Impact of our local environment on cosmological statistics
  We conduct a thorough investigation into the possibility that residing in an
overdense region of the Universe may induce bias in measurements of the
large-scale structure. We compute the conditional correlation function and
angular power spectrum of density and lensing fluctuations while holding the
local spherically averaged density fixed and show that for Gaussian fields this
has no effect on the angular power at $l>0$. We identify a range of scales
where a perturbative approach allows analytic progress to be made, and we
compute leading-order conditional power spectra using an Edgeworth expansion
and second-order perturbation theory. We find no evidence for any significant
bias to cosmological power spectra from our local density contrast. We show
that when smoothed over a large region around the observer, conditioning on the
local density typically affects density power spectra by less than a percent at
cosmological distances, below cosmic variance. We find that while typical
corrections to the lensing angular power spectrum can be at the 10% level on
the largest angular scales and for source redshifts $z_s \lesssim 0.1$, for the
typical redshifts targeted by upcoming wide imaging surveys the corrections are
sub-percent and negligible, in contrast to previous claims in the literature.
Using an estimate of the local spherically averaged density from a composite
galaxy redshift catalogue we find that the corrections from conditioning on our
own local density are below cosmic variance and subdominant to other non-linear
effects. We discuss the potential implications of our results for cosmology and
point out that a measurement of the local density contrast may be used as a
consistency test of cosmological models.
