Le Modèle Cosmologique Avec Et Après Planck Et Questions Ouvertes

Francis Bernardeau PNCG, 23 novembre 2016

IAP Paris and IPhT Saclay

Le modèle cosmologique avec et après Planck et questions ouvertes

Avec les contributions de J. Martin, S. Renaux-Petel, S. Clesse, C. Caprini

1 Temperature

Polarization 1. Introduction Adeterminationoftheamplitudeofthefluctuationsofthe Archeops, 2002 cosmic microwave background (CMB) is one of the most promising techniques to overcome a long standing prob- lem in cosmology – setting constraints on the values of the cosmological parameters. Early detection of a peak in the region of the so-called first acoustic peak (ℓ ≈ 200) by the Saskatoon experiment (Netterfield et al. 1997), as well as the availability of fast codes to compute theoretical amplitudes (Seljak et al. 1996) has provided a first constraint on the geometry of the Universe (Lineweaver et al. 1997, Hancock et al. 1998). The spectacular results of Boomerang and Maxima have firmly established the fact that the geometry of the Universe is very close to flat (de Bernardis et al. 2000, Hanany et al. 2000, Lange et al. 2000, Balbi et al. 2000). Tight constraints on most cosmological parameters are an- ticipated from the Map (Bennett, et al. 1997) and Planck (Tauber, et al. 2000) satellite experiments. Although experiments have already provided accurate measurements over a wide range of ℓ,degeneraciespreventaprecisede- Une petite perspective historique : termination of some parameters using CMB data alone. Fig. 1. Measurements of the CMB angular power spec- For example, the matter content Ωm cannot be obtained trum by ArcheopsArcheops (in red dots) compared2002 with CBDMVC independently of the Hubble constant. Therefore, combi- datasets. A ΛCDM model (see text for parameters) is over- nations with other cosmological measurements (such as plotted and appears to be in good agreement with all the supernovæ, Hubble constant, and light element fractions) data. are used to break these degeneracies. Multiple constraints can be obtained on any given parameter by combining Hubble constant (H0 =100h km/s/Mpc), the spectral CMB data with anyone of these other measurements. It index of the scalar primordial fluctuations, the normal- is also of interest to check the consistency between these ization of the power spectrum and the optical depth to multiple constraints. In this letter, we derive constraints reionization, respectively. The predictions of inflationary on a number of cosmological parameters using the mea- motivated adiabatic fluctuations, a plateau in the power surement of CMB anisotropy by the Archeops experiment spectrum at large angular scales followed by a first acous- et al. (Benoˆıt 2002). This measurement provides the most tic peak, are in agreement with the results from Archeops accurate determination presently available of the angular and from the other experiments. Moreover, the data from power spectrum at angular scales of the first acoustic peak Archeops alone provides a detailed description of the and larger. power spectrum around the first peak. The parameters of the peak can be studied without a cosmological prejudice 2. Archeops angular power spectrum (Knox et al. 2000, Douspis & Ferreira 2002) by fitting a constant term, here fixed to match COBE amplitude, The first results of the February 2002 flight of Archeops and a Gaussian function of ℓ. Following this procedure are detailed in Benoˆıt et al. 2002. The band powers used and using the Archeops and Cobe data only, we find in this analysis are plotted in Fig. 1 together with those (Fig. 2) for the location of the peak ℓpeak =220± 6, of other experiments (CBDMVC for Cobe, Boomerang, for its width FWHM =192± 12, and for its amplitude Dasi, Maxima, VSA, and CBI; Tegmark et al. 1996, δT =71.5 ± 2.0 µK(errorbarsaresmallerthanthe Netterfield et al. 2002, Halverson et al. 2002, calibration uncertainty from Archeops only, because Lee et al. 2001, Scott et al. 2002, Pearson et al. 2002). COBE amplitude is used for the constant term in the fit). Also plotted is a ΛCDM model (computed using This is the best determination of the parameters of the CAMB, Lewis et al. 2000), with the following cosmo- first peak to date, yet still compatible with other CMB 2 logical parameters: Θ =(Ωtot, ΩΛ, Ωbh ,h,n,Q,τ)= experiments. (1.00, 0.7, 0.02, 0.70, 1.00, 18µK, 0.)wheretheparameters are the total energy density, the energy density of a cosmological constant, the baryon density, the normalized 3. Model grid and likelihood method Send offprint requests to:[email protected] To constrain cosmological models we constructed a 4.5 × ⋆ 8 Richard Gispert passed away few weeks after his return 10 Cℓ database. Only inflationary motivated models from the early mission to Trapani with adiabatic fluctuations are being used. The ratio of Correspondence to:[email protected] tensor to scalar modes is also set to zero. As the hot 2 1 INTRODUCTION

Angular scale

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Planck 2015 103 CMB- TT Planck ACT SPT 102 ACTPol SPTpol POLARBEAR BICEP2/Keck/Planck BICEP2/Keck 101 2 K] µ [

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Figure 2: Top CMB angular power spectra determinations as of mid-2015 (Modiﬁed from Planck Collaboration et al. (2015g) thanks to E. Calabrese). This corresponds to the determination (with S/N > 1) of 1 114 000 modes measured with TT, 96 000 with EE (60 000 with TE, not shown), and tens of modes in BB (and weak constraints on TBand EB). Bottom Lensing potential power spectrum measurement from Planck (Planck Collaboration et al. 2015f), as well as earlier measurements. The goal for the future is now to measure the million polarisation modes which are still unknown. .

French roadmap for CMB science 30/06/2016 2 1 INTRODUCTION

First measure of full sky CMB lensing

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French roadmap for CMB science 30/06/2016 The early Universe physics and the origin of the Large-Scale structure of the Universe after Planck

➡ Everything is consistent with inflation, that is with the fact that the LSS emerged out of early metric perturbations.

➡ Physics in the early Universe is non trivial (“dynamical”) since deviation from scale invariance has been unambiguously detected.

➡ Inflation seems to be realized in its simplest incarnation (single slow roll field) although a large fractions of the models are disfavored. The simplest models of inflation make several key predictions:

✓ Universe spatially flat ✓ Phase coherence of Doppler peaks/ adiabatic modes ✓ Almost Gaussian perturbations

✓ Almost scale invariant power spectrum

- Background of quantum gravitational waves : only upper limit on r

- Consistency check between nT and r : not feasible (in foreseeable future) The Planck 2015 data constraints are shown with the red and blue contours. Steeper models with V ∼ φ3 or V ∼ φ2 appear ruled out, whereas R2, à la Starobinsky, inﬂation looks quite attractive. Beyond Planck: the « key »questions

Questions that we would like to be ideally addressed by next generations of CMB missions comprise, • Find a way to validate the general paradigm, i.e. to show that metric fluctuations have been generated from quantum field fluctuations of scalar and tensorial degrees of freedom ; determine the energy scale of inflaton ; better characterize its potential - its shape and the various

degrees of freedom at play - during the inflationary phase; • Explore the thermal history of the universe from the end of inflation to recombination to better characterize inflationary models, explore the stability of dark matter, find exotic phenomena ; • Assess the matter/energy content of universe with better precision (a still missing part is the mass of the neutrinos). 2.1 The early universe 5

CMB+, SCIENCE CASE 3 what is the energy scale of the inflation ? • what is the field content during that period ? • what is the shape of the coupling operators (shape of potential, etc.)? • Measurements of r would determine the absolute energy scale of the inflationary phase and would set the stage for any subsequent attempts to build global models of inflation. More precisely the energy scale of inflation is CMB+, SCIENCE CASE1/4 3 1/4 16 r (1) Figure 2: Existing and expected constraintsV on10n andGeVr. The orange⇤ and yellow contours show the 68% and Figure 1: Existing and expected constraints on ns and r. TheS orange and yellow0.01 contours show the 68% and 95% confidence regions95% confidence expectedwhat from regions is the the expected baseline energy fromconfiguration scale the baseline of⇡ of the COrE configuration inflation+. The possibility of COrE ? to+. improve The possibility the error barsto improve by delensing the error is not bars by delensing is not included in this forecast. The fiducial model is the Starobinsky R2 model [7]. The blue and included• in this forecast. The fiducial model is the Starobinsky R2 model.⇣ The⌘ blue and cyan contours show the Planck This is thecyan primary contourswhat show is goal the the Planck fieldof any2013 content constraints, stage during 3-4 while CMB the that gray missions. period contours show ? the ThereWMAP is9-year however constraints. no The clear goals or 2013symbols constraints,• show predictions while the of grey a few contours other show well known the WMAP inflationary 9-year models. constraints. The The violet, symbols yellow, show and predictions red regions of show a few thresholdother values wellwhat known for is inflationaryr thealthough shape models. of the The the violet, class coupling yellow, of favored and operators red regions models show (shape vacuum-dominated evolve of potential, when convex the etc.)? potentials constraints on r vacuum-dominated convex potentials (V > 0), convex potentials vanishing at their minimum, and concave potentials (V >•0), convex potentials vanishing at their minimum, and concave potentials (V < 0; hilltop or plateau inflation), tighten. (MeasurementsV00 < 0; hilltop or plateau of r inflation),would respectively. determine the absolute energy00 scale of the inflationary phase and respectively. Taken from Martin et al. (2014). In principle,would set model the stage independent1. 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This of the behavior primary 1.2. Theof thein spectral the vacuum scalar fluctuations distorsions. expectation has now value beenAn convincingly of emerging the inflaton detected new field. by observationalWMAP Although[13, 14] and not windowPlanck to be[8]. is a While priori provided excluded, by the such measurementsituation2 This lower of is the bound uncomfortable spectral can be obtained distortions. either from by imposinga theoretical Spectral that the energy point distortions scale of during view inflation induced as, should from by be an large second e↵ enoughective to order theory e↵ects field of or interactionsview,allow baryogenesis it changes with hot to take the electron place relative (at least gaz atimportance the along TeV scale) the7 or of that line operators classical of sight rolling (that should are cannot be of the the dominant bey-type ranked evolution (it in of corresponds powers of the to a non-thermalPlanckthe field comparedmass). distortion to This quantum is fluctuations. a of general the black trend. body There spectrum is however with no a precise conserved threshold number value. density A r in of the 3 10 range would however put such constructions on a safe ground. FB: to be commented photons).French On CMB the roadmap other hand annihilation or dissipations of particles or field 7/ modes06/2016 are bound to induceinµ more-type details distorsions. ? Such mechanisms are very generic. They provide a lower bound for the emergence of µ-types distortions as they are unavoidably produced in ⇤-CDM model, being 1.2. The spectral distorsions. An emerging new observational window is provided by the generated by the damping of very primordial metric fluctuations. It leads to an amplitude of measurement8 of the spectral distortions. Spectral distortions induced by second order e↵ects order µ = (10 ). or interactionsO with hot electron gaz along the line of sight are of the y-type (it corresponds Theto primary a non-thermal use of such distortion observables of the would black body be to spectrum further tighten with a constraints conserved number on ns and density its of possiblephotons). variation. On Our the ability other hand to do annihilation so is illustrated or dissipations on Fig. 2. of It particles shows what or field is the modes mode are range bound (in k) thatto induce sourcesµ-type the y distorsions.and more importantly Such mechanismsµ distortions are very types. generic. As They can provide be seen a from lower this bound plot for the k-rangethe emergence extents to of aboutµ-types 10000 distortions h/Mpc as scale. they As are a unavoidably consequence, produced it allows in tighter⇤-CDM constraints model, being on ns.generated This is illustrate by the ondamping Fig. 2. of These very primordial are however metric broad fluctuations. band observations It leads as to unlike an amplitude the left of 8 hand bandorder forµ = which(10 observations ). of each mode can be made, y and µ type observations provide O only a globalThe integrated primary use (monopole) of such observables value of the would mode be amplitudes. to further tighten As such constraints it provides on usns withand its little discriminatorypossible variation. power Our on ability the basic to do cosmological so is illustrated parameters. on Fig. 2. It shows what is the mode range (in k) that sources the y and more importantly µ distortions types. As can be seen from this plot the k-range extents to about 10000 h/Mpc scale. As a consequence, it allows tighter constraints on ns. This is illustrate on Fig. 2. These are however broad band observations as unlike the left hand band for which observations of each mode can be made, y and µ type observations provide only a global integrated (monopole) value of the mode amplitudes. As such it provides us with little discriminatory power on the basic cosmological parameters. Constraining specific models for r and ns

However models can be found everywhere…

Figure 2: Existing and expected constraints on nS and r. The orange and yellow contours show the 68% and 95% confidence regions expected from the baseline configuration of COrE+. The possibility to improve the error bars by delensing is not included in this forecast. The fiducial model is the Starobinsky R2 model [7]. The blue and cyan contours show the Planck 2013 constraints, while the gray contours show the WMAP 9-year constraints. The symbols show predictions of a few other well known inflationary models. The violet, yellow, and red regions show vacuum-dominated convex potentials (V 00 > 0), convex potentials vanishing at their minimum, and concave potentials (V 00 < 0; hilltop or plateau inflation), respectively.

parity ‘E mode’ and an odd parity ‘B mode’ [9, 10]. The scalar fluctuations produce only E modes, whereas the tensor fluctuations produce both E and B modes. Thus B mode polarization o↵ers a sensitive and highly model-independent probe of tensor fluctuations. Detection of the long wavelength, nearly scale-invariant tensor fluctuations is considered as an observational tell-tale sign that inflation occurred at energies a trillion times higher than the ones achieved by the Large Hadron Collider (LHC) at CERN. At such high energies we may also see hints of quantum gravity. Consequently, the main science goal of COrE+ will give us a powerful clue concerning how the Universe began and the precise character of the fundamental laws of nature (i.e., how gravity and the other forces in nature are unified). Inflation is thought to be powered by a single energy component called ‘inflaton’. The precise physical nature of the inflaton is unknown but it is often assumed to be a scalar field, just like the Higgs field recently discovered by the LHC [11, 12]. The simplest models of inflation are based on a single scalar field with a potential energy density V (). We can easily generalize to models involving more fields. The potential energy drives the scale factor of the Universe to evolve as a(t) exp(Ht)whereH2 (8⇡G/3)V (). As a / ⇡ result, the Universe is quickly driven to a spatially flat, Euclidean geometry, and any memory of the initial state of the observable Universe is e↵ectively erased, since a patch of space that undergoes inflation becomes exponentially stretched and smoothed. According to inflation, the large patch of the Universe that we live in originated from a tiny region in space that was stretched to a large size by inflation. The original region was so tiny that quantum mechanics played an important role. Namely, the energy density stored in the inflaton field varied from place to place according to the laws of quantum mechanics. This scalar quantum fluctuation is the seed for all the structures that we see in the Universe today [6]. This is a remarkable prediction of inflation, which agrees with all the observational data we have collected so far [8]. The only missing piece is the existence of tensor quantum fluctuations, which would appear as long-wavelength gravitational waves propagating through our Universe [7]. We wish to detect this using the B mode polarization of CMB. An important prediction of inflation is that the scalar and tensor fluctuations are nearly, but not exactly, scale-invariant—namely that the variance of fluctuations depends only weakly on the spatial length scale. More specifically, the variance of fluctuations decreases slowly toward smaller length scales [6]. This behavior in the scalar fluctuations has now been convincingly detected by WMAP [13, 14] and Planck [8]. While

7 2 cause of the damping of acoustic modes. The strong about the running, given these posteriors for µ.Thedis- lever arm makes this observable an ideal probe to im- cussion is divided in three sections: we start with the pre- prove the bounds on the running from large scale CMB dicted bounds on µ-distortions from current Planck data anisotropies. In addition, the cosmic variance of the (Sec. III). We proceed with a Fisher analysis (Sec. IV), µ monopole and of the higher multipoles is minuscule discussing also the optimal choice of pivot scale for a (see [28] for a discussion). With a suciently broad combined study of CMB anisotropies and spectral dis- frequency coverage, instrumental noise will be the main tortions. The MCMC analysis and forecasts are carried source of uncertainty for any foreseeable future, leaving out in Sec. V. Finally, Sec. VI studies the implications ample room for improvements. of these results for single-clock slow-roll inﬂation, and we In this context, we address several questions: draw our conclusions in Sec. VII. is there a benchmark sensitivity for CMB spectrometry, • i.e. which should be the target of the next generation experiments? How can we design an experiment to II. PHOTON THERMODYNAMICS ensure a discovery even in the absence of a detection?

At very early times, for redshifts larger than zdC what sensitivity to the spectrum is needed to detect 6 ⇡ • 2 10 , processes like double Compton scattering and µ-distortions when accounting for the prior knowledge bremsstrahlung⇥ are very ecient and maintain thermo- from Planck? dynamic equilibrium: any perturbation to the system is how much will a joint analysis of large scale CMB thermalized and the spectrum of the CMB is given to • anisotropies and CMB spectral distortion strengthen very high accuracy by a black-body. At later times the the bounds on the running? How does this quantita- photon number is e↵ectively frozen, since photons can be tively depend on the improvement over PIXIE sensi- created at low frequencies by elastic Compton scatter- tivity?2 ing but their re-scattering at high frequencies via double Compton scattering and bremsstrahlung is not ecient To articulate the answers to these questions, we con- due to the expansion of the universe [34]. sider the following three fiducial cosmologies: The end result is a Bose-Einstein distribution x+µ(x) 1/(e 1) (x h⌫/kBT ) with chemical potential a cosmology with zero running, which gives a µ- ⌘ • µ. Since photons can still be created at low frequencies, amplitude of order µ8 =1.6. We stress that for the µ will not exactly be frequency independent: it can be sensitivities considered in this work, this fiducial is 3 approximated as µ exp( xc/x), with xc 5 10 . indistinguishable from models with running of order However, no planned/proposed1 experiments⇡ will⇥ be able (1 n )2, such as typical slow-roll models; s to probe such low frequencies: for this reason we will take the chemical potential to be a constant (and drop a fiducial spectral distortion amplitude µ(fid) equal to • 8 the subscript ). the best-fit of the the Planck analysis, i.e. µ(fid) =1.06. 1 8 For a given energy release d(Q/⇢ )/dz, one can write This value of µ is roughly correspondent to what one 2. thespectral value of µ distorsions:as (see Sec. VIII Aa) new window ? obtains for a running ↵ = 0.01 which is close to the s mean value predicted by current Planck data; zdC d(Q/⇢ ) ⌧ (z0) µ(z)=1.4 dz0 e dC , (1) 11 (fid) dz0 ↵s = 0.02 (corresponding to µ8 =0.73), at the z 1.5 Z • edge of the 2 bounds of Planck. We note that it whereµ ¯a are the fiducial values of the amplitudes, and I(⌫c) is the noise at each frequency channel c: is possible to obtain such large negative runnings in where the distortion1.0 visibility function ⌧dC(z) can be approximated as (z/z )5/2 [35]. PIXIE will have 400 channels (15 GHz-wide) from some models of single-field inflation like, e.g., extra- 0.5 dC • 30 GHz to 6 THz: however, we see from Fig. 8 that 5 the signals that we consider go quickly to zero beyond dimensional versions of Natural Inflation [29, 30] or re- Below redshifts0.0 around z = zµ-i 2 10 , Compton ⇡ ⇥ ⌫ 1000, so the sum over channels in Eq. (28)will scattering is not sucient to maintain a Bose-Einstein⇡ cent developments in axion monodromy inflation [31– -0.5 stop there; 33]. spectrum in the presence of energy injection. The dis- -1.0 I for PIXIE, as from Fig. 12 of [2], is expected to be • 26 2 1 1 tortions generated will then be neither of the µ-type5 nor10 Wm Hz sr . -1.5 ⇥ The paper is organized as follows: after a brief review of the y-type:10 they will depend50 100 on the500 redshift1000 at whichIf we want to marginalize over some of the amplitudes of photon thermodynamics in the early universe and of energy injection occurs [36, 37], and must be calculatedµa (see [55], for example), we can use the fact that for a distortions from Silk damping (Sec. II), we compute the numerically by solving the Boltzmann equation (knownGaussian with inverse covariance matrix (Fisher matrix) FIG. 8. This plot shows the spectral shapes (normalized at the F given by µ-distortion parameter allowed by current Planck bounds as Kompaneetsmaximum) I equation(⌫)forµ-, y-and [38t-type], when distortions, restricted together with to Comp- the spectra for i-type distortions at redshifts z = (2 105), z = FS˜ O ⇥ F = , (29) for a ⇤CDM and ⇤CDM + ↵s model (Sec. III). We then ton scattering).(1 105)and Recently,z = (5 104). We in see [36 that, for37 increasing], a redshift, set of Green’s ST M theO maximum,⇥ minimumO ⇥ and zero of the occupation numbers are ✓ ◆ analyze what a PIXIE-like mission will be able to say functionsmoved for towards the computation lower frequencies. of these intermediate dis- where F˜ is the sub-matrix that spans the parameters that tortions has been provided: they sample the intermedi-we are interested in, the marginalized Fisher matrix will (i) ate photon spectrum n for a energy release Qrefbe/ equal⇢ = to and so on. Besides µ-, i- and y-type distortions, that we 5 3 5 1 T 4 10 havein discussed(10 ) in redshiftSec. II, one must bins also from considerz the fact2 10 to Fmarg = F˜ SM S . (30) 2 For example the PRISM imager [3, 4]correspondstoapproxi- z ⇥ 1.5 that10 theO4.The uniform parti-type of temperature occupation perturbations number,⇡⇥ is ⇥ for a mately 10 PIXIE. ⇡ ⇥not known a priori and must be fit simultaneously with For Eq. (28), we will want to marginalize over t and y, ⇥ generic energythe spectral injection distortions: history for this reason d(Q/ we also⇢ ) consider/dz,willthenso M will be the 2 2 matrix the t-type occupation number, i.e. [37] ⇥ (⌫ ) (⌫ ) M = Ia c Ib c , (31) ab I(⌫ ) I(⌫ ) 2h⌫3 xex c c c = X It c2 (ex 1)2 (27) with a, b = y, t. Similar expressions can be derived for 2h⌫3 S and its transpose, while F˜ is simply given by Eq. (28) n(t)(⌫) . ⌘ c2 ⇥ with a running on all components except y and t.Ifwe had instead supposed that the two y and t amplitudes We do not include foregrounds in our analysis since, for were known, we could just have taken F˜ as Fisher matrix PIXIE, the noise penalty for rejecting foregrounds is only for Eq. (28). 2%, and this noise penalty has been included in all the In this work we have not considered i-distortions, so estimates of CMB sensitivity by the PIXIE collaboration F will be a 3 3 matrix with a, b, c = µ, y, t: marginal- ⇥ [2]. izing over y and t amplitudes, as described in Eqs. (30) and (31), we obtain = 1 for the standard PIXIE con- We can then write down the signal-to-noise, in terms µ8 figuration. The increments in PIXIE sensitivity that we of amplitudes µa and spectra a as (dropping factors of 2 for simplicity) I considered in the text, then, can be interpreted as either an increase in the number N of frequency channels (that PIXIE new 2 would decrease µ8 by a factor N /N ), or a de- 2 crease in the instrumental noise I (which instead gives S a a(⌫c) (µa µ¯a) = I ⇥ , (28) a linear improvement Inew/IpPIXIE). N h (I(⌫ ))2 i c P c ✓ ◆ X

[1] P. A. R. Ade et al. [Planck Collaboration], [5] F. R. Bouchet et al. [COrE Collaboration], arXiv:1502.02114 [astro-ph.CO]. arXiv:1102.2181 [astro-ph.CO]. [2] A. Kogut et al.,JCAP1107, 025 (2011) [arXiv:1105.2044 [6] T. Matsumura et al.,J.Low.Temp.Phys.176 (2014) [astro-ph.CO]]. 733 [arXiv:1311.2847 [astro-ph.IM]]. [3] P. Andr´e et al. [PRISM Collaboration], arXiv:1306.2259 [7] M. Zaldarriaga and U. Seljak, Phys. Rev. D 55,1830 [astro-ph.CO]. (1997) [astro-ph/9609170]. [4] P. Andr´e et al. [PRISM Collaboration], JCAP 1402,006 [8] M. Kamionkowski, A. Kosowsky and A. Stebbins, Phys. (2014) [arXiv:1310.1554 [astro-ph.CO]]. Rev. D 55 (1997) 7368 [astro-ph/9611125]. 14 Chluba and Jeong

zX 6 6 5 5 5 4 4 4 5 times PIXIE sensitivity A 4.8x10 2x10 5x10 2x10 10 5x10 2x10 10 4800 ζ A x -8 n Reference ζ = 5 10 S -1 -5 10 10 1 ]

ζ 10 A / -8 10 x -6 10 0 [ 5 10 x 3 γ He / D ρ / n n [ eV ] -2 bound γ run = 0 = -0.2 X 10 run z ∆ρ / -7 X

f 10 10-1 Relative Error n = 0.2 run µ µ1 Spectral distorsions from annihilating particles -8 µ2 10 -2 -3 10 µ3 10 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.52.3 1.6For1.7 Constraining such 1.8 1.9processes 2 the matter the content distortion of the has universe a ﬁxed shape (but neither of y- or of μ types) and 9 6 7 8 9 10 11 12 n 10 10 10 10 10 10 10 S only the overall amplitude changes, depending on the annihilation efﬁciency, fann.. tX [ sec ] z 5 times PIXIE sensitivity A X ζ 6 6 5 5 5 4 4 4 -8 n 4.8x10 2x10 5x10 2x10 10 5x10 2x10 10 4800 Reference A = 5 x 10 and n = 0 -12 ζ run nS 10 run

] -1 ζ 10 A -13 / 10 -8 Absolute error

10 3 x He / D bound [ 5 x -14 10

Relative error [ GeV ] X Y Errors vis

E large new -15 10 µ discovery window µ1 -2 µ2 10 µ 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 10-16 3 n S 6 7 8 9 10 11 12 10 10 10 10 10 10 10 1 t Figure 13. Expected uncertainties of A⇣ (k0 = 45 Mpc ), nS, and nrun using X [ sec ] measurements of µ, µ1, and µ2. We assumed 5 times the sensitivity of PIXIE 8 and A⇣ = 5 10 as reference value (other cases can be estimated by simple Figure 14. Detectability of µ, µ , µ and µ . The upper panel shows the lim- ⇥ Figure 6: Constraints on the yield parameter as a function1 of2 the particle3 lifetime for decaying particles. What is computed rescaling). For the upper panel we also varied nrun as indicated, while in the its for X = fX/zX, while the lower panel uses the standard yield variable, is the required value of YX for which a 1 -detection of the corresponding variable is possible with PIXIE. The violet lower panel it was fixed to nrun = 0. shaded area is excluded byE measurementsvisYX (cp., Kawasaki of the primordialet al. 2005). 3 For He/ aD given abundance particle ratio lifetime, (1 we level, com- adapted from Kawasaki et al. 2005). From Chluba &pute Jeong the required(2014). value of X for which a 1 -detection of the corresponding variable is possible with PIXIE. The violet shaded area is excluded by mea- dicted uncertainties for some representative cases using the MCMC surements of the primordial 3He/D abundance ratio (1-level, adapted from method of Chluba (2013a), finding excellent agreement. Overall, Fig. 42 of Kawasaki et al. 2005). our analysis shows that CMB SD measurement provide an unique probe of the small-scale power spectrum, which2.3. can Constraining be utilized the matter content of the universe range. To directly constrain tX, at least a measurement of µ1 is to directly constraint inflationary models. Especially,2.3.1. if From the small- of the shape of the angular power spectrum scale power spectrum is close to scale-invariant with small running, needed. At PIXIE sensitivity this means that the lifetime of par- 9 10 very robust constraints can be expected from PIXIE and PRISM, if ticles↵ with 2 10 sec . tX . 6 10 sec for X 0.1 eV and The key example is the e ective number⇥ of neutrinos.12 [P. Binetruy].⇥ 1 8 7 3 108 sec . t . 10 sec for 1 eV will be directly measur- A⇣ (k0 = 45 Mpc ) 10 10 . ⇥ X X ' able. Most of this parameter space is completely unconstrained [see 2.3.2. The lensing potentialupper limit from measurements of the primordial 3He/D abundance 5.3.4 Decaying relic particles ratio9 (from Fig. 42 of Kawasaki et al. 2005) in Fig. 14]. Higher sensitivity will allow cutting deeper into the parameter space and The distortion signals for the three decaying particle scenarios pre- sented in Table 2 will all be detectable with a PIXIE-like experiment. More generally, Fig. 14 shows the 1-detection limits for 9 In the particle physics community the abundance yield, YX = NX/S , µ, µ , µ , and µ , as a function of the particle lifetime. CMB 1 2 3 and deposited particle energy, Evis [GeV], are commonly used. Here, NX SDs are sensitive to decaying particles with X = fX/zX as low 4 is the particle number density at t tX and S = 3 kT 7 N 2 7 10 3 3 3 ⌧ ' ' as 10 eV for particle lifetimes 10 sec . tX . 10 sec. For 2.9 10 (1 + z) cm denotes the total entropy density. We thus find ' 3 ⇥ 9 19 PRISM the detection limit will be as low as 10 eV in this (E Y ) 10 S/[N (1 + z )] 1.5 10 (E Y )/(1 + z ). X ' X vis X H X ' ⇥ vis X X

c 0000 RAS, MNRAS 000, 000–000

Figure 7: TheFigure signal 3: to Reconstruction noise ratio for noise the determination of the lensing deflection of the lensing power potential spectrum powerfrom Planck spectra.2015 The (left) Core and+ asconcept allows forecast for COrE+ at the goal and required specifications (right). The deflection power spectrum is plotted to dramaticallybased extend on the the linear range matter of modes power for spectrum which (black it can solid) be accurately and with nonlinear measured. corrections (black dashed).

by cosmic variance of the primary CMB fluctuations because their amplitude on small scales is essentially zero regardless of the value of r. Such polarization-based reconstructions have been demonstrated recently French CMBfrom roadmap ground-based experiments [24, 44], and also Planck, but are currently very noisy. This situation will 7/06/2016 be completely transformed with COrE+, which will reconstruct lensing with S/N > 1 per mode up to multipoles l 600 (see Fig. 3) over nearly the full sky. Significantly, COrE+ can extract essentially all the information in the lensing deflection power spectrum on scales where linear theory is reliable. Weak gravitational lensing directly probes the clustering of all matter integrated along the line-of-sight back to the source. This makes lensing potentially a very powerful probe of the matter (clustering) power spectrum, which is free from astrophysical uncertainties such as biasing (i.e., the uncertain relation between the clustering of luminous objects and the underlying mass distribution) that complicate the interpretation of galaxy redshift surveys. Lensing by large-scale structure can be probed using optical imaging surveys through the coherent distortion of the shapes of background galaxies (cosmic shear), and also using CMB lensing. As discussed in Sec. 2.6, cosmic shear and CMB lensing are highly complementary. Their combination is particularly powerful (see below for Euclid combined with COrE+). We summarize some of the science enabled by the lensing measurements from COrE+. COrE+ will be a powerful probe of neutrino physics through the combination of its lensing measurement (for neutrino masses), and its precision measurements of the damping tail of the polarization power spectra (for the eective number of relativistic degrees of freedom at last scattering)2. Neutrino oscillation data show neutrinos must be massive, but the oscillation data are insensitive to the absolute neutrino mass scale. For a normal hierarchy of masses (m ,m m ), the mass summed over all 1 2 3 eigenstates is at least 0.06 eV, while for an inverted hierarchy (m m ,m ) the minimal summed mass 3 1 2 is 0.1eV. The individual neutrino masses in these hierarchical limits are well below the detection limit of current and future laboratory -decay experiments but can be probed by cosmology. Massive neutrinos suppress gravitational clustering on scales below the horizon size at the non-relativistic transition, thus reducing the lensing power spectrum. Combining the anisotropy and lensing power spectra of COrE+we

2The accuracy of parameter inferences from the temperature power spectrum measured by Planck [42] are now close to being limited by errors in the modelling of extragalactic foregrounds. Fortunately, further progress can be made with the polarization anisotropies on small angular scales [57], since the degree of polarization of the anisotropies is relatively larger there (around 4% by l = 2000) than the foreground emission.

10 6 CMB+, SCIENCE CASE 3. lensing measurements, towards a precise determination2. ofConstraining the mass the matterof the content neutrinos of the universe

Figure 3: Reconstruction noise of the lensing deflection power spectrum from Planck 2015 (left) and as forecastFigure for COrE 5.+The at the signal goal and to required noise ratio specifications for the (right). determination The deflection of the power lensing spectrum poten- is plotted basedtial on the power linear spectra. matter power The spectrum Core+ concept (black solid) allows and with to dramatically nonlinear corrections extend (black the dashed). range of modes for which it can be accurately measured. by cosmic variance of the primary CMB fluctuations because their amplitude on small scales is essentially 2.1. zeroThe regardless lensing of the potential. value of r. SuchCMB polarization-based observations reconstructionsallow to measure have been the demonstrated lensing potential recently pro- from ground-based experiments [24,a 44],dramatic and also Planck improvement, but are currently very compared noisy. This situation to will Planck jectedbe power completely spectra... transformed This with is illustratedCOrE+, which on will Fig. reconstruct 5 lensing with S/N > 1 per mode up to multipoles l 600 (see Fig. 3) over nearly the full sky. Significantly, COrE+ can extract essentially all the ⇡ 2.2. informationThe neutrino in the lensing mass. deflectionThe measurement power spectrum of on the scales lensing where linear projected theory is potential reliable. along the line of sightWeak o↵ers gravitational a unique lensing possibility directly for probes constraining the clustering the of shapeall matter and integrated time evolution along the line-of-sight of the matter powerback spectrum. to the source. It Thisis expected makes lensing to shed potentially light a on very the powerful matter probe content of the of matter the (clustering) universe. power It can in particularspectrum, help which in isdetermining free from astrophysical the total uncertainties neutrino mass such as we biasing know (i.e., does the notuncertain vanish. relation between Ifthe su clusteringciently of massive luminous the objects neutrinos and the underlying can account mass fromdistribution) a fraction that complicate of the current the interpretation energy density of of thegalaxy universe redshift3 which surveys. is Lensing directly by large-scale proportional structure to can their be probedtotal mass. using optical It is imaging roughly surveys given through by the coherent distortion of the shapes of background galaxies (cosmic shear), and also using CMB lensing. As discussed in Sec. 2.6, cosmic shear and CMB lensing arem highly complementary. Their combination is (3) ⌦ h2 ⌫ particularly powerful (see below for Euclid combined⌫ ⇡ with93eVCOrE+). We summarize some of the science enabled by the lensing measurements from COrE+. P And weCOrE know,+ will from be a neutrino powerful probe flavor of oscillationneutrino physics experiments, through the combination that the total of its masslensing of measurement the neutrinos should(for be neutrino above masses), 50meV. and its precision measurements of the damping tail of the polarization power spectra Our(for ability the e↵ective to constrain number of relativistic the massif degrees the neutrinos of freedom at comes last scattering) from the2. fact that they become non- relativisticNeutrino during oscillation the formation data show neutrinos of the must large-scale be massive, structure but the oscillation of the universe. data are insensitive The presence to the of absolute neutrino mass scale. For a normal hierarchy of masses (m ,m m ), the mass summed over all species that are initially relativistic indeed changes the growth1 2 ⌧ rate3 of structures for modes k eigenstates is at least 0.06 eV, while for an inverted hierarchy (m m ,m ) the minimal summed mass 3 ⌧ 1 2 thatis are 0.1eV. larger The that individual the free neutrino streaming masses scale in these of hierarchicalthe neutrinos limitskfs are. This well below change the of detection growth limit is related of to thecurrent mass and fraction future laboratoryf⌫ in the-decay neutrinos experiments species. but can Thus be probed during by the cosmology. matter Massive dominated neutrinos era the growthsuppress of structure gravitational is proportional clustering on scales to below the horizon size at the non-relativistic transition, thus reducing the lensing power spectrum. Combining the anisotropy and lensing power spectra of COrE+we 1 3/5f⌫ (4) cdm a 2The accuracy of parameter inferences from the temperature/ power spectrum measured by Planck [42] are now close to being limited by errors in the modelling of extragalactic foregrounds. Fortunately, further progress can be made with the polarization 3Ifanisotropies massless on the small energy angular density scales of [57], a given since the species degree decays of polarization similarly of the to anisotropies that of the is radiation relatively larger and is there now (around negligible. 4% by l = 2000) than the foreground emission.

10 On the phenomenology side, next generations of CMB missions can provide

• A genuine chance to determine the absolute energy scale of inflation with the detection of r; • A unique discovery potential with the exploration of the spectral distorsions of the CMB; • A capacity of getting the better precision on the fundamental cosmological parameters such as - values of ns and its running (from polarization E- mode power spectrum) - mass of the neutrinos from lensing reconstruction On the theory side - Identification of the most relevant models of inflation with the current datasets and futures surveys with novel constraints on r and spectral distortions but also one may need to revisit calculations in complex settings (Higgs inflation, geometrical destabilization, etc.);

- the end of inflation and importance of the (p)reating mechanisms; limitations of the current constraints based on global parameterized shape of the inflaton potential , gravitational wave production of the end of inflation ;

- Stability of dark matter/baryogenesis/(sterile) neutrinos/axion mass/ … from spectral distortions ?

- Gravitational lensing effects and complementarity with LSST/Euclid type missions (impact of the existence of an extra source plane on data analysis and parameter constraints) ; The geometrical destabilization of inﬂation Renaux-Petel and Turzynski, PRL 2016 Generic models in high-energy physics have several ﬁelds, which live in an internal space with curved geometry. Initially neighboring geodesic tend to fall away from each other in the presence of negative curvature (very common)

This effect applies during inﬂation, and easily overcomes the effect of the potential, destabilizing inﬂationary trajectories.

Generic trend of prematurely ending inﬂation:

With GD - smaller amplitude of GWs - closer to scale invariance

Without GD

Destabilization of inﬂation despite Observational status of models steep walls from the potential are reshufﬂed On the theory side

- Identification of the most relevant models of inflation with the current datasets and futures surveys with novel constraints on r and spectral distortions but also one may need to revisit calculations in complex settings (Higgs inflation, geometrical destabilization, etc.);

- Stability of dark matter/baryogenesis/(sterile) neutrinos/axion mass/ … from spectral distortions ?

- Gravitational lensing effects and complementarity with LSST/Euclid type missions (impact of the existence of an extra source plane on data analysis and parameter constraints) ; CMB+, SCIENCE CASE 5

7 µ as high as 10 or for waterfall trajectories (in hybrid type inflation) for which µ can be as 6 high as 10 . 1.3. Exploring the phenomenology of specific inflationary models. The literature is rich with models. Few models are already excluded from recent observations, namely the simplest stochastic models. Precise observations of ns and r can bring constraints on specific models of inflation. The constraint is e↵ective when one assumes such model is valid from inflationary period to the reheating phase. Constraints on such models are illustrated on Fig. ??. A particularly suitable target is the R2 inflation model by Starobinsky (SI model). This model has the advantage of having little ingredients (FB: and can be seen as the incarnation of a Higgs inflation model - quite an interesting feature - although the model has not been shown to be robust against radiative corrections. to be further commented). It could be tested stage-4 level mission. Families of other models though cannot be so easily constrained from CMB observations alone. FB: One should give the expression of the SFI4 model and note that there are families of models that can cover the whole r ns diagram. FB: ModelsA multi-messenger motivated from strings approach or other and extensions model of the standard model of particlesconstruction are to be mentioned. : generation of gravitational waves 5

FIG. 1. Experimental constraints on (f); the black star is the current PPTA upper limit and all black curves and data Figure 4. Experimentalgw constraints on ⌦GW(f); the black star is the current points are current 95% confidence upper limits. The grey curve and triangle are respectively the predicted aLIGO sensitivity andParkes PPTA sensitivity Pulsar with Timing five more years Array of data. (PPTA) The indirect upper GW limits limit are from and CMB all temperature black curves and polarization and data power spectra,points lensing, are BAOs, current and BBN. 95% Models confidence predicting a power-law upper spectrum limits. that The intersect grey with an curve observational and constraint triangle are ruled out at > 95% confidence. We show five predictions for the GW background, each with r =0.11, and with nt =0.68 (orange curve), nt =0.54 (blue), nt =0.36 (red), nt =0.34 (magenta), and the consistency relation, nt = r/8 (green), are respectively the predicted advanced LIGO sensitivity and PPTA sensitivity correspondingwith five to more minimal years inflation. of data. The indirect GW limits are from CMB temperature and polarization power spectra, lensing, BAOs, and BBN. Models predicting a the PPTA limit are the upper limits from the EPTA [61] mological backgrounds based only on arguments of the andpower-law NANOGrav [ spectrum62]. Both the that EPTA intersect and NANOGrav with anenergy observational budget of the Universe constraint at early are times. ruled They out pre- presentat > limits95% on the confidence. GW energy density We show from inflation- five predictionssented optimistic, for the realistic GW and background, pessimistic upper each limits ary relics assuming nt = 0; our new limit for nt =0(cf. for ⌦gw(f), with the optimistic limit representing the ourwith limit onr ⌦=gw( 0.11,f) for n andt =0.5 with whichn onlyt = di↵ 0.68ers in the (orangelargest curve), value of n⌦tgw=(f) 0.54 possible (blue), given an reasonablet = 0.36 set second(red), decimalnt place)= 0.34 is a factor (magenta), of 4.1 better and than the the consistencyof conditions. relation, The new PPTAnt limit= reportedr/8 (green), here is the previouscorresponding best limit from to [62 minimal]. inflation. first time a GW limit in either the PTA or LIGO band The grey triangle below the star in Fig. 1 is a predicted has gone under this optimistic threshold, thus marking GW upper limit derived by simulating an additional five the first time the detection of cosmological GWs could ac- years of PPTA data. We took the maximum likelihood tually have been possible according to arguments in [64]. Interestingred noise parameters aspects in of the high-energy existing data sets, physics estimated motivatedConventional models models is of that early-Universe they can particle be studied physics from a multiplethe white probe noise level perspective. using the most It recent is interesting data that rep- in particulardo not predict to such explore a large GW how background such models in the PTA can also resents current observation quality, and assumed a two- frequency band. The temperature of the Universe at the be approachedweek observing from cadence their to derive late the time 95% CL amplification upper limit time or production when such GWs of are gravitational produced is 1 GeV waves. (see top 95% 11 axis of Fig. 1), a temperature at which physics of the of ⌦gw (f) 5 10 . However, the PPTA limit will be superseded before 2020 with limits placed from col- early Universe is relatively well known. We note that the lating datasets from the three existing PTAs as part of possibility of first-order phase transitions that generate the International Pulsar Timing Array [IPTA; 63]. From a strong GW background in the PTA frequency band is Fig. 1, it becomes clear that PTAs may not play a sig- not completely ruled out [e.g., 65–68] Of course it is possi- nificant role in constraining inflationary models where ble that there is unknown physics that influences gravity the GW spectrum is described by Eq. (3) when aLIGO without coupling strongly to the standard model of parti- reaches design sensitivity, given the significant improve- cle physics that could produce a strong GW background ments in the latter experiment. However, PTAs can still in the PTA frequency band. play an important role for cosmological models with a varying spectral index; that is, with a non-negligible running of the spectral index t. Giblin and Thrane [64] recently proposed a “rule of thumb” for the maximum GW energy density for cos- Ondes gravitationnelles : une sondes unique sur l’univers primordial, T T>T reh BBN C. Caprini, APC • La détection d’un fond stochastique d’Ondes Gravitationnelles nous permettrait de : - sonder des modèles d’inflation non-standard: tester l’index spectral du fond d’OG 10-20 ordres de grandeurs au delà des échelles du CMB (PTA, LISA, LIGO) - tester les interactions et le potentiel de l’inflaton (reheating) (LIGO?) - tester la présence de brisures de symétrie fondamentales (défauts topologiques) (PTA, LISA, LIGO) - tester des possibles solutions au problème de la hiérarchie (LISA), transitions de phase de premier ordre liées à la présence de dimensions supplémentaires - tester des modèles au delà du modèle standard et la baryogénèse (LISA), transition de phase éléctrofaible de première ordre - tester la QCDPT à nombre baryonique différent de zéro (PTA), transition de phase QCD de première ordre On the theory side

- Stability of dark matter/baryogenesis/(sterile) neutrinos/axion mass/ … from spectral distortions ?

CMB is (still) our best chance to explore the physics of the early universe - constraints on r ; - enormous discovery potential with spectral distorsions ; Other probes such as GW can be complementary to such observations

French theory community is active on - ﬁrst principle calculations (S. Renaux-Petel, J. Martin, ) - model constructions with GW (Caprini, …) - alternatives to standard picture (Peter, Rovelli) - strong connexion with Dark Energy theory community (Martin, Brax, Vernizzi, Deffayet, Esposito-Farèse, Blanchet, Charmousis, Polarski, etc.)