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 $sum m_ u = 0.041,$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 $sum m_ u = 0.032,$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.
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