http://arxiv.org/abs/1911.07855
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.
A. Hall
Wed, 20 Nov 19
65/73
Comments: 20 pages, 9 figures. Submitted to Physical Review D
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