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 $M_\nu$. 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 $M_\nu$, 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 $M_\nu$. 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 $M_\nu$ 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.
