Constraints on Neutrino Mass and Light Degrees of Freedom in Extended Cosmological Parameter Spaces

TL;DR

The paper investigates how cosmological constraints on the effective number of neutrino species $N_\mathrm{eff}$ and the sum of neutrino masses $\sum m_\nu$ respond to extending the cosmological parameter space beyond $\Lambda$CDM, including curvature $\Omega_k$, running $\mathrm{d}n_s/\mathrm{d}\ln k$, primordial helium $Y_p$, and both late-time and early dark energy. Using MCMC analyses with WMAP7+SPT+BAO+H_0+Union2 data, the authors explore scenarios with inflation priors enforced or relaxed and project Planck Fisher forecasts for these parameters. They find a mild $\sim2.2\sigma$ hint for extra relativistic species in extended spaces, but $N_\mathrm{eff}$ tends toward the canonical value ($\sim3$) when allowing evolving dark energy and relaxing priors; the $\sum m_\nu$ constraint remains robust around $\lesssim1.2$ eV, increasing to $\sim2.0$ eV if $Y_p$ and early dark energy are free. Planck alone is predicted to detect extra relativistic species at ~4$\sigma$ and bound $\sum m_\nu$ to about 0.2 eV, highlighting its pivotal role in precisely probing neutrino physics from cosmology.

Abstract

From a combination of probes including the cosmic microwave background (WMAP7+SPT), Hubble constant (HST), baryon acoustic oscillations (SDSS+2dFGRS), and supernova distances (Union2), we have explored the extent to which the constraints on the effective number of neutrinos and sum of neutrino masses are affected by our ignorance of other cosmological parameters, including the curvature of the universe, running of the spectral index, primordial helium abundance, evolving late-time dark energy, and early dark energy. In a combined analysis of the effective number of neutrinos and sum of neutrino masses, we find mild (2.2 sigma) preference for additional light degrees of freedom. However, the effective number of neutrinos is consistent with the canonical expectation of 3 massive neutrinos and no extra relativistic species to within 1 sigma when allowing for evolving dark energy and relaxing the strong inflation prior on the curvature and running. The agreement improves with the possibility of an early dark energy component, itself constrained to be less than 5% of the critical density (95% CL) in our expanded parameter space. In extensions of the standard cosmological model, the derived amplitude of linear matter fluctuations sigma_8 is found to closely agree with low-redshift cluster abundance measurements. The sum of neutrino masses is robust to assumptions of the effective number of neutrinos, late-time dark energy, curvature, and running at the level of 1.2 eV (95% CL). The upper bound degrades to 2.0 eV (95% CL) when further including the early dark energy density and primordial helium abundance as additional free parameters. Even in extended cosmological parameter spaces, Planck alone could determine the possible existence of extra relativistic species at 4 sigma confidence and constrain the sum of neutrino masses to 0.2 eV (68% CL).

Figures (4)

• Figure 1: Joint two-dimensional marginalized constraints on $\sigma_8 (\Omega_m/0.25)^{0.47}$ against $\{N_\mathrm{eff}, \sum{m_{\nu}}\}$. The black confidence regions (inner 68%, outer 95%) are for the extended parameter combination "vanilla$+N_\mathrm{eff}$$+\sum{m_{\nu}}$$+w$$+\Omega_k$$+dn_s/d\ln k$" using the data from "WMAP7+SPT+$H_0$+BAO+SNe," while the vertical red lines denote the 68% confidence interval about the mean from the local ($0.025 < z < 0.25$) galaxy cluster abundance measurement of Vikhlinin et al. (2009) Vikhlinin:2008ym.
• Figure 2: Joint two-dimensional marginalized constraints (inner 68% CL, outer 95% CL) for the extended parameter combination "vanilla$+N_\mathrm{eff}$$+\sum{m_{\nu}}$$+w$$+\Omega_k$$+dn_s/d\ln k$," showing $N_\mathrm{eff}$ against $\{w, \Omega_c h^2, n_s\}$ and $\sum{m_{\nu}}$ against $\{w, \Omega_c h^2, N_\mathrm{eff}\}$. The purple shaded confidence regions are for "WMAP+SPT+$H_0$+BAO" and the regions enclosed by black lines are for "WMAP+SPT+$H_0$+BAO+SNe," where the BAOs and SNe are from SDSS+2dF and Union2, respectively. For Planck (T, E, $\phi$) in dashed white, we have centered the $1\sigma$ error ellipses on the fiducial values of the parameters that went into computing the Fisher matrix. The exception to this convention is $\sum{m_{\nu}}$, which we have shifted down to 0 eV from its fiducial value of 0.17 eV for simpler visual comparison with the upper bounds from present data.
• Figure 3: Same as Fig. \ref{['fig:nuw']}, but for $\Omega_k$ against $\{N_\mathrm{eff}, \sum{m_{\nu}}, dn_s/d\ln k\}$ and $dn_s/d\ln k$ against $\{N_\mathrm{eff}, \sum{m_{\nu}}, n_s\}$.
• Figure 4: Joint two-dimensional marginalized constraints on the early dark energy density $\Omega_e$ against $\{N_\mathrm{eff}, \sum{m_{\nu}}\}$ for the extended parameter combination "vanilla$+N_\mathrm{eff}$$+\sum{m_{\nu}}$$+w_0$$+\Omega_e$$+\Omega_k$$+dn_s/d\ln k$." The black confidence regions (inner 68%, outer 95%) are for "WMAP+SPT+$H_0$+BAO+SNe," while the forecasted $1\sigma$ error ellipses for Planck temperature, E-mode polarization, and lensing potential power spectra (T, E, $\phi$) are shown in dashed red. Although the Fisher matrix constraints on the parameters $\{\sum{m_{\nu}}, \Omega_e\}$ were evaluated at $\{0.17~{\rm{eV}}, 0.01\}$, they have been shifted down to $\{0, 0\}$ for simpler visual comparison with the upper bounds from present data.