Observational bounds on the cosmic radiation density

TL;DR

This work probes the cosmic radiation density through the effective number of neutrino species $N_{\rm eff}$ using a broad set of cosmological data and a careful Bayesian framework. By dissecting the impact of scale-dependent galaxy bias and Ly$\alpha$ forest normalization, the authors show that previous claims of high $N_{\rm eff}$ often arise from modeling choices rather than data demand. In a minimal model, $N_{\rm eff}$ is consistent with the standard value $N_{\rm eff}^0=3.046$ when Ly$\alpha$ is excluded and bias is properly handled, though Ly$\alpha$ data push $N_{\rm eff}$ higher due to normalization tensions. Extended models with neutrino masses, running spectral index, and a w parameter maintain consistency with $N_{\rm eff}\approx 3$ within uncertainties, and the study highlights the potential for Planck and LSST to achieve much tighter constraints, potentially revealing or ruling out additional relativistic species.

Abstract

We consider the inference of the cosmic radiation density, traditionally parameterised as the effective number of neutrino species N_eff, from precision cosmological data. Paying particular attention to systematic effects, notably scale-dependent biasing in the galaxy power spectrum, we find no evidence for a significant deviation of N_eff from the standard value of N_eff^0=3.046 in any combination of cosmological data sets, in contrast to some recent conclusions of other authors. The combination of all available data in the linear regime prefers, in the context of a ``vanilla+N_eff'' cosmological model, 1.1<N_eff<4.8 (95% C.L.) with a best-fit value of 2.6. Adding data at smaller scales, notably the Lyman-alpha forest, we find 2.2<N_eff<5.8 (95% C.L.) with 3.8 as the best fit. Inclusion of the Lyman-alpha data shifts the preferred N_eff upwards because the sigma_8 value derived from the SDSS Lyman-alpha data is inconsistent with that inferred from CMB. In an extended cosmological model that includes a nonzero mass for N_eff neutrino flavours, a running scalar spectral index and a w parameter for the dark energy, we find 0.8<N_eff<6.1 (95% C.L.) with 3.0 as the best fit.

Figures (4)

• Figure 1: The 1D marginal (red/solid) and profile (blue/dotted) posteriors with respect to $N_{\rm eff}$ for our minimal model, the data set WMAP+SDSS-DR2-lin and top hat prior $0.2 \leq h \leq 2.0$. The shaded regions are, from top to bottom, the Bayesian 68% central credible interval, the 68% minimum credible interval, and the $1\sigma$ interval derived from maximisation. The dashed vertical lines mark, from top to bottom, the posterior mean $\langle N_{\rm eff} \rangle$, the 1D marginal posterior mode $\hat{N}_{\rm eff}^{(1)}$, and the global best fit $\hat{N}_{\rm eff}$.
• Figure 2: The 2D marginal 68% and 95% allowed regions in the minimal model for $N_{\rm eff}$ and $Q_{\rm nl}$, using the data set WMAP+SDSS-DR2-Q+SNIa and prior 2. The horizontal dotted lines indicate the $1 \sigma$ range of the Gaussian prior $Q_{\rm nl}=10\pm5$.
• Figure 3: The 2D marginal 68% and 95% allowed regions in the minimal model for the indicated pairs of parameters. Plots in the left column use the All-Q+HST data set, while those in the right column include also Ly$\alpha$ (All-Q+Ly$\alpha$+HST).
• Figure 4: The 2D marginal 68% and 95% allowed regions in $\sum m_\nu$ and $N_{\rm eff}$ in the extended model vanilla+$N_{\rm eff}$+$f_\nu$+$\alpha_s$+$w$, using the data set All-Q+HST. The corresponding contours for the model vanilla+$N_{\rm eff}$+$^3f_\nu$+$\alpha_s$+$w$ are similar, but with a cut-off at $N_{\rm eff}=3$.