Robustness of cosmic neutrino background detection in the cosmic microwave background Viviana Niro UAM and IFT Madrid, 23 June, 2015 B. Audren, E. Bellini, A. J. Cuesta, S. Gontcho A Gontcho, J. Lesgourgues, VN, M Pellejero-Ibanez, I. P´ erez-R` afols, V. Poulin, T. Tram, D. Tramonte, L. Verde, JCAP 1503 (2015) 036 V. Niro (UAM and IFT) Cosmic neutrino background detection Invisibles 15 Workshop 1 / 15
Outline 1 Introduction 2 The cosmic neutrino background Introducing the ( c 2 eff , c 2 vis ) parameters Robustness of the detection Planck results 3 Conclusions V. Niro (UAM and IFT) Cosmic neutrino background detection Invisibles 15 Workshop 2 / 15
The cosmic neutrino background Neutrinos decouples from matter after 2 s ( ∼ MeV), C ν B ∼ 100 ν / cm 3 Neutrino DM is HDM → they are not the dominant component of DM in the Universe First indirect confirmation of the existence of a cosmological neutrino background: adding only one extra parameter to the standard ΛCDM model, the effective number of neutrino species, N eff Using CMB observations, N eff = 0 is disfavoured at the level of about 17 σ → indirect confirmation of the cosmic neutrino background Planck collaboration, 2015 But departures from N eff could be caused by any ingredient contributing to the expansion rate of the Universe in the same way as a radiation background V. Niro (UAM and IFT) Cosmic neutrino background detection Invisibles 15 Workshop 3 / 15
The cosmic neutrino background free streaming particles like decoupled neutrinos leave specific signatures on the CMB, not only through their contribution to the background evolution effect on perturbations: their density/pressure perturbations, bulk velocity and anisotropic stress are additional sources for the gravitational potential via the Einstein equations → introduce two phenomenological parameters ( c 2 eff , c 2 vis ) Postulate a linear relation between isotropic pressure perturbations and density perturbations given by a squared sound speed c 2 eff . The approach is then extended to anisotropic pressure by introducing another constant, the viscosity coefficient c 2 vis . The CMB seems to prove that the perturbation of neutrinos are needed to explain the data ⇒ Are these bounds stable when considering massive neutrinos? ⇒ Could ( c 2 eff , c 2 vis ) be degenerate with other cosmological parameters, like e.g., N eff , a running of the primordial spectrum index, or the equation of state of dynamical dark energy? V. Niro (UAM and IFT) Cosmic neutrino background detection Invisibles 15 Workshop 4 / 15
Cosmological perturbation theory Massless neutrinos − 4 ˙ (1) δ ν = 3( θ ν + M continuity ) , � 1 � ˙ k 2 (2) θ ν = 4 δ ν − σ ν + M Euler , σ ν = 8 15( θ ν + M shear ) − 3 ˙ (3) = 2 ˙ 5 kF ν 3 , F ν 2 2 l + 1 F ν l − l ˙ ˙ (4) F ν ( l − 1) = − ( l + 1) F ν l +1 , l ≥ 3 . k δ : density fluctuations, θ : divergence of fluid velocity, σ : shear stress, F νℓ are the Legendre multipoles of the momentum integrated neutrino distribution function. (1) continuity equation, related to density contrast; (2) Euler equation; (3) anisotropic pressure/shear; (4) distribution function moments ( M continuity , M Euler ) refer to combination of metric perturbations, e.g. (˙ h / 2 , 0) in the synchronous gauge and ( − 3 ˙ φ, k 2 ψ ) in the Newtonian gauge. M shear is 0 in the Newtonian gauge and (˙ h + 6 ˙ η ) / 2 in the synchronous gauge. C.-P. Ma, E. Bertschinger, astro-ph/9506072 V. Niro (UAM and IFT) Cosmic neutrino background detection Invisibles 15 Workshop 5 / 15
Introducing the ( c 2 eff , c 2 vis ) parameters Massless neutrinos � ˙ � � a δ ν + 4 a ˙ − 4 � ˙ 1 − 3 c 2 δ ν = a θ ν 3( θ ν + M continuity ) , eff k 2 a k 2 � � δ ν + 4 a ˙ − ˙ a ˙ 4 (3 c 2 a θ ν − k 2 σ ν + M Euler , θ ν = eff ) a θ ν k 2 vis ) 8 15( θ ν + M shear ) − 3 ˙ σ ν = (3 c 2 F ν 2 = 2 ˙ 5 kF ν 3 , perturbations of relativistic free-streaming species: ( c 2 eff , c 2 vis ) = (1/3, 1/3) perfect relativistic fluid (isotropic pressure; σ ν and all multipoles F νℓ with ℓ ≥ 3 remain zero at all times): ( c 2 eff , c 2 vis ) = (1/3, 0) a scalar field: ( c 2 eff , c 2 vis ) = (1, 0), more general case: arbitrary ( c 2 eff , c 2 vis ). assume ˆ eff ˆ δρ , identify the source terms corresponding to ˆ δ p = c 2 δ p in the continuity/Euler equation and multiply them by (3 c 2 eff ); identify the source term for σ in the quadrupole equation and multiply it by (3 c 2 vis ). See also W. Hu, D. J. Eisenstein, M. Tegmark, M. White, astro-ph/9806362; W. Hu astro-ph/9801234; R. Trotta and A. Melchiorri, astro-ph/0412066; M. Archidiacono, E. Calabrese, A. Melchiorri, 1109.2767; M. Gerbino, E. Di Valentino, N. Said, 1304.7400 [astro-ph.CO] V. Niro (UAM and IFT) Cosmic neutrino background detection Invisibles 15 Workshop 6 / 15
Introducing the ( c 2 eff , c 2 vis ) parameters Massive neutrinos � q 2 ˙ � Ψ 0 + 3 ˙ 5 p − ˜ ǫ � ǫ Ψ 1 + 1 3 M continuity d ln f 0 a a p − qk � ˙ 1 − 3 c 2 Ψ 0 = kq Ψ 1 d ln q , eff a ǫ 2 a ρ + p � � qk Ψ 0 + 3 ˙ a 5 p − ˜ p ǫ − ˙ a 5 p − ˜ ρ + p Ψ 1 − 2 p qk 3 qk M euler d ln f 0 ǫ ˙ c 2 Ψ 1 = qk Ψ 1 ǫ Ψ 2 − d ln q , eff ǫ a ρ + p a 3 15 M shear d ln f 0 2 qk � � ˙ 6 c 2 − 3 c 2 Ψ 2 = vis Ψ 1 − 3Ψ 3 d ln q . vis 5 ǫ In the case of light relics experiencing a non-relativistic transition such as massive neutrinos, the Boltzmann equation cannot be integrated over momentum, and one must solve one hierarchy per momentum bin. The previous parametrisation can be extended to the case of light relics experiencing a non-relativistic transition such as massive neutrinos ⇒ obtain a modified Boltzmann hierarchy for each momentum q . f 0 : unperturbed phase space distribution function; Ψ l : l th Legendre component of perturbation to f 0 C.-P. Ma, E. Bertschinger, astro-ph/9506072 V. Niro (UAM and IFT) Cosmic neutrino background detection Invisibles 15 Workshop 7 / 15
Impact of ( c 2 eff , c 2 vis ) on CMB CMB power spectra of our four models with non-standard values of c 2 eff and c 2 vis , normalised to the reference model with c 2 eff = c 2 vis = 1 / 3. CMB power spectrum multipoles for the temperature and E -mode polarisation. Solid (dashed) red lines correspond to a c 2 eff of 0 . 36 (0 . 30), solid (dashed) blue lines correspond to a c 2 vis of 0 . 36 (0 . 30). V. Niro (UAM and IFT) Cosmic neutrino background detection Invisibles 15 Workshop 8 / 15
Impact of ( c 2 eff , c 2 vis ) on CMB In the polarisation power spectrum: the change in amplitude is similar to the one in the temperature power spectrum but the shift in the position of the peaks is more clear: for polarisation there is no contribution from Doppler effects ⇒ strong oscillations in the ratios V. Niro (UAM and IFT) Cosmic neutrino background detection Invisibles 15 Workshop 9 / 15
Degeneracies Degeneracies between the parameters ( c 2 vis , c 2 eff ) and the parameters ω b , ω cdm , A s and n s (CMB+lensing data). 0.36 eff c 2 0.32 0.27 1 vis c 2 0.56 0.21 2 2.2 2.3 0.11 0.12 0.13 2 2.3 2.7 0.92 0.98 1 10 +9 A s 100 ω b ω cdm n s ⇒ c 2 eff and c 2 vis parametersa are degenerate with combinations of ω b , ω cdm , n s and A s V. Niro (UAM and IFT) Cosmic neutrino background detection Invisibles 15 Workshop 10 / 15
Degeneracies Constraints in the ( c 2 vis , c 2 eff ) plane for combination of CMB, CMB+lensing and CMB+lensing+BAO data. cmb cmb lensing cmb lensing bao 1 vis 0.6 c 2 0.21 0.27 0.31 0.36 0.21 0.6 1 c 2 c 2 eff vis ⇒ c 2 eff and c 2 vis parameters are anti-correlated V. Niro (UAM and IFT) Cosmic neutrino background detection Invisibles 15 Workshop 11 / 15
Degeneracies Constraints on ( c 2 vis , c 2 eff ) and the running spectral index α s for CMB+lensing data ⇒ small anti-correlation between c 2 eff and the running of the primordial spectrum tilt α s ≡ dn s / d log k , but c 2 eff is compatible with the standard value of 1/3 and α s is consistent with 0 V. Niro (UAM and IFT) Cosmic neutrino background detection Invisibles 15 Workshop 12 / 15
Robustness of C ν B evidence ΛCDM+ c 2 eff + c 2 vis : The standard values ( c 2 eff , c 2 vis ) are always well within the 95% confidence intervals ⇒ the data gives no indication of exotic physics, but further evidence in favour of the detection of the C ν B. The bounds on the parameters of the ΛCDM model are significantly broader than in the base ΛCDM case ⇒ polarization data can help break these degeneracies. Measurements of the shape of the matter power spectrum should also greatly help to lift the { n s , c 2 eff , c 2 vis } degeneracies. The ( c 2 eff , c 2 vis ) constraints are robust to the addition of extra cosmological parameters vis and the total neutrino mass M ν ≡ � m ν , the no degeneracy between c 2 eff + c 2 effective number of relativistic species N eff and the dark energy equation of state parameter w . There is a slight anti-correlation between α s and c 2 eff . V. Niro (UAM and IFT) Cosmic neutrino background detection Invisibles 15 Workshop 13 / 15
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