Patrick Peter. Institut d Astrophysique de Paris Institut Lagrange de Paris. Evidences for inflation constraints on alternatives

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1 Patrick Peter Institut d Astrophysique de Paris Institut Lagrange de Paris Evidences for inflation constraints on alternatives Thanks to Jérôme Martin For his help

2 Planck 2015 almost scale invariant quantum vacuum fluctuations of a single scalar d.o.f excluded compatible with INFLATION gaussian signal isocurvature

3 Inflation: phase of accelerated expansion needs a fluid with negative pressure Inflaton (compatible with the cosmological principle) Slow-roll

4 Standard questions and inflationary answers Singularity Horizon Not solved... actually not addressed! can be made as big as one wishes Flatness accelerated expansion (inflation) Homogeneity & Isotropy Initial Universe = very small patch Accelerated expansion drives the shear to zero... Bonus of the theory: predictions!!! Perturbations Others dark matter/energy, baryogenesis,... vacuum state!

5 Almost constant Hubble radius

6 Everything depends on the slow roll parameters Evaluated at (pivot scale leaves Hubble radius): Spectral indices Consistency relation + running

7 Various models, various predictions (one example) Predictions Predictions in in the the slow-roll slow-roll space: space one example Large field inflation Different values of Different values of p Different= different reheating era parameters for the reheating era Different value of φ* 7 7

8 3 point correlation function... Predictions in the slow-roll space: one example Unobservable at the moment 8

9 Comparing with data: pb = 100 s of different models

10 Planck 2015 L A M I! N! I! A M T H A T ED I W H L T L Y O R DB W E O R L O S V D A L F E quantum vacuum fluctuations of a single scalar d.o.f almost scale invariant I M F R E excluded E L T G compatible with gaussian signal C N I I INFLATION S ET N isocurvature I K

11 CMB constraints on the slow-roll parameters 11

12 Planck 2015 constraints: Slow-roll parameters Deviation from exact scale invariance Inflaton potential No detection: GW Running Bayesian analysis Energy scale best models: J. Martin, C. Ringeval & V. Vennin, arxiv: Encyclopedia Inflationaris

13 Inflation: solves cosmological puzzles uses GR + scalar fields [(semi-)classical] can be implemented in high energy theories string implementation (brane inflation,...) makes falsifiable predictions consistent with all known observations why bother with alternatives? When you have eliminated the impossible, whatever remains, however improbable, must be the truth. Sherlock Holmes (The sign of the four):

14 From R. Brandenberger, in M. Lemoine, J. Martin & PP (Eds.), Inflationary cosmology, Lect. Notes Phys. 738 (Springer, Berlin, 2007). Singularity Trans-Planckian Hierarchy (amplitude)? Classical GR? problem & Lyth bound Initial condition & entropy Eternal inflation & measure (anthropic)

15 Singularity problem Quantum effect?

16 Pre Big Bang scenario: hep-th/ & hep-th/ Einstein frame String frame WdW quantum cosmology: PLA 241, 229 (1998) arxiv:

17 A brief history of bouncing cosmology R. C. Tolman, On the Theoretical Requirements for a Periodic Behaviour of the Universe, PRD 38, 1758 (1931) G. Lemaître, L Univers en expansion, Ann. Soc. Sci. Bruxelles (1933) Singularity pb no solved A. A. Starobinsky, On one non-singular isotropic cosmological model, Sov. Astron. Lett. 4, 82 (1978) V. N. Melnikov, S.V. Orlov, Phys. Lett. A 70, 263 (1979). R. Durrer & J. Laukerman, The oscillating Universe: an alternative to inflation, Class. Quantum Grav. 13, 1069 (1996) Many new ideas, models M. Novello & S.E. Perez Bergliaffa, Bouncing cosmologies, Phys. Rep. 463, 127 (2008) D. Battefeld & PP, A Critical Review of Classical Bouncing Cosmologies, Phys. Rep. 571, 1 (2015) R. Brandenberger & PP, Bouncing cosmologies: Progress and problems, Found. Phys. (2017)

18 Model listing: Quantum gravity LQG & LQC Non relativistic quantum gravity Canonical quantum gravity (WdW) String theory

19 Model listing: Quantum gravity LQG & LQC Non relativistic quantum gravity Canonical quantum gravity (WdW) Ekpyrotic & cyclic Branes String theory

20 Ekpyrotic scenario: Singular

21 contracting

22 Cyclic extension

23 Model listing: Quantum gravity LQG & LQC Non relativistic quantum gravity Canonical quantum gravity (WdW) Ekpyrotic & cyclic Branes String theory Horava-Lifshitz String gas cosmology Lee-Wick & Quintom Antigravity F(R), f(t), Gauss-Bonnet Galileon Massive gravity Mimetic matter Non-linear electromagnetic action Multiverse models Strings & AdS/CFT Spinors & torsion

24 (see Encyclopedia Inflationaris)

25 Standard questions and bouncing answers arxiv: Singularity Merely a non issue in the bounce case!

26 Standard questions and bouncing answers arxiv: Singularity Merely a non issue in the bounce case!

27 Standard questions and bouncing answers arxiv: Singularity Horizon Merely a non issue in the bounce case! can be made divergent easily if Example:

28 Standard questions and bouncing answers arxiv: Singularity Horizon Merely a non issue in the bounce case! can be made divergent easily if Flatness decelerated contraction (bounce) [accelerated expansion (inflation)]

29 Standard questions and bouncing answers arxiv: Singularity Horizon Merely a non issue in the bounce case! can be made divergent easily if Flatness accelerated expansion (inflation) or decelerated contraction (bounce) Homogeneity Large & flat Universe + low initial density + diffusion enough time to dissipate any wavelength quantum vacuum fluctuations...

30 Implementing a bounce = problem with GR! Null Energy Condition (NEC) Many working examples: K-bounce, Ghost condensates, Galileons...? Instabilities

31 Standard questions and bouncing answers arxiv: Singularity Merely a non issue in the bounce case! Horizon can be made divergent easily if Flatness accelerated expansion (inflation) or decelerated contraction (bounce) Homogeneity Large & flat Universe + low initial density + diffusion enough time to dissipate any wavelength quantum vacuum fluctuations... Isotropy Potentially problematic: model dependent

32 The problem with contraction: BKL/shear instability Ricci flat Bianchi I anisotropic universe Average scale factor Mean Hubble parameter Friedman equations

33 Ekpyrotic solution: when Problem: regular bounce NEC phase with So finally... back to the singularity!

34 A nonsingular bounce model: ghost condensate & Galileon Specific choices: kinetic term

35

36 Summary of possible problems + phase initial conditions

37 Standard questions and bouncing answers arxiv: Singularity Merely a non issue in the bounce case! Horizon can be made divergent easily if Flatness accelerated expansion (inflation) or decelerated contraction (bounce) Homogeneity Large & flat Universe + low initial density + diffusion enough time to dissipate any wavelength quantum vacuum fluctuations... Isotropy Others Potentially problematic: model dependent dark matter/energy, baryogenesis,...