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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