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Inflation after Planck Jerome Martin CNRS/Institut dAstrophysique de Paris Collaborators: Interplay between Particle and - C. Ringeval (Louvain University), Astroparticle Physics - R. Trotta (Imperial College, London) LAL-Orsay - V.

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Inflation after Planck

Interplay between Particle and Astroparticle Physics LAL-Orsay September 05-09, 2016

Jerome Martin

CNRS/Institut d’Astrophysique de Paris

Collaborators:

  • C. Ringeval (Louvain University),
  • R. Trotta (Imperial College, London)
  • V. Vennin (Portsmouth University)
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The talk

Outline  Which class of inflationary scenarios after Planck 2013 & 2015?  What is the best model of inflation? Model comparison.  Constraints on reheating (aka end of inflation).  The next generation of CMB experiments and inflation.  Conclusions.

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The talk

Outline  Which class of inflationary scenarios after Planck 2013 & 2015?  What is the best model of inflation? Model comparison.  Constraints on reheating (aka end of inflation).  The next generation of CMB experiments and inflation.  Conclusions.

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Inflation in brief If the scalar field moves slowly (the potential is flat), then pressure is negative which, in the context of GR, means accelerated expansion and, hence, inflation takes place.

Inflation is (usually) realized with one (or many) scalar field(s) Inflation is a phase of accelerated expansion taking place in the very early

  • Universe. It solves the puzzles of the standard model of cosmology.
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Inflation in brief The field oscillates, decays and the decay products thermalize …Then the radiation dominated era starts …

Inflation (usually) stops when the field reaches the bottom of the potential

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Planck: third CMB experiment generation

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COBE (1992) WMAP (2003) Planck (2013 & 2015)

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CMB Temperature anisotropies in Fourier space

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90’s 00’s 10’s

From COBE to Planck …

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  • Universe spatially flat
  • Phase coherence
  • Adiabatic perturbations
  • Gaussian perturbations
  • Almost scale invariant power spectrum
  • Background of quantum gravitational waves

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The status of inflation

Planck Measurements

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  • Universe spatially flat
  • Phase coherence
  • Adiabatic perturbations
  • Gaussian perturbations
  • Almost scale invariant power spectrum
  • Background of quantum gravitational waves

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The status of inflation

Planck Measurements Single field slow-roll models, with minimal kinetic terms, are preferred

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The talk

Outline  Which class of inflationary scenarios after Planck 2013 & 2015?  What is the best model of inflation? Model comparison.  Constraints on reheating (aka end of inflation).  The next generation of CMB experiments and inflation.  Conclusions.

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What is the best model of inflation?

The performance of an inflationary model can be described by two numbers

  • the Bayesian evidence (integral of the likelihood over prior space)
  • the effective number of unconstrained parameters (aka Bayesian complexity)
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What is the best model of inflation?

 The performance of an inflationary model can be described by two numbers

Evidence Nb of unconstrained parameters

+1 +2

“bad” models

  • 1

“good” models

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What is the best model of inflation?

 The performance of an inflationary model can be described by two numbers

Evidence Nb of unconstrained parameters

+1 +2

“bad” models

  • 1

“good” models

Model X

The performance of a model can be represented by a point in the space (Nb of

  • uncons. params / evidence)
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What is the best model of inflation?

 The performance of an inflationary model can be described by two numbers

Evidence Nb of unconstrained parameters

+1 +2

“bad” models

  • 1

“good” models

Model X

The best models are here

Model Y

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arXiv:1303.3787

Encyclopedia Inflationaris

  • We have carried out a survey of

all (single field slwo-roll) models invented since 1979

  • This complete survey includes

≈ 200 scenarios ≈ 700 slow roll formulas ≈ 365 pages ≈ 74 potentials ≈ 30 000 lines of code

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Model Predictions

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Inflation in the evidence-Number of unconstrained parameter space

Model performance

No unconstrained parameter

Nb of unconstrained parameters

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Inflation in the evidence-Number of unconstrained parameter plane

Starobinsky model Model performance

No unconstrained parameter

Nb of unconstrained parameters

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Planck: and the winners are …

Starobinsky Model/ HI inflation ESI Plateau inflationary models are the winners!

  • J. Martin, C. Ringeval and V. Vennin, Phys. Dark Univ. 5-6 (2014) 75, arXiv:1303.3787
  • J. Martin, C. Ringeval, R. Trotta and V. Vennin, JCAP 1403 (2014) 039, arXiv1312.3529
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The Jeffreys’ scale

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Constraining power of Planck

The distribution of models over the Jeffreys’ scale gives a measure

  • f the constraining power of an experiment
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Constraining power of Planck

The distribution of models over the Jeffreys’ scale gives a measure

  • f the constraining power of an experiment
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Constraining power of Planck

The distribution of models over the Jeffreys’ scale gives a measure

  • f the constraining power of an experiment

P 26 % inconclusive zone 21 % weak zone 18 % moderate zone 34 % strong zone Planck can ruled out ~ 1/3

  • f the models
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SLIDE 24

The talk

Outline  Which class of inflationary scenarios after Planck 2013 & 2015?  What is the best model of inflation? Model comparison.  Constraints on reheating (aka end of inflation).  The next generation of CMB experiments and inflation.  Conclusions.

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Inflation in brief The field oscillates, decays and the decay products thermalize …Then the radiation dominated era starts …

Inflation (usually) stops when the field reaches the bottom of the potential

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  • The reheating phase can parameterized by and .

In fact, the CMB only depends on a specific combination, the Reheating parameter

  • The reheating parameter is like the optical depth for reionization:

at the atomic level, reionization is a very complicated phenomenon but, as long as the CMB is concerned, only one parameter matter. Reheating can be very complicated but as long the CMB is concerned, only the reheating parameter is important.

  • So the constraints on the reheating era are expressed as constraints on

the reheating parameter (posterior distribution).

The reheating parameter

  • J. Martin, C. Ringeval and V. Vennin, Phys. Rev. Lett. 114 (2015) 8, 081303, arXiv:1410.7958
  • J. Martin and C. Ringeval, Phys. Rev. D82 (2010) 023511, arXiv:1004.5525
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Planck 2013 constraints on reheating

Constraints

  • n reheating

Model performance

No constraint

  • n reheating
  • J. Martin, C. Ringeval and V. Vennin, Phys. Rev. Lett. 114 (2015) 8, 081303, arXiv:1410.7958
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Planck2013 constraints on reheating

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The talk

Outline  Which class of inflationary scenarios after Planck 2013 & 2015?  What is the best model of inflation? Model comparison.  Constraints on reheating (aka end of inflation).  The next generation of CMB experiments and inflation.  Conclusions.

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The future

 Tensor modes is the only inflationary prediction not yet checked …

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The future

 Tensor modes is the only inflationary prediction not yet checked …  This can be done by measuring CMB B-mode polarization

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Message 1: the energy scale of inflation

Consequences of a B-modes detection

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Consequences of a B-modes detection

Message 2: first derivative of the potential

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Message 3: the field excursion

Consequences of a B-modes detection

  • Also known as the Lyth bound.
  • Important for model building
  • Planckian excursions correspond to r>0.001
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LiteBIRD: Lite satellite for the studies of B-mode polarization and Inflation from cosmic background Radiation Detection (Japan) PRISM: the Polarized Radiation Imaging and Spectroscopy Mission (Europe) Message 4: Significant improvement of model comparison

Consequences of a B-modes detection

We have simulated data and data analysis for two missions: PRISM & LiteBIRD Should obviously be updated for Core++ Satellite CT

noise

CE

noise

CB

noise

𝜄fwhm fsky PRISM 5 x 10-7 μK2 2CT

noise

2CT

noise

3.2’ 0.7 LiteBIRD 7 x 10-7 μK2 2CT

noise

2CT

noise

38.5’ 0.7

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Fiducial Model V(𝜚)/M4 Parameters nS r LFIfid (𝜚/MPl)2 0.961 1.52 x 10-1 DWIfid [(𝜚/𝜚0)-1]2 𝜚0=25Mpl 0.962 8.45 x 10-2 HIfid [1-exp(-√2/3 𝜚 /Mpl)]2 0.961 4.12 x 10-3 ESIfid 1-exp(-q𝜚/Mpl) q=8 0.959 5.09 x 10-5 MHIfid 1-sech(𝜚/μ) μ=0.01Mpl 0.958 3.40 x 10-7

with Ωbh2=0.0223, Ωdmh2=0.120, Ω𝜉h2=0.000645, 𝜐=0.0931, h=0.674, Treh=108 GeV, wreh=0, P*=2.203 x 10-9.

Message 4: Significant improvement of model comparison

Consequences of a B-modes detection

5 fiducial models from “Encyclopedia Inflationaris” predicting different values of r

  • J. Martin, C. Ringeval and V. Vennin, JCAP 1410 (2014) 10, 038, arXiv:1407.4034
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Consequences of a B-modes detection

Message 4: Significant improvement of model comparison

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Consequences of a B-modes detection

Planck: 1/3 of the models excluded; PRISM & LiteBIRD > 4/5

  • J. Martin, C. Ringeval and V. Vennin, JCAP 1410 (2014) 10, 038, arXiv:1407.4034
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Constraining the running

Message 5: Prism can detect the slow-roll running …

  • J. Martin, C. Ringeval and V. Vennin, JCAP 1410 (2014) 10, 038, arXiv:1407.4034
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Performances Constraints

  • n reheating

Going beyond Planck

Reheating

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Performances Constraints

  • n reheating

Going beyond Planck

Reheating

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SLIDE 42

Performances Constraints

  • n reheating

Going beyond Planck

Reheating

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Planck 2013 LiteBIRD HI Prism HI

Message 6: Significant improvement of the constraints of reheating

Consequences of a B-modes detection

  • J. Martin, C. Ringeval and V. Vennin, Phys. Rev. Lett. 114 (2015) 8,

081303, arXiv:1410.7958

  • J. Martin, C. Ringeval and V. Vennin, JCAP 1410 (2014) 10, 038,

arXiv:1407.4034

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The talk

Outline  Which class of inflationary scenarios after Planck 2013 & 2015?  What is the best model of inflation? Model comparison.  Constraints on reheating (aka end of inflation).  The next generation of CMB experiments and inflation.  Conclusions.

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Recap

 Planck 2013: single field inflation are preferred. More complicated models (multiple field scenarios, non-minimal kinetic term scenario etc … ) should all have a “bad” Bayesian evidence …  Planck2013: 1/3 of the models are now ruled out  KMIII, ESI, Starobinsky model, ie plateau inflation … are the winners  Reheating is now constrained, average reduction of the prior to posterior width of about 40%. But this is mainly driven by “exotic” equations of state.  The inflationary gravitational waves background remains to be detected  Fourth generation of CMB experiments aims at detecting B-modes. This can significantly improve our knowledge of inflation