30 Ruling out slow-roll inflation Assuming: perturbations generated by single scalar inflaton with canonical kinetic term rolling down a smooth potential (slow-rolling) its fluctuations initially in the vacuum Detection of NG could rule out the largest class of inflationary models Major breakthrough in cosmology Classes of models generating sizeable Modified actions equilateral Multi-field models local

31 Beyond slow-roll Modified kinetic term: k-inflation Amendariz-Picon, Damour, Mukhanov 99 Expand it around an inflationary background t : r π ( t, x ) t = const φ = const H & ( ) δφ π = = & φ ζ H Speed of sound: m H& 2 2 P cs = 2 2 mph& 2X P,XX P,XXX = 0

32 Beyond slow-roll 2 1 c s Standard action equil f NL ~ 0 2 <<1 c s DBI inflation f equil 1 NL ~ 2 cs Silverstein, Tong 04 2 c s > % CL Speed of sound enters in another observable: c s Way of constraining operators of the inflaton

33 Non-Gaussianity detected? A detection of NG was claimed recently (note: only 95% CL) local 27 < f NL < 147 & Wandelt '07 [WMAP 3yr, l max Yadav = 750] but it was not confirmed by new data local 9 < f NL < 111 et al '08 [WMAP 5yr, l max Komatsu = 500] In this case we need a second field! Consistency relation applies to any single field models: Maldacena 02 k r 2 2 k r 1 The effect of the large scale mode is to rescale the background: ζ r k 1 x r x r 3 a k r 3 0 r ζ ( x1 ) ( t) a( t) = a ( t) e 0

34 More than one field Inhomogeneous reheating Inflaton decay rate depends on a light field: beginning of radiation era end of inflation Γ = m reheating φ g 2 ( σ ) Bernardeau, Uzan, 02 Kofman 04 Dvali, Gruzinov, Zaldarriaga 03 FV 04 modulated perturbations no perturbations ζ = δσ b + σ δσ σ local 1 f NL ~ b Local relation, same point x: peaked in the squeezed configuration k r 2 k r 1 k r 3

35 Intrinsic non-linearities When perturbations re-enter the Hubble radius, nonlinearities develop at the level of 2 nd -order perturbations: Planck CMBPOL LSS f NL ~ 5 f NL ~ 2 local ~ 1 f NL Using the same nonlinear machinery of inflation we can also study the post-inflationary Universe: Creminelli, D Amico, Norena, FV 08 What is the 3-point function of the CMB in absence of primordial non-gaussianies? Pitrou, Uzan, Bernardeau 08 Creminelli, D Amico, Norena, FV, in progress

36 Observations confirm inflation: Conclusions Tilt (deviation from scale-invariant spectrum): hint of inflation Gravity waves (still far-away): strongest confirmation of inflation but faraway Non-Gaussianities (alternative to standard methods): solid smoking-gun of new physics

37 Conclusions Non-Gaussianities: powerful tool to discriminate between models If observed of local form, then single field inflation is ruled-out If observed of equil. form, then standard slow-roll inflation is ruled-out If nothing is observed, we hope to see 2 nd -order effects f NL ~ 100 Experimental constraints Non-minimal models local f NL vs. f equil NL ~ 1 Second order effects on observables ~ O( ε ) Single-field slow-roll inflation