Tests of Neutrino and Dark Radiation Models from Galaxy and CMB surveys

We analyze the ability of galaxy and CMB lensing surveys to constrain massive neutrinos and new models of dark radiation. We present a Fisher forecast analysis for neutrino mass constraints with the LSST galaxy survey and the CMB S4 survey. A joint analysis of the three galaxy and shear 2-point functions, along with key systematics parameters and Planck priors, constrains the neutrino masses to $\sum m_\nu = 0.041\,$eV at 1-$\sigma$ level, comparable to constraints expected from Stage 4 CMB lensing. If low redshift information from upcoming spectroscopic surveys like DESI is included, the constraint becomes $\sum m_\nu = 0.032\,$eV. These constraints are derived having marginalized over the number of relativistic species ($N_{\rm eff}$), which is somewhat degenerate with the neutrino mass. We also explore the gain by combining LSST and CMB S4, that is, using the five relevant auto- and cross-correlations of the two datasets. We conclude that advances in modeling the nonlinear regime and the measurements of other parameters are required to ensure a neutrino mass detection. Using the same datasets, we explore the ability of LSST-era surveys to test "nonstandard" models with dark radiation. We find that if evidence for dark radiation is found from $N_{\rm eff}$ measurements, the mass of the dark radiation candidate can be measured at a 1-$\sigma$ level of $0.162\,$eV for fermionic dark radiation, and $0.137\,$eV for bosonic dark radiation, for $\Delta N_{\rm eff} = 0.15$. We also find that the NNaturalness model of Arkani-Hamed et al 2016, with extra light degrees of freedom, has a sub-percent effect on the power spectrum: even more ambitious surveys than the ones considered here will be needed to test such models.