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 $z_{\rm obs}$, 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.