The CMB and Particle Physics - PDF Free Download

The CMB and Particle Physics Ruth Durrer Département de Physique Théorique and CAP, Université de Genève WIN2015 Heidelberg, June 10, 2015 Ruth Durrer (Université de Genève) CMB WIN2015 1 / 26

Contents 1 Introduction 2 Fluctuations in the CMB 3 Parameter estimation 4 Neutrinos in the CMB 5 Inflation 6 Conclusions Ruth Durrer (Université de Genève) CMB WIN2015 2 / 26

Introduction Why is the cosmic microwave background of interest for particle physicists? Ruth Durrer (Université de Genève) CMB WIN2015 3 / 26

Introduction Why is the cosmic microwave background of interest for particle physicists? Dark matter, dark energy Ruth Durrer (Université de Genève) CMB WIN2015 3 / 26

Introduction Why is the cosmic microwave background of interest for particle physicists? Dark matter, dark energy Neutrinos Ruth Durrer (Université de Genève) CMB WIN2015 3 / 26

Introduction Why is the cosmic microwave background of interest for particle physicists? Dark matter, dark energy Neutrinos Contains the cleanest information about inflation, the ultimate high energy laboratory Ruth Durrer (Université de Genève) CMB WIN2015 3 / 26

Introduction Why is the cosmic microwave background of interest for particle physicists? Dark matter, dark energy Neutrinos Contains the cleanest information about inflation, the ultimate high energy laboratory The CMB is a beautiful immensely rich dataset which every real physicist must admire. Ruth Durrer (Université de Genève) CMB WIN2015 3 / 26

The cosmic microwave background discovery 1965 by Penzias & Wilson Ruth Durrer (Université de Genève) CMB WIN2015 4 / 26

The cosmic microwave background (CMB) The Universe is expanding. In the past it was much denser and hotter. Ruth Durrer (Université de Genève) CMB WIN2015 5 / 26

The cosmic microwave background (CMB) The Universe is expanding. In the past it was much denser and hotter. At T > 3000K hydrogen was ionised and the cosmic plasma of protons, electrons and photons was strongly coupled by Thomson scattering and in thermal equilibrium. At T 3000K protons and electrons combined to neutral hydrogen. The photons became free and their distribution evolved simply by redshifting of the photon energies to a thermal distribution with T 0 = 2.7255 ± 0.0006K today. This corresponds to about 400 photons per cm 3 with typical energy of E γ = kt 0 2.3 10 4 ev 150GHz (λ 0.2cm). This is the observed CMB. At T > 9300K 0.8eV the Universe was radiation dominated, i.e. its energy density was dominated by the contribution from these photons (and 3 species of relativistic neutrinos which made up about 35%). Hence initial fluctuations in the energy density of the Universe should be imprinted as fluctuations in the CMB temperature. Ruth Durrer (Université de Genève) CMB WIN2015 5 / 26

The cosmic microwave background (CMB) Ruth Durrer (Université de Genève) CMB WIN2015 6 / 26

Fluctuations in the CMB T 0 = 2.7255K T (n) = lm a lmy lm (n) C l = a lm 2, D l = l(l + 1)C l /(2π) Planck Collaboration: Cosmological parameters 6000 5000 D TT [µk 2 ] D TT 4000 3000 2000 1000 0 600 300 0-300 -600 2 10 30 500 1000 1500 2000 2500 60 30 0-30 -60 From the Planck Collaboration Planck Results XIII (2015) arxiv:1502.01589 Ruth Durrer (Université de Genève) CMB WIN2015 7 / 26

The cosmic microwave background (CMB) 6 Hu & Dodelson Planck Collaboration: Cosmological parameters 6000 DT T [µk2 ] 5000 4000 3000 2000 1000 DT T 0 600 60 30 0-30 -60 300 0-300 -600 2 10 30 500 1000 1500 2000 2500 100 Fig. 1. The Planck 2015 temperature power spectrum. At multipoles ` 30 we show the maximum likelihood frequency averaged temperature spectrum computed from the Plik cross-half-mission likelihood with foreground and other nuisance parameters determined from the MCMC analysis of the base CDM cosmology. In the multipole range 2 ` 29, we plot the power spectrum estimates from the Commander component-separation algorithm computed over 94% of the sky. The best-fit base CDM theoretical spectrum fitted to the Planck TT+lowP likelihood is plotted in the upper panel. Residuals with respect to this model are shown in the lower panel. The error bars show ±1 uncertainties. (Hu & Dodelson, 2002) 10 ΔT (µk) reionization 1 0.1 Ruth Durrer (Universite de Gene ve) (Planck Collaboration 2015) ΘE EE BB gravitational lensing sults to the likelihood methodology by developing several independent analysis pipelines. Some of these are described in Planck Collaboration XI (2015). The most highly developed of these are the CamSpec and revised Plik pipelines. For the 2015 Planck papers, the Plik pipeline was chosen as the baseline. Column 6 of Table 1 lists the cosmological parameters for base CDM determined from the Plik cross-half-mission likelihood, together with the lowp likelihood, applied to the 2015 full-mission data. The sky coverage used in this likelihood is identical to that used for the CamSpec 2015F(CHM) likelihood. However, the two likelihoods di er in the modelling of instrucmb the full TT,TE,EE likelihoods) would di er in any substantive way had we chosen to use the CamSpec likelihood in place of Plik. The overall shifts of parameters between the Plik 2015 likelihood and the published 2013 nominal mission parameters are summarized in column 7 of Table 1. These shifts are within 0.71 except for the parameters and As e 2 which are sensitive to the low multipole polarization likelihood and absolute calibration. In summary, the Planck 2013 cosmological parameters were pulled slightly towards lower H0 and ns by the ` 1800 4-K line WIN2015 but the 8 26 of systematic in the 217 217 cross-spectrum, net/e ect

D`T E Polarisation of the CMB 10 0-10 30 500 1000 1500 2000 ` CMB Anisotropies 23 y µk2 ] 100 E mode C EE [10 5 Quadrupole Thomson Scattering e x 80 60 40 20 k 0 B mode C EE z 24 4 0-4 Linear Polarization 30 500 1000 1500 2000 Plate 2: Polarization generation and classification. Left: Thomson quadrupole Fig. 3. Frequency-averaged T E scattering and EE spectraof (without fitting for T -P leakage). The theoretical T E and EE spectra plott panel ofgenerates each plot are computed from the Planck TT+lowP best-fit model of Fig. 1. Residuals with respect to this th temperature anisotropies (depicted here in the x upper y plane) linear polarization. Right: model are shown depends in the lower panel inon plot. The error bars show ±1 errors. The green lines in the lower panels s scattering polarisation. Polarization in the x y plane Thomson along the outgoing z axis. The component each of the polarization best-fit temperature-to-polarization leakage model of Eqs. (11a) and (11b), fitted separately to the T E and EE spectra. that is parallel oraperpendicular to the wavevector k is called the polarisation, E-mode and the one local quadrupole induces linear Q at 6=450 and U 6= 0. angles is called the B-mode. is Θ(n, η0 ) =!!m " Y!m (n ) ( i)! Ruth Durrer (Universite de Gene ve) # $ d3 k a! (k)y!m (k ), (2π)3 CMB (21) WIN2015 9 / 26

The physics of CMB fluctuations In the radiation dominated Universe small density fluctuations perform acoustic oscillations at constant amplitude, δ cos(k c sdτ). On large scales, the gravitational potential (metric fluctuation) is constant, on sub-hubble scales, kτ > 1 it decays like a 2. The wavelength corresponding to the first acoustic peak is λ = 2π/k with τ k c 0 sdτ = π. In a matter-radiation Universe this gives (ω x = Ω xh 2 ) H 0 h (1 + z )λ = 4 1 + (1+z z + r + )rω r ω log m + r ( ), 3rωm 1 + z 1 + rωr ω m r = 3ω b 4ω γ. In the matter dominated Universe density fluctuations grow δ a and the gravitational potential remains constant. Ruth Durrer (Université de Genève) CMB WIN2015 10 / 26

The physics of CMB fluctuations In the radiation dominated Universe small density fluctuations perform acoustic oscillations at constant amplitude, δ cos(k c sdτ). On large scales, the gravitational potential (metric fluctuation) is constant, on sub-hubble scales, kτ > 1 it decays like a 2. The wavelength corresponding to the first acoustic peak is λ = 2π/k with τ k c 0 sdτ = π. In a matter-radiation Universe this gives (ω x = Ω xh 2 ) H 0 h (1 + z )λ = 4 1 + (1+z z + r + )rω r ω log m + r ( ), 3rωm 1 + z 1 + rωr ω m r = 3ω b 4ω γ. In the matter dominated Universe density fluctuations grow δ a and the gravitational potential remains constant. On small scales fluctuations are damped by free streaming (Silk damping). Ruth Durrer (Université de Genève) CMB WIN2015 10 / 26

The physics of CMB fluctuations In the radiation dominated Universe small density fluctuations perform acoustic oscillations at constant amplitude, δ cos(k c sdτ). On large scales, the gravitational potential (metric fluctuation) is constant, on sub-hubble scales, kτ > 1 it decays like a 2. The wavelength corresponding to the first acoustic peak is λ = 2π/k with τ k c 0 sdτ = π. In a matter-radiation Universe this gives (ω x = Ω xh 2 ) H 0 h (1 + z )λ = 4 1 + (1+z z + r + )rω r ω log m + r ( ), 3rωm 1 + z 1 + rωr ω m r = 3ω b 4ω γ. In the matter dominated Universe density fluctuations grow δ a and the gravitational potential remains constant. On small scales fluctuations are damped by free streaming (Silk damping). In a Λ-dominated Universe δ is constant and the gravitational potential decays. Ruth Durrer (Université de Genève) CMB WIN2015 10 / 26

The distance to the CMB The angle onto which the scale k is projected depends on the angular diameter distance to the CMB, θ = λ /(2d A (z ) This is the best measured quantity of the CMB, with a relative error of about 3 10 4 θ s = rs d A (z s) = (1.04077 ± 0.00032) 10 2. (Planck Collaboration: Planck results 2015 XIII) Ruth Durrer (Université de Genève) CMB WIN2015 11 / 26

The distance to the CMB The angle onto which the scale k is projected depends on the angular diameter distance to the CMB, θ = λ /(2d A (z ) This is the best measured quantity of the CMB, with a relative error of about 3 10 4 θ s = rs d A (z s) = (1.04077 ± 0.00032) 10 2. (Planck Collaboration: Planck results 2015 XIII) The distance to the CMB is given by (1 + z )d A (z ) = z 0 H(z) 1 dz = h H 0 z 0 1 ωm(1 + z) 3 + ω K (1 + z) 2 + ω x(z) dz Ruth Durrer (Université de Genève) CMB WIN2015 11 / 26

Cosmological parameters The CMB fluctuations into a direction n in the instant decoupling approximation are given by [ ] T 1 τ0 T (n) = 4 Dg + n V + Ψ + Φ (n, τ ) + τ (Ψ + Φ)ds. τ The power spectrum C l of CMB fluctuations is given by T T (n) T T (n ) = 1 (2l + 1)C l P l (n n ) Planck Collaboration: 4π Cosmological parameters l 6000 5000 D TT [µk 2 ] 4000 3000 2000 1000 D TT 0 600 300 0-300 -600 2 10 30 500 1000 1500 2000 2500 60 30 0-30 -60 Ruth Durrer (Université de Genève) CMB WIN2015 12 / 26

The Planck base model Curvature K = 0 Ruth Durrer (Université de Genève) CMB WIN2015 13 / 26

The Planck base model Curvature K = 0 No tensor perturbations, r = 0 Ruth Durrer (Université de Genève) CMB WIN2015 13 / 26

The Planck base model Curvature K = 0 No tensor perturbations, r = 0 Three species of thermal neutrinos, N eff = 3.046 with temperature T ν = (4/11) 1/3 T 0 Ruth Durrer (Université de Genève) CMB WIN2015 13 / 26

The Planck base model Curvature K = 0 No tensor perturbations, r = 0 Three species of thermal neutrinos, N eff = 3.046 with temperature T ν = (4/11) 1/3 T 0 2 neutrino species are massless and the third has m 3 = 0.06eV such that i m i = 0.06eV. Helium fraction Y p = 4n He/n b is calculated from N eff and ω b. Parameters Amplitude uf curvature perturbations, A s Scalar spectral index, n s Ruth Durrer (Université de Genève) CMB WIN2015 13 / 26

The Planck base model Curvature K = 0 No tensor perturbations, r = 0 Three species of thermal neutrinos, N eff = 3.046 with temperature T ν = (4/11) 1/3 T 0 2 neutrino species are massless and the third has m 3 = 0.06eV such that i m i = 0.06eV. Helium fraction Y p = 4n He/n b is calculated from N eff and ω b. Parameters Amplitude uf curvature perturbations, A s Scalar spectral index, n s Baryon density ω b = Ω b h 2 Ruth Durrer (Université de Genève) CMB WIN2015 13 / 26

The Planck base model Curvature K = 0 No tensor perturbations, r = 0 Three species of thermal neutrinos, N eff = 3.046 with temperature T ν = (4/11) 1/3 T 0 2 neutrino species are massless and the third has m 3 = 0.06eV such that i m i = 0.06eV. Helium fraction Y p = 4n He/n b is calculated from N eff and ω b. Parameters Amplitude uf curvature perturbations, A s Scalar spectral index, n s Baryon density ω b = Ω b h 2 Cold dark matter density ω c = Ω ch 2 Ruth Durrer (Université de Genève) CMB WIN2015 13 / 26

The Planck base model Curvature K = 0 No tensor perturbations, r = 0 Three species of thermal neutrinos, N eff = 3.046 with temperature T ν = (4/11) 1/3 T 0 2 neutrino species are massless and the third has m 3 = 0.06eV such that i m i = 0.06eV. Helium fraction Y p = 4n He/n b is calculated from N eff and ω b. Parameters Amplitude uf curvature perturbations, A s Scalar spectral index, n s Baryon density ω b = Ω b h 2 Cold dark matter density ω c = Ω ch 2 Present value of Hubble parameter H 0 = 100hkm/sec/Mpc (Ω Λ = 1 (ω b + ω c)/h 2 ). Ruth Durrer (Université de Genève) CMB WIN2015 13 / 26

The Planck base model Curvature K = 0 No tensor perturbations, r = 0 Three species of thermal neutrinos, N eff = 3.046 with temperature T ν = (4/11) 1/3 T 0 2 neutrino species are massless and the third has m 3 = 0.06eV such that i m i = 0.06eV. Helium fraction Y p = 4n He/n b is calculated from N eff and ω b. Parameters Amplitude uf curvature perturbations, A s Scalar spectral index, n s Baryon density ω b = Ω b h 2 Cold dark matter density ω c = Ω ch 2 Present value of Hubble parameter H 0 = 100hkm/sec/Mpc (Ω Λ = 1 (ω b + ω c)/h 2 ). optical depth to reionization τ Ruth Durrer (Université de Genève) CMB WIN2015 13 / 26

Cosmological parameters from Planck 2015 arxiv:1502.01589 Planck Collaboration: Cosmological parameters Planck EE+lowP Planck TE+lowP Planck TT+lowP Planck TT,TE,EE+lowP bh 2 ch 2 0.0275 0.0250 0.0225 0.0200 0.13 0.12 0.11 0.10 3.20 n s = 0.9645 ± 0.0049 Ω ch 2 = 0.1198 ± 0.0015 Ω b h 2 = 0.02225 ± 0.00016 ln(10 10 A s) = 3.094 ± 0.034 H 0 = 67.27 ± 0.66 τ = 0.079 ± 0.017 ln(10 10 As) 3.12 3.04 2.96 1.02 0.99 ns 0.96 0.93 0.16 0.12 0.08 0.04 1.038 1.040 1.042 100 MC 0.0200 0.0225 0.0250 0.0275 0.10 0.11 0.12 0.13 2.96 3.04 3.12 3.20 bh 2 ch 2 ln(10 10 As) 0.93 0.96 0.99 1.02 ns 0.04 0.08 0.12 0.16 Fig. 6. Ruth Comparison Durrer of (Université the base CDM de Genève) model parameter constraints from Planck temperature CMBand polarization data. WIN2015 14 / 26

Planck Collaboration: Cosmological parameters Polarization spectra Planck Collaboration: Cosmological parameters (Planck 2015 arxiv:1502.01589) E 2 2 D`TDE`T[µK ] ] [µk 140 140 70 70 0 0-70 -70-140 -140 10 10 0 T-E correlation `(`+1) TE C` 2π D`TDE`T E D`TE = 0-10 -10 30 30 500 500 1000 1000 ` 1500 1500 2000 2000 C EE C EE 5 2 2 C EE [10[105 µk ] ] C EE µk ` 100 100 80 80 60 60 40 40 20 20 0 0 4 4 0 0-4 -4 E-E spectrum D`EE = 30 500 1000 500e de Gene ve) 1000 Ruth 30 Durrer (Universit 1500 1500 2000 2000CMB `(`+1) EE C` 2π WIN2015 15 / 26

Lensing spectrum (Planck 2015 arxiv:1502.01591) φ(n) = 2 r Z dr 0 Planck Collaboration: Gravitational lensing by large-scale structures with Planck 2 [L(L + 1)]2 CL /2 [ 107 ] ensing by large-scale structures with Planck e e W ed rxi u- Planck (2015) Planck (2013) 1.5 SPT ACT 1 0.5 0 0.5 ˆ WF (Data) g 5) (r r ) Ψ(r n, τ0 r ) r r Fig. 2 Lensing potential estimated from the SMICA full-mission CMB maps using the MV estimator. The power spectrum of this map forms the basis of our lensing likelihood. The estimate has been Wiener filtered following Eq. (5), and band-limited to 8 L 2048. Ruth Durrer (Universite de Gene ve) 1 10 100 500 1000 2000 L Fig. 6 Planck 2015 full-mission MV lensing potential power spectrum measurement, as well as earlier measurements using Planck 2013 nominal-mission temperature data (Planck Collaboration XVII 2014), the South Pole Telescope (SPT, van Enge et al. 2012), and the Atacama Cosmology Telescope (ACT, Das et al. 2014). The fiducial CDM theory power spectrum based the parameters given in Sect. 2 is plotted as the black solid line. In addition to the priors above, we adopt the same sampling priors and methodology as Planck Collaboration XIII (2015), using CosmoMC and camb for sampling and theoretical predictions (Lewis & Bridle 2002; Lewis et al. 2000). In the CDM CMB model, as well as b h2 and ns, we sample As, c h2, and the Appendix E; see also Pan et al. (2014). Here, we aim to simple physical arguments to understand the parameter deg eracies of the lensing-only constraints. In the flat CDM mo the bulk of the lensing signal comes from high redshift (z > WIN2015 26 where the Universe is mostly matter-dominated16 (so /potentials

Fig. 25. Power spectra drawn from the Planck TT+lowP posterior for the correlated matter isocurvature model, colour-coded by the value of the isocurvature amplitude parameter, compared to the Planck data points. The left-hand figure shows how the negativelycorrelated modes lower the large-scale temperature spectrum, slightly improving the fit at low multipoles. Including polarization, the negatively-correlated modes are ruled out, as illustrated at the first acoustic peak in EE on the right-hand plot. Data points at ` < 30 are not shown for polarization, as they are included with both the default temperature and polarization likelihood combinations. Lensing breaks degeneracies +TE+EE +lensing +lensing+bao 0.75 68 64 60 0.60 H0 56 52 0.45 48 44 0.30 40 0.30 0.45 0.60 0.75 m Fig. 26. Constraints in the m plane from the Planck 0.040 TT+lowP data (samples; colour-coded by the value± of 0.04 H0 ) and Planck TT,TE,EE+lowP (solid The geometric degen± 0.016 Ωcontours). K = 0.005 eracy between m and is partially broken because of the ef 0.000 ± 0.005 fect of lensing on the temperature and polarization power spectra. These limits are improved significantly by the inclusion of the Planck lensing reconstruction (blue contours) and BAO (solid red contours). The red contours tightly constrain the geometry of our Universe to be nearly flat. Ruth Durrer (Universite de Gene ve) CMB The geometric degeneracy (Bond et al. 1997; Zaldarriaga et al. 1997) allows for the small-scale linear CMB spectrum to remain almost unchanged if changes in K are compensated by changes in H0 to obtain the same angular diameter distance to last scattering. The Planck constraint is therefore mainly determined by the (wide) priors on H0, and the e ect of lensing smoothing on the power spectra. As discussed in Sect. 5.1, the Planck temperature power spectra show a slight preference(planck for more lensing than expected in the base CDM 1502.01589) cosmology, and since positive curvature increases the amplitude of the lensing signal, this preference also drives K towards negative values. Taken at face value, Eq. (47) represents a detection of positive curvature at just over 2, largely via the impact of lensing on the power spectra. One might wonder whether this is mainly a parameter volume e ect, but that is not the case, since the best 2 fit closed model has 6 relative to base CDM, and the fit is improved over almost all the posterior volume, with the mean chi-squared improving by h 2 i 5 (very similar to the phenomenological case of CDM+AL ). Addition of the Planck (TT,EE,TE) polarization spectra shifts K towards zero by K 0.015: add lensing+0.038 K = 0.040 0.041 add BAO s 95% (95%, Planck TT,TE,EE+lowP), (48) but K remains negative at just over 2. However the lensing reconstruction from Planck measures the lensing amplitude directly and, as discussed in Sect. 5.1, this does not prefer more lensing than base CDM. The combined constraint shows impressive consistency with a flat universe: WIN2015 17 / 26

Neutrino properties (Planck 2015 arxiv:1502.01589) Single extension best constraints: Planck Collaboration: Cosmological parameters 0.00 0.06 Planck TT+lowP Planck TT,TE,EE+lowP Planck TT,TE,EE+lowP+BAO N eff = 3.04 ± 0.2 (0.18) Planck (+ BAO) Σ i m i = 0.49 (0.17) ev 95% Planck (+ BAO) K 0.12 0.18 Ω b h 2 Ω ch 2 n s H 0 σ 8 1.6 m [ev] 1.2 0.8 0.4 4.2 3.6 Ne 3.0 2.4 0.32 0.28 YP Ruth Durrer (Université de Genève) CMB WIN2015 18 / 26

Cosmic neutrinos are collisionless (E. Sellentin & RD arxiv:1412.6427) Treating neutrinos as perfect fluid or viscous fluid affects CMB spectra significantly. (Here fixing the other parameters.) Marginalizing over the other parameters Ruth Durrer (Université de Genève) CMB WIN2015 19 / 26

Cosmic neutrinos are collisionless (E. Sellentin & RD arxiv:1412.6427) Ruth Durrer (Université de Genève) CMB WIN2015 20 / 26

8 8 Sterile neutrinos m eff ν,sterile = 94.1Ω ν,sterileev. m eff ν,sterile = N eff ν,sterilem thermal ν,sterile, cut: m thermal ν,sterile < 10eV. N eff m eff ν,sterile < 0.7 ν,sterile < 0.52 95% (Planck + gal. lensing + BAO) Planck Collaboration: Cosmological parameters Planck TT+lowP +lensing +lensing+bao CDM 0.9 +Ne +Ne + m +Ne +Ne + m 0.8 0.7 0.9 + m +Ne +m e, sterile + m +Ne +m e, sterile 0.8 0.7 0.24 0.32 0.40 0.48 0.24 0.32 0.40 0.48 56 64 72 56 64 72 m m H0 H0 Fig. 33. 68 % and 95 % constraints from Planck TT+lowP (green), Planck TT+lowP+lensing (grey), and Planck TT+lowP+lensing+BAO (red) on the late-universe parameters H0, 8, and m in various neutrino extensions of the base CDM Ruth Durrer (Université de Genève) CMB WIN2015 21 / 26

Inflation The fluctuations in the CMB stem from a very early phase of inflationary expansion of the Universe. They contain inform,ation on the physics of this very hot early phase. Inflation is a phase of very fast expansion during which the Universe becomes large and flat. This can be achieved with the energy density of a scalar field if it is dominated by the scalar field potential, V. When inflation ends the inflaton field decays into the standard model particles which thermalize and generate a hot thermal Universe. Ruth Durrer (Université de Genève) CMB WIN2015 22 / 26

Inflation The fluctuations in the CMB stem from a very early phase of inflationary expansion of the Universe. They contain inform,ation on the physics of this very hot early phase. Inflation is a phase of very fast expansion during which the Universe becomes large and flat. This can be achieved with the energy density of a scalar field if it is dominated by the scalar field potential, V. When inflation ends the inflaton field decays into the standard model particles which thermalize and generate a hot thermal Universe. During inflation quantum fluctuations of both, the inflaton and of the metric are stretched and amplified. Ruth Durrer (Université de Genève) CMB WIN2015 22 / 26

Inflation Once a quantum mode exits the horizon λ > H 1, they freeze in as classical fluctuations of the energy density and of the metric with a nearly scale invariant spectrum. 14 12 Or even simpler: A wave function scatters at a time dependent potential and gets amplified. 10 8 6 4 2 4 2 2 4 6 Ruth Durrer (Université de Genève) CMB WIN2015 23 / 26

Inflation Slow-roll inflationary models can be described with a few (mainly 2) slow-roll parameters and the Hubble scale during inflation, H. The scalar and tensor spectra from inflation are given by P ζ (k) H2 k 6ɛ+2η 12.2 10 9 ɛmp 2 ( r E = 0.1 Planck Collaboration: Cosmological parameters ) 1/4 1.7 10 16 GeV P h H2 k 2ɛ Mp 2 ( ) 4 E M p lanck TT+lowP+lensing ( Ne = 0.39) N=60 CDM Planck TT+lowP +lensing+ext 0.25 0.20 N=50 N=60 Planck TT+lowP Planck TT+lowP+BKP +lensing+ext 2 0.15 2 r0.002 Convex Concave e 0.10 0.05 0.00 0.96 0.97 0.98 0.99 1.00 0.95 0.96 0.97 0.98 0.99 1.00 Ruth Durrer ns (Université de Genève) CMBns WIN2015 24 / 26

Tensor to scalar ratio E-mode and B-mode B-modeB Tensor perturbations can generate B-polarisation. E B Polarization fields can be linearly Polarization fields can be linearly decomposed 1 to E and B mode BK+P 1 decomposed to E and B mode B+P K+P 0.8 E-mode polarization is perpendicular/parallel 0.8 E-mode polarization is perpendicular/parallel to 0.6 the direction of modulation 0.6 to the direction of modulation 0.4 0.4 B-mode polarization is oriented at 45 to the B-mode polarization is oriented at 45 to the direction 0.2 of modulation 0.2 direction of modulation 0 0 Linear, 0 0.05 scalar 0.1 perturbation 0.15 0.2 0.25cannot 0.3 generate 0 1B Linear, scalar perturbation r generate B-B A mode polarizations Bicep2 mode polarizations KeckArray Planck FIG. 6. Likelihood results from a basic lensed- CDM+r+ arxiv:1502.00612 at 150 GHz, No No Cosmic Cosmic 217, and 353 Variance Variance GHz. The 217 and 353 GHz m 150 GHz combined maps from BICEP2/Keck. Alternat BICEP2 and Keck Array only maps are used. In all cases d =1.59 ± 0.11. In the right panel the two dimensional L/L peak Ruth Durrer (Université de Genève) CMB WIN2015 25 / 26 L/L peak

Conclusion Cosmology provides the strongest (only?) experimental evidence for physics beyond the standard model. Ruth Durrer (Université de Genève) CMB WIN2015 26 / 26

Conclusion Cosmology provides the strongest (only?) experimental evidence for physics beyond the standard model. What is dark matter? Ruth Durrer (Université de Genève) CMB WIN2015 26 / 26

Conclusion Cosmology provides the strongest (only?) experimental evidence for physics beyond the standard model. What is dark matter? What is dark energy? Ruth Durrer (Université de Genève) CMB WIN2015 26 / 26

Conclusion Cosmology provides the strongest (only?) experimental evidence for physics beyond the standard model. What is dark matter? What is dark energy? What is the inflaton? The CMB is the most precious cosmological dataset. It is very precise and very well understood. Apart from addressing the above questions it can also be used to test the cosmic neutrinos. Ruth Durrer (Université de Genève) CMB WIN2015 26 / 26

Conclusion Cosmology provides the strongest (only?) experimental evidence for physics beyond the standard model. What is dark matter? What is dark energy? What is the inflaton? The CMB is the most precious cosmological dataset. It is very precise and very well understood. Apart from addressing the above questions it can also be used to test the cosmic neutrinos. Cosmological perturbations are generated by quantum excitation in a time dependent background. Ruth Durrer (Université de Genève) CMB WIN2015 26 / 26