Jerome Martin 0 a 2 t 0 2 1 V ( ) = M 4 ln 2 2 2 / 3 - PowerPoint PPT Presentation

◆ ⌘ ◆� ◆� ◆ ◆� ◆ φ ✓ φ ✓ φ l V ( φ ) = M 4 ln 2 ✓ φ P µ ✓ φ φ 0 ✓ 0 M 1 − sech φ φ 0 ✓ φ V ( φ ) = M 4 ln 2 µ 2 / n φ  l 1 − sech q V ( φ ) = M 4 4 f − M e 1 + cos ◆ = − ) φ  � ( ◆ 1 ⇣ V φ V ( φ ) = M 4 e − φ /M Pl ✓  µ 4 h c M e � s V ( φ ) = M 4 −  3 1 = ◆ 4 − M φ ) = φ ) # 2 α φ ( Pl ( M ✓ ◆ 1 − α φ V V √ 2 2 ✓ φ n ◆ M Pl Jerome Martin 0 a ⌘ 2 ✓ φ φ t � φ 0 2 − 1 V ( φ ) = M 4 ln 2 α 2 2 / 3 φ /M Pl ln −  3 ◆ 2 � 1 − e − √ 4 4 V ( φ ) = M M ◆� ✓ = ✓ φ ) "✓ φ φ V ( φ ) = M 4 ⇣ 1 − sech µ (  V V ( φ ) = M 4 V ( φ ) = M 4 φ 0 ( φ /M Pl ) 2 � # CNRS/Institut 3 ◆ 2 ✓ φ ◆ − ◆ α + ( φ /M Pl ) 2 φ V ( φ ) = M 4 ln 2 V ( φ ) = M 4 l φ φ 0 P M α ✓ " √ 2 ✓ 2 n φ V ( φ ) = M 4 d’Astrophysique de Paris 0 a 2 t � n 2 ◆ α l − φ 3 �  ✓ 4 M � ◆ = φ ◆ 3 4 0 ) ✓ φ φ φ − ( M α φ 0 V ✓ M Pl − V ( φ ) = M 4 ln 2 n 2 √ 2 = a t 1 ) � ) α 2 ( − φ 2 n  ( 3 � − φ M 4 V ) 3 = 2 ) 2 ( n − φ λ � ( n φ + ◆ − 3 V n M ✓ α φ l P λ M Pl tan 2 √ 2 3 3 − α 2 � n � n − ) V ( φ ) = M 4 M θ l + n P 0 θ n ◆� ( s o c A + 2 1 2 φ ✓ φ m φ = ◆# ) 2 φ ✓ φ ( V ◆� µ ◆ 4 ✓ φ ✓ φ ln Q M Pl π arctan 1 + α ln "  1 + α Q V ( φ ) = M 4 V ( φ ) = M 4 ◆# � 1 − 2 φ ✓ φ A I � Q M √ l 6 P ◆ 2 + π ) 6 ln 1 M Pl φ ◆ 4 √  6 ( / ✓ φ 2 ✓ φ e − #  2 � ◆ M l ◆ Q P 1 φ 2 V ( φ ) = M 4 n − ✓ 4 φ φ l l M ◆ 4 P M ✓ 1 + α = n Q ) φ l φ ✓ n ( l 2 ◆� V ◆� α " α + " M α Q 2 l + P ✓ φ 1  1  M Pl M 4 V ( φ ) = M 4 4 M 1 + α ln 1 − 2 = = ) φ  φ φ ) ( V ( φ ) = M 4 φ V ( M Pl V 4 2 ◆# M M l P ✓ α ◆� = 2 ✓ φ √ 2 ! ◆� ) φ φ ◆� ✓ Q ( P l ✓ φ M M Pl V 1 + α ln ◆ 4 ln tanh 2 1 + α ln 1 + α φ 2  ✓ φ M Pl ✓ φ  4 V ( φ ) = M V ( φ ) = M 4 Q M Pl 1 + α 3 + α 2 � � " ◆ l P M V ( φ ) = M 4 1 + α ln φ l P / M ✓ φ Frontiers of Fundamental � ◆ α � n In collaboration with C. Ringeval φ l α ✓ M Pl − V ( φ ) = M 4 φ 2 3 − M 2 Pl n − l  e α + 4   1  1 4 Physics 14, Marseille, M 4 M ◆ V ( φ ) = M 4 (Louvain University) & V. Vennin (IAP) V ( φ ) = M 4 = ) φ φ � ( = l P ◆ V M ✓ φ l P M ✓ ) 4 July 17th, 2014 n φ M l α + ( =  1 V 4 ) M φ = ( ) φ V ( V

The talk Outline � Planck results and their implications for inflation � Are the Planck and BICEP2 results compatible (given slow-roll inflation)?? � Looking beyond Planck & BICEP2: how well can the future CMB missions constrain inflation? � Conclusions & summary

The talk Outline � Planck results and their implications for inflation � Are the Planck and BICEP2 results compatible (given slow-roll inflation)?? � Looking beyond Planck & BICEP2: how well can the future CMB missions constrain inflation? � Conclusions & summary

Planck results in brief: Planck (2013) Flat universe with adiabatic, Gaussian and almost scale invariant fluctuations: The simplest models are the best ones! 4

- One only needs to analyze single arXiv:1303.3787 field slow-roll inflation : still a very populated landscape … - Among these favored scenarios, what are the best ones, what is the Encyclopædia Inflationaris best model according to Planck? ome Martin, a Christophe Ringeval b and Vincent Vennin a J´ erˆ - We have carried out a survey of a Institut d’Astrophysique de Paris, UMR 7095-CNRS, Universit´ e Pierre et Marie Curie, 98bis boulevard Arago, 75014 Paris (France) b Centre for Cosmology, Particle Physics and Phenomenology, Institute of Mathematics and all models invented since 1979 Physics, Louvain University, 2 Chemin du Cyclotron, 1348 Louvain-la-Neuve (Belgium) E-mail: jmartin@iap.fr, christophe.ringeval@uclouvain.be, vennin@iap.fr Keywords: Cosmic Inflation, Slow-Roll, Reheating, Cosmic Microwave Background, Aspic - This complete survey includes ≈ 74 potentials ≈ 200 scenarios ≈ 700 slow roll formulas ≈ 365 pages ≈ 30 000 lines of code

Inflation is an accelerated, quasi-exponential, phase of expansion The energy scale of inflation is, a priori, not fixed In the early Universe, field theory is the relevant framework for matter V ( φ ) Slow-rol l ◆ 2 ✓ V φ 1 ✏ 1 ' 2 M 2 V Pl "✓ V φ # ◆ 2 2 � V φφ ✏ 2 ' M 2 V V Pl φ Reheating

- The amplitude is controlled by H The power spectra are scale-invariant plus - For the scalar modes, the amplitude also logarithmic corrections the amplitude of depends on ε 1 which depend on the sr parameters, ie on the microphysics of inflation C~ -0.7 - Consistency relation: The spectral indices are given by Gravitational waves are subdominant The running, i.e. the scale dependence of the spectral indices, of dp and gw are 7

V ( φ ) φ V ( φ ) V ( φ ) φ φ

V ( φ ) φ

The CMB can constrain the end of inflation! 12

� Bayesian evidence: quantify statistically whether a model is “better” than another. One can rank inflationary models according to their “performance” and find the “best model” of inflation � Thus, for model comparison, we compute the Bayesian evidence (integral of the likelihood over all parameter priors~probability of a model), ie the probability of a model, for each inflationary scenario Bayesian evidence posterior odds of the model “i” Model “i” is better than REF REF is better than model “i” Bayesian evidence of the reference model

Bayesian evidences for all models (Planck data) Model “i” is REF is better better than REF than model “i” Bad Good Best model Different models

Planck: and the winners are … KMIII HI (Starobinsky ES I model) Conclusion: plateau inflation are the winners!

Detection of primordial Detection of B-mode polarization of the CMB gravity waves 16

Here we assumed that the BICEP2 result is correct!! Of course, it needs to be confirmed by other experiments to see if it stands the time. 17

� Message 1: the energy scale of inflation measured: GUT scale 18

� Message 1: the energy scale of inflation measured: GUT scale � Message 2: derivatives of the potential measured 19

� Message 1: the energy scale of inflation measured: GUT scale � Message 2: derivatives of the potential measured � Message 3: more complicated class of models? Before BICEP2 Simplest models favored (ie more complicated not needed) because no isocurvature modes, no NG etc … After BICEP2: still true!! • K-inflation • Multiple field inflation 20

� Message 1: the energy scale of inflation measured: GUT scale � Message 2: derivatives of the potential measured � Message 3: more complicated class of models? � Message 4: model building issues? • Difficult because of the Lyth bound: • Break-down of EFT?? 21

Bayesian evidences for all models (BICEP2 data) LFI2 Best models Conclusion: large fields are the winners 22

The Jeffreys’ scale: constraining power of an experiment NB: Here, the reference is the best model!!

r is a powerful observable! Have we finally proven inflation???? 24

The compatibility between to data sets can be estimated by means of the following factor 25

Compatibility Performance 26

The talk Outline � Planck results and their implications for inflation � Are the Planck and BICEP2 results compatible (given slow-roll inflation)?? � Looking beyond Planck & BICEP2: how well can the future CMB missions constrain inflation? � Conclusions & summary

The future: EPIC, LiteBIRD, PRISM, COrE … - Simulate 5 models with different tensor to scalar ratio r - Study how this would be seen by PRISM & LiteBIRD 28

Three quarters of the models are ruled out with certainty, compared to one third with Planck 29

The talk Outline � Planck results and their implications for inflation � Are the Planck and BICEP2 results compatible (given slow-roll inflation)?? � Looking beyond Planck & BICEP2: how well can the future CMB missions constrain inflation? � Conclusions & summary