Are priors responsible for cosmology favoring additional neutrino species?

TL;DR

Problem: determine whether cosmology truly requires an extra relativistic degree of freedom, $N_{ m eff}$, beyond the standard value $N_{ m eff}=3.04$. Approach: a prior-independent assessment using profile likelihoods derived from CosmoMC outputs across multiple datasets (including WMAP7, BAO, LRG, SN, ACT/ACBAR) with $Y_P$ fixed and a flat $H_0$ prior. Contributions: finds that while the maximum likelihood favors $ {Delta}N_{ m eff}>0$, $ {Delta}N_{ m eff}=0$ is always within the 95.4% interval, and no robust evidence for extra species emerges from the profile likelihood, indicating prior-volume effects in some marginalized posteriors. Significance: provides a robust, prior-independent framework for cosmological constraints on $N_{ m eff}$ and argues that current data do not support additional neutrino species; advocates using generalized likelihood ratio as a standard check as data improve.

Abstract

It has been suggested that both recent cosmological data and the results of flavor oscillation experiments (MiniBooNE and LSND) lend support to the existence of low-mass sterile neutrinos. The cosmological data appear to weakly favor additional forms of radiation in the Universe, beyond photons and three standard neutrino families. We reconsider the cosmological evidence by making the resulting confidence intervals on the additional effective neutrino species as prior-independent as possible. We find that, once the prior-dependence is removed, the latest cosmological data show no evidence for deviations from the standard number of neutrino species.

Figures (4)

• Figure 1: One and two $\sigma$ constraints on the number of additional neutrino species from several datasets including combinations of WMAP7, LRG, BAO and SN. Note that the value corresponding to no extra species, $\Delta N_{\rm eff} =0$, is always well within the 2-$\sigma$ interval and always very close to the 1-$\sigma$ interval.
• Figure 2: As an illustrative example we show the probability curve obtained from the profile likelihood ratio for the data combination WMAP+LRG. The curve is jagged because of the binning procedure used to compute the profile likelihood. We have checked that changing the bin size (within reason) only slightly changes the shape of the curve and does not change the inferred confidence regions.
• Figure 3: Overview of one and two $\sigma$ constraints on extra number of neutrino species from several dataset combinations involving WMAP7 in combination with higher resolution CMB experiments. Note that the point corresponding to no additional relativistic species, $\Delta N_{\rm eff} =0$, is always well within the 2-$\sigma$ interval and in few cases within the 1-$\sigma$ interval. the fact that all constraints seems to be systematically shifted (although by less than 1-$\sigma$) towards $\Delta N_{\rm eff} >0$ is due to the fact that these are not independent constraints: the WMAP data, which has a lot of statistical power, is common to all combinations of datasets.
• Figure 4: As an illustrative example we show the probability curve obtained from the profile likelihood ratio for one of the data combinations.