Robustness of cosmic neutrino background detection in the cosmic microwave background

TL;DR

This work tests the robustness of cosmological evidence for the cosmic neutrino background by generalizing neutrino perturbation properties through the effective parameters $c_ ext{eff}^2$ and $c_ ext{vis}^2$, extending the framework to massive neutrinos and several extended cosmologies. By implementing these phenomenological parameters in the Boltzmann hierarchy and performing MCMC analyses on Planck, lensing, and BAO data across multiple model variants, the authors show that current bounds on $c_ ext{eff}^2$ and $c_ ext{vis}^2$ remain close to the standard values $(1/3,1/3)$ even when neutrino masses are nonzero or when $N_ ext{eff}$, dynamical dark energy, or a running spectral tilt are allowed. Importantly, they find no significant degeneracy between $(c_ ext{eff}^2,c_ ext{vis}^2)$ and the total neutrino mass $M_ u$, and extended cosmologies only weakly affect these parameters, preserving a robust detection of the cosmic neutrino background. The study also reveals that $c_ ext{eff}^2$ primarily modulates the small-scale matter power spectrum while $c_ ext{vis}^2$ has a subtler effect, suggesting that future large-scale structure measurements and polarization data could further sharpen these constraints and help disentangle residual degeneracies. Overall, the results solidify the interpretation that CMB observations robustly require neutrino perturbations consistent with the standard cosmological model, while outlining avenues for refinement with upcoming data and momentum-dependent generalizations.

Abstract

The existence of a cosmic neutrino background can be probed indirectly by CMB experiments, not only by measuring the background density of radiation in the universe, but also by searching for the typical signatures of the fluctuations of free-streaming species in the temperature and polarisation power spectrum. Previous studies have already proposed a rather generic parametrisation of these fluctuations, that could help to discriminate between the signature of ordinary free-streaming neutrinos, or of more exotic dark radiation models. Current data are compatible with standard values of these parameters, which seems to bring further evidence for the existence of a cosmic neutrino background. In this work, we investigate the robustness of this conclusion under various assumptions. We generalise the definition of an effective sound speed and viscosity speed to the case of massive neutrinos or other dark radiation components experiencing a non-relativistic transition. We show that current bounds on these effective parameters do not vary significantly when considering an arbitrary value of the particle mass, or extended cosmological models with a free effective neutrino number, dynamical dark energy or a running of the primordial spectrum tilt. We conclude that it is possible to make a robust statement about the detection of the cosmic neutrino background by CMB experiments.

Figures (7)

• Figure 1: Neutrino density perturbations as a function of scale factor for a $\Lambda$CDM model with massless neutrinos (top panels), three degenerate neutrinos with $m_{\nu}=0.02$ eV each (middle panels), and $m_{\nu}=0.10$ eV (bottom panels). All panels show the evolution of the perturbations for a fixed scale of 0.03 Mpc$^{-1}$. Solid black lines show a reference model with $c^2_{\rm eff}=c^2_{\rm vis}=1/3$. In the left panels, solid red lines and dashed red lines correspond to $c^2_{\rm eff}=0.36$ and $0.30$ respectively, whereas in the right panels solid blue lines and dashed blue lines correspond to $c^2_{\rm vis} = 0.36$ and $0.30$ respectively. For reference, the evolution of the ratios of the gravitational potentials are shown for every case.
• Figure 2: CMB power spectrum multipoles for the temperature (left column) and $E$-mode polarisation (right column) for a $\Lambda$CDM model with massless neutrinos (top panels), and three degenerate neutrinos with $m_{\nu}=0.10$ eV (bottom panels). All models are normalised to a reference model with $c^2_{\rm eff}=c^2_{\rm vis}=1/3$. Solid red lines and dashed red lines correspond to a $c^2_{\rm eff}$ of $0.36$ and $0.30$ respectively, whereas solid blue lines and dashed blue lines correspond to a $c^2_{\rm vis}$ of $0.36$ and $0.30$ respectively. Top and bottom panels are almost identical, showing that the relative effect of $(c_\mathrm{eff}^2$, $c_\mathrm{vis}^2)$ is independent of neutrino masses.
• Figure 3: Matter power spectrum for a $\Lambda$CDM model with massless neutrinos (left panel) and three degenerate neutrinos with $m_{\nu}=0.10$ eV each (right panel). All models are normalised to a reference model with $c^2_{\rm eff}=c^2_{\rm vis}=1/3$. Solid red lines and dashed red lines correspond to $c^2_{\rm eff}=0.36$ and $0.30$ respectively, whereas solid blue lines and dashed blue lines correspond to $c^2_{\rm vis}=0.36$ and $0.30$ respectively. These two plots are almost identical, showing that the relative effect of $(c_\mathrm{eff}^2$, $c_\mathrm{vis}^2)$ is independent of neutrino masses.
• Figure 4: Degeneracies between the parameters $(c^2_{\rm vis}, c^2_{\rm eff})$ and the parameters $\omega_b$, $\omega_{cdm}$, $A_s$ and $n_s$. A combination of CMB+lensing data is used for this plot, in which a $\Lambda$CDM+$c^2_{\rm vis}{+}c^2_{\rm eff}$ model is assumed. Dashed lines correspond to the standard values $(c_{\rm eff}^2, c_{\rm vis}^2)=(1/3, 1/3)$.
• Figure 5: Left. Constraints in the ($c^2_{\rm vis}, c^2_{\rm eff}$) plane for combination of CMB, CMB+lensing and CMB+lensing+BAO data, in the $\Lambda$CDM+ $c^2_{\rm vis}+c^2_{\rm eff}$ model. Marginalised posterior distributions for both parameters are also shown. Right. Constraints on $(c^2_{\rm vis}$, $c^2_{\rm eff})$ and the total neutrino mass $M_\nu$ for CMB and CMB+lensing datasets in the $\Lambda$CDM+$c^2_{\rm vis}{+}c^2_{\rm eff}{+}m_{\nu}$ model. Dashed lines correspond to the standard values $(c_{\rm eff}^2, c_{\rm vis}^2)=(1/3, 1/3)$.