Constraints on dark radiation from cosmological probes

TL;DR

This study jointly constrains the effective number of neutrino species $N_{ m eff}$ and the sum of neutrino masses $\sum m_{\\nu}$ by exploiting the full one-dimensional Ly$\\alpha$ forest flux power spectrum, complemented by CMB and BAO data. A suite of hydrodynamical simulations with massive neutrinos, together with a Taylor-expanded, simulation-backed Ly$\\alpha$ model, underpins a frequentist multidimensional likelihood that is extended to non-standard dark radiation via an analytic remapping. The resulting constraints yield $N_{ m eff} = 2.91^{+0.21}_{-0.22}$ and $\sum m_{\\nu} < 0.15$ eV (95% CL) with CMB+Ly$\\alpha$, and $N_{ m eff} = 2.88 \pm 0.20$ and $\sum m_{\\nu} < 0.14$ eV (95% CL) when BAO is added, effectively ruling out a fully thermalized sterile neutrino ($N_{ m eff}=4$) at $>5\sigma$ and providing strong evidence for the Cosmic Neutrino Background. These results support the minimal $\Lambda$CDM model without requiring extra relativistic degrees of freedom and illustrate the power of Ly$\\alpha$ data to break degeneracies in neutrino parameter space when combined with CMB measurements.

Abstract

We present joint constraints on the number of effective neutrino species N_eff and the sum of neutrino masses M_nu, based on a technique which exploits the full information contained in the one-dimensional Lyman-Alpha forest flux power spectrum, complemented by additional cosmological probes. In particular, we obtain N_eff=2.91(+0.21)(-0.22) (95% CL) and M_nu<0.15 eV (95% CL) when we combine BOSS Lyman-Alpha forest data with CMB (Planck+ACT+SPT+WMAP polarization) measurements, and N_eff=2.88(+0.20)(-0.20) (95% CL) and M_nu<0.14 eV (95% CL) when we further add baryon acoustic oscillations. Our results provide evidence for the Cosmic Neutrino Background from N_eff~3 (N_eff=0 is rejected at more than 14 sigma), 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 Delta N_eff ~ 1 - at a significance of over 5 sigma, the strongest bound to date, implying that there is no need for exotic neutrino physics in the concordance LCDM model.

Figures (5)

• Figure 1: Linear theory test of the accuracy of our analytic approximation to include non-standard dark radiation models. [Left] Linear matter power spectra for a series of models $\tilde{\mathcal{M}}$ having $\Delta N_{\rm eff}=1$ at $z=3$ (chosen as a representative central value for the redshift range considered in this study), normalized by the baseline model $\mathcal{M}$ with $N_{\rm eff}=3.046$ and three active neutrinos of degenerate mass, when $M_{\rm \nu}=0.3$ 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$\alpha$ likelihood.
• Figure 2: Snapshots at $z=3$ from simulations with a canonical value of $N_{\rm eff}$ (left panels), and when $N_{\rm eff}=4$ (right panels). The two cosmologies are related by our analytic remapping: $\tilde{M}_{\rm \nu}=0.35$ eV for the baseline model, while $\tilde{M}_{\rm \nu}=0.4$ eV for the non-standard 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 $25~h^{-1}{\rm Mpc}$ box size and a resolution $N_{\rm p}=192^3$ 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 (\ref{['eq3']}-\ref{['eq5']}) 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.
• Figure 3: Ratios of synthetic one-dimensional Ly$\alpha$ flux power spectra extracted from a baseline model $\cal{M}$ having three degenerate massive neutrinos and no extra relativistic degrees of freedom ($N_{\rm eff}=3$, $M_{\rm \nu}=0.35$ eV), and from a non-standard dark radiation model $\tilde{\cal{M}}$ characterized by a massless sterile neutrino and three active neutrinos of degenerate mass ($\tilde{N}_{\rm eff}=4$, $\tilde{M}_{\rm \nu}=0.4$ eV). The cosmological parameters of $\cal{M}$ and $\tilde{\cal{M}}$ are fixed according to (\ref{['eq3']}) and (\ref{['eq4']}). 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.
• Figure 4: Sensitivity of the Ly$\alpha$ flux power spectrum to a variation in $N_{\rm eff}$. Assuming a central reference value $N_{\rm eff}=3$, the diagram illustrates that a change $\Delta N_{\rm eff} = \pm 1$ in $N_{\rm eff}$ (solid or dotted lines in the figure, respectively) produces a global change in the Ly$\alpha$ flux up to 3% at the representative redshifts considered, more significant than the uncertainty associated with our simulations or with our dark radiation approximation (Eqns. \ref{['eq3']}-\ref{['eq5']}).
• Figure 5: Joint constraints on the number of effective neutrino species $N_{\rm eff}$ and the total neutrino mass $\sum m_{\rm \nu}$, obtained from different cosmological probes. Red contours refer to the combination of CMB+Ly$\alpha$ data, while green contours include additional information from BAOs; in the first case we obtain $N_{\rm eff}= 2.91^{+ 0.21}_{- 0.22}$ and $\sum m_{\rm \nu} <0.15$ eV, while in the second $N_{\rm eff}= 2.88 \pm 0.20$ and $\sum m_{\rm \nu} <0.14$ eV -- all at 95% CL. Our results exclude the possibility of a sterile neutrino -- thermalized with active neutrinos -- at a significance of over 5 $\sigma$, and provide strong evidence for the CNB from $N_{\rm eff}\sim 3$ -- as $N_{\rm eff} = 0$ is rejected at more than $14~\sigma$.