The impact of our local environment on cosmological statistics. (arXiv:1911.07855v1 [astro-ph.CO])
<a href="http://arxiv.org/find/astro-ph/1/au:+Hall_A/0/1/0/all/0/1">Alex Hall</a>
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.
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.
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