Neutrino mass constraints beyond linear order: cosmology dependence and systematic biases

We demonstrate the impact on forecasted neutrino mass constraints of extending galaxy clustering and CMB lensing predictions from linear to next-to-leading-order power spectra. The redshift-space 1-loop power spectrum model we adopt requires an additional four free bias parameters, a velocity bias parameter and two new stochastic parameters. These additional nuisance parameters appreciably weaken the constraints on $M_ u$. CMB lensing plays a significant role in helping to alleviate these degeneracies and tighten the final constraints. The constraint on the optical depth to reionisation $tau$ has a strong effect on the constraint on $M_ u$, but only when CMB lensing is included in the analysis to keep the degeneracies with the nuisance parameters under control. We also extract constraints when 1) using the BAO signature only as a distance probe, and 2) isolating the scale-dependence of the power spectrum, which, as shown in previous work, provides a cosmology-independent probe of $M_ u$. All constraints except the latter remain strongly sensitive to the assumption of a flat $Lambda$CDM universe. We perform an analysis of the magnitude of the shift introduced in the inferred $M_ u$ value when neglecting nonlinear corrections, and show that, for a Euclid-like survey, this shift becomes roughly equal to the 1$sigma$ constraint itself even with a conservative cut-off scale of $k_{max} = 0.1~h~{rm Mpc}^{-1}$. We also perform a calculation of the appropriate expected bias in neutrino mass caused by not including the next, 2-loop order and expect a shift of only about 20% of the 1$sigma$ error for $k_{max}=0.2~h~{rm Mpc}^{-1}$ in a Euclid-like survey.