The impact of relativistic effects on cosmological parameter estimation
  Future surveys will access large volumes of space and hence very long
wavelength fluctuations of the matter density and gravitational field. It has
been argued that the set of secondary effects that affect the galaxy
distribution, relativistic in nature, will bring new, complementary
cosmological constraints. We study this claim in detail by focusing on a subset
of wide-area future surveys: Stage-4 cosmic microwave background experiments
and photometric redshift surveys. In particular, we look at the magnification
lensing contribution to galaxy clustering and general relativistic corrections
to all observables. We quantify the amount of information encoded in these
effects in terms of the tightening of the final cosmological constraints as
well as the potential bias in inferred parameters associated with neglecting
them. We do so for a wide range of cosmological parameters, covering neutrino
masses, standard dark-energy parametrizations and scalar-tensor gravity
theories. Our results show that, while the effect of lensing magnification to
number counts does not contain a significant amount of information when galaxy
clustering is combined with cosmic shear measurements, this contribution does
play a significant role in biasing estimates on a host of parameter families if
unaccounted for. Since the amplitude of the magnification term is controlled by
the slope of the source number counts with apparent magnitude, $s(z)$, we also
estimate the accuracy to which this quantity must be known to avoid systematic
parameter biases, finding that future surveys will need to determine $s(z)$ to
the $\sim$5-10\% level. On the contrary, large-scale general-relativistic
corrections are irrelevant both in terms of information content and parameter
bias for most cosmological parameters, but significant for the level of
primordial non-Gaussianity.
