Density Weighted Angular Redshift Fluctuations: a New Cosmological Observable

Abstract

We propose the use of angular fluctuations in the galaxy redshift field as a new way to extract cosmological information in the Universe. This new probe $\delta z(\hat{n})$ consists on the statistics of sky maps built by projecting redshifts under a Gaussian window of width ${\sigma }_z$ centred upon a redshift $z_{\mathrm{obs}}$, and weighted by the galaxy density field. We compute the angular power spectrum of the $\delta z(\hat{n})$ field in both numerical simulations and in linear perturbation theory. From these we find that the $\delta z(\hat{n})$ field: {\it (i)} is sensitive to the underlying density and peculiar velocity fields; {\it (ii)} is highly correlated, at the $\gtrsim 60\%$ level, to the line-of-sight projected peculiar velocity field; {\it (iii)} for narrow windows $({\sigma }_z<0.03$), it is almost completely uncorrelated to the projected galaxy angular density field under the same redshift window; and {\it (iv)} it is largely unaffected by multiplicative and additive systematic errors on the observed number of galaxies that are redshift-independent over $\sim {\sigma }_z$. We conclude that $\delta z(\hat{n})$ is a simple and robust tomographic measure of the cosmic density and velocity fields, complementary to angular clustering, that will contribute to more complete exploitations of current and upcoming galaxy redshift surveys.

arXiv comment6 pages, 3 figures, matches accepted version in MNRAS letters, companion paper of Chaves-Montero et al., arXiv:1911.10690

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