Density Weighted Angular Redshift Fluctuations: a New Cosmological
  Observable
  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.
