Testing standard and nonstandard neutrino physics with cosmological data

Cosmological constraints on the sum of neutrino masses and on the effective number of neutrino species in standard and nonstandard scenarios are computed using the most recent available cosmological data. Our cosmological data sets include the measurement of the baryonic acoustic oscillation (BAO) feature in the data release 9 CMASS sample of the baryon oscillation spectroscopic survey. We study in detail the different degeneracies among the parameters, as well as the impact of the different data sets used in the analyses. When considering bounds on the sum of the three active neutrino masses, the information in the BAO signal from galaxy clustering measurements is approximately equally powerful as the shape information from the matter power spectrum. The most stringent bound we find is $\sum _{}^{}{m}_{\nu }<0.32\mathrm{eV}$ at 95% C.L. When nonstandard neutrino scenarios with $N_{\mathrm{eff}}$ massless or massive neutrino species are examined, power spectrum shape measurements provide slightly better bounds than the BAO signal only, due to the breaking of parameter degeneracies. Cosmic microwave background data from high multipoles from the South Pole Telescope turns out to be crucial for extracting the number of effective neutrino species. Recent baryon oscillation spectroscopic survey data combined with cosmic microwave background and Hubble Space Telescope measurements give $N_{\mathrm{eff}}={3.66}_{-0.21-0.69}^{+0.20+0.73}$ in the massless neutrino scenario, and similar results are obtained in the massive case. The evidence for extra radiation $N_{\mathrm{eff}}>3$ often claimed in the literature therefore remains at the $2\sigma$ level when considering up-to-date cosmological data sets. Measurements from the Wilkinson Microwave Anisotropy Probe combined with a prior on the Hubble parameter from the Hubble Space Telescope are very powerful in constraining either the sum of the three active neutrino masses or the number of massless neutrino species. If the former two parameters are allowed to freely vary, however, the bounds from the combination of these two cosmological probes get worse by an order of magnitude.

Figure 1

The largest red contours show the 68% and 95% C.L. constraints in the $(\sum _{}^{}{m}_{\nu },H_0)$ plane from our basic WMAP data set. The smallest blue contours show the results from the combination of WMAP and HST data, while the green contours depict the results from the combination of WMAP and SNLS3 data sets. Notice that the strong degeneracy present in the case of WMAP data alone gets alleviated when a prior on ${\mathrm{H}}_0$ from HST data is added in the analysis. SNIa luminosity distance data are unable to independently determine the Hubble constant $H_0$ but measure the ${\Omega }_m$ quantity, and, since WMAP measures ${\Omega }_m{h}^2$, the combination of WMAP plus SNIa data is able to determine $H_0$.

Figure 2

The largest red contours show the 68% and 95% C.L. constraints in the $(\sum _{}^{}{m}_{\nu },{\Omega }_m)$ plane from WMAP plus HST data sets. The blue contours show the results from the combination of WMAP, HST, and galaxy clustering measurements from SDSS-II interpreted in the form of BAO signals, while the smallest green contours depict the results from the combination of WMAP, HST, and ${\mathrm{BAO}}_{2012}$ data sets. The errors on the ${\Omega }_m$ parameter are significantly improved when considering either the SDSS-II BAO or the ${\mathrm{BAO}}_{2012}$ measurements. Also, due to the higher mean value of ${\Omega }_m$ when adding BAO information to the WMAP and HST measurements, a slightly higher neutrino mass is allowed.

Figure 3

Left panel: The largest yellow contours show the 68% and 95% C.L. constraints in the $(N_{\mathrm{eff}},\sum _{}^{}{m}_{\nu })$ plane from our basic WMAP data set combined with old BAO data. The blue contours show the results from the combination of WMAP, SPT, and HST measurements, while the red contours depict the results from the combination of WMAP, SPT, and SNLS3 measurements. Finally, the green contour denotes the constraints from the combination of WMAP, SPT, SNLS3, and BAO data. Right panel: As in the left panel but using recent ${\mathrm{BAO}}_{2012}$ data. The red and green contours are almost identical.