Constraints on dark radiation from cosmological probes

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Constraints on dark radiation from cosmological probes

Graziano Rossi, Christophe Yèche, Nathalie Palanque-Delabrouille, and Julien Lesgourgues

Phys. Rev. D 92, 063505 – Published 8 September 2015

Abstract

We present joint constraints on the number of effective neutrino species $N_{eff}$ and the sum of neutrino masses $\sum m_{ν}$ , based on a technique which exploits the full information contained in the one-dimensional Lyman- $α$ forest flux power spectrum, complemented by additional cosmological probes. In particular, we obtain $N_{eff} = 2.9 1_{- 0.22}^{+ 0.21}$ (95% C.L.) and $\sum m_{ν} < 0.15 eV$ (95% C.L.) when we combine BOSS Lyman- $α$ forest data with CMB ( $Planck + ACT + SPT + WMAP$ polarization) measurements, and $N_{eff} = 2.88 \pm 0.20$ (95% C.L.) and $\sum m_{ν} < 0.14 eV$ (95% C.L.) when we further add baryon acoustic oscillations. Our results provide strong evidence for the cosmic neutrino background from $N_{eff} \sim 3$ ( $N_{eff} = 0$ is rejected at more than $14 σ$ ), and rule out the possibility of a sterile neutrino thermalized with active neutrinos (i.e., $N_{eff} = 4$ )—or more generally any decoupled relativistic relic with $Δ N_{eff} ≃ 1$ —at a significance of over $5 σ$ , the strongest bound to date, implying that there is no need for exotic neutrino physics in the concordance $Λ CDM$ model.

Received 23 February 2015

DOI:https://doi.org/10.1103/PhysRevD.92.063505

This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Authors & Affiliations

Graziano Rossi^1,*, Christophe Yèche², Nathalie Palanque-Delabrouille², and Julien Lesgourgues^3,4

¹Department of Astronomy and Space Science, Sejong University, Seoul 143-747, Korea
²CEA, Centre de Saclay, Irfu/SPP, F-91191 Gif-sur-Yvette, France
³CERN, Theory Division, CH-1211 Geneva 23, Switzerland
⁴LAPTh, Université de Savoie, CNRS, B.P. 110, Annecy-le-Vieux F-74941, France

^*graziano@sejong.ac.kr

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Vol. 92, Iss. 6 — 15 September 2015

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Images

Figure 1
Linear theory test of the accuracy of our analytic approximation to include nonstandard dark radiation models. (Left) Linear matter power spectra for a series of models $\tilde{M}$ having $Δ N_{eff} = 1$ at $z = 3$ (chosen as a representative central value for the redshift range considered in this study), normalized by the baseline model $M$ with $N_{eff} = 3.046$ and three active neutrinos of degenerate mass, when $M_{ν} = 0.3 eV$ . See the main text for more details. (Right) Corresponding CMB temperature power spectra for the same models. Both panels show small differences in the scale of BAO and CMB peaks, but those differences do not affect the $Ly α$ likelihood.
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Figure 2
Snapshots at $z = 3$ from simulations with a canonical value of $N_{eff}$ (left panels), and when $N_{eff} = 4$ (right panels). The two cosmologies are related by our analytic remapping: ${\tilde{M}}_{ν} = 0.35 eV$ for the baseline model, while ${\tilde{M}}_{ν} = 0.4 eV$ for the nonstandard model which contains an additional massless sterile neutrino assumed to be in thermal equilibrium with three degenerate active massive neutrinos. Top panels show projections of the gas density along the $x$ and $y$ directions (and across $z$ ) for a $25 h^{- 1} Mpc$ box size and a resolution $N_{p} = 192^{3}$ particles per type; bottom panels display slices of the internal energy of the gas, for the same redshift interval. Although the two cosmologies are rather different, our remapping (6)–(8) produces almost identical nonlinear total matter and flux power spectra, and therefore a similar LSS morphology with no perceptible visual differences in the cosmic web structure.
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Figure 3
Ratios of synthetic one-dimensional $Ly α$ flux power spectra extracted from a baseline model $M$ having three degenerate massive neutrinos and no extra relativistic degrees of freedom ( $N_{eff} = 3$ , $M_{ν} = 0.35 eV$ ), and from a nonstandard dark radiation model $\tilde{M}$ characterized by a massless sterile neutrino and three active neutrinos of degenerate mass ( ${\tilde{N}}_{eff} = 4$ , ${\tilde{M}}_{ν} = 0.4 eV$ ). The cosmological parameters of $M$ and $\tilde{M}$ are fixed according to (6) and (7). At any given redshift, indicated by different colors in the figure, deviations in the corresponding power spectra are all within 1% (comparable to those obtained from linear theory), validating our analytic remapping also in the nonlinear regime.
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Figure 4
Sensitivity of the $Ly α$ flux power spectrum to a variation in $N_{eff}$ . Assuming a central reference value $N_{eff} = 3$ , the diagram illustrates that a change $Δ N_{eff} = \pm 1$ in $N_{eff}$ (solid or dotted lines in the figure, respectively) produces a global change in the $Ly α$ flux up to 3% at the representative redshifts considered, more significant than the uncertainty associated with our simulations or with our dark radiation approximation [Eqs. (6)–(8)].
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Figure 5
Joint constraints on the number of effective neutrino species $N_{eff}$ and the total neutrino mass $\sum m_{ν}$ , obtained from different cosmological probes. Red contours refer to the combination of $CMB + Ly α$ data, while green contours include additional information from BAOs; in the first case we obtain $N_{eff} = 2.9 1_{- 0.22}^{+ 0.21}$ and $\sum m_{ν} < 0.15 eV$ , while in the second $N_{eff} = 2.88 \pm 0.20$ and $\sum m_{ν} < 0.14 eV$ —all at 95% C.L. Our results exclude the possibility of a sterile neutrino—thermalized with active neutrinos—at a significance of over $5 σ$ , and provide strong evidence for the CNB from $N_{eff} \sim 3$ —as $N_{eff} = 0$ is rejected at more than $14 σ$ .
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