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We demonstrate the impact on forecasted neutrino mass constraints ofextending galaxy clustering and CMB lensing predictions from linear tonext-to-leading-order power spectra. The redshift-space 1-loop power spectrummodel we adopt requires an additional four free bias parameters, a velocitybias parameter and two new stochastic parameters. These additional nuisanceparameters appreciably weaken the constraints on $M_\nu$. CMB lensing plays asignificant role in helping to alleviate these degeneracies and tighten thefinal constraints. The constraint on the optical depth to reionisation $\tau$has a strong effect on the constraint on $M_\nu$, but only when CMB lensing isincluded in the analysis to keep the degeneracies with the nuisance parametersunder control. We also extract constraints when 1) using the BAO signature onlyas a distance probe, and 2) isolating the scale-dependence of the powerspectrum, which, as shown in previous work, provides a cosmology-independentprobe of $M_\nu$. All constraints except the latter remain strongly sensitiveto the assumption of a flat $\Lambda$CDM universe. We perform an analysis ofthe magnitude of the shift introduced in the inferred $M_\nu$ value whenneglecting nonlinear corrections, and show that, for a Euclid-like survey, thisshift becomes roughly equal to the 1$\sigma$ constraint itself even with aconservative cut-off scale of $k_{max} = 0.1~h~{\rm Mpc}^{-1}$. We also performa calculation of the appropriate expected bias in neutrino mass caused by notincluding the next, 2-loop order and expect a shift of only about 20% of the1$\sigma$ error for $k_{max}=0.2~h~{\rm Mpc}^{-1}$ in a Euclid-like survey.

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