http://arxiv.org/abs/1911.12056

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 consists on the statistics of sky maps built by projecting redshifts under a Gaussian window of mean $z_{\rm obs}$ and width $\sigma_z$; $z(\hat{\mbox{n}}) = \bar{z}+\sum_{j\in \hat{\mbox{n}}} W_j (z_j-\bar{z}) / \langle \sum_i W_i \rangle= \bar{z} + \delta z (\hat{\mbox{n}})$, with $z_j$ and $W_j$ the redshift and the Gaussian weight, respectively, for the $j$-th galaxy falling on the pixel along sky direction $\hat{\mbox{n}}$, $\bar{z}=\sum_i W_i z_i / \sum_i W_i$ is the average redshift under the Gaussian shell, and the $\langle … \rangle$ brackets denote an angular average over the entire footprint. We compute the angular power spectrum of the $\delta z (\hat{\mbox{n}})$ field in both numerical simulations and in linear perturbation theory. From these we find that the $\delta z (\hat{\mbox{n}})$ 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 $\delta z (\hat{\mbox{n}})$ is a simple and robust tomographic measure of the cosmic density and velocity fields, complementary to angular clustering, that will contribute to a more complete exploitation of current and upcoming galaxy redshift surveys.

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C. Hernandez-Monteagudo, J. Chaves-Montero and R. Angulo
Thu, 28 Nov 19
4/70

Comments: 5 pages, 3 figures, to be (re-)submitted to PRL shortly, companion paper of Chaves-Montero et al., arXiv:1911.10690