Redshift weighted galaxy number counts
  In this paper we introduce the `redshift fluctuation' as a gauge-invariant
cosmological observable and give its fully relativistic expression at first
order in cosmological perturbation theory. In a detailed analysis of its
angular power spectrum, we study the relevance of different relativistic
contributions, and how it differs from the conventional observable galaxy
number count fluctuations. In order to investigate its utility for future
spectroscopic surveys, we perform Fisher forecasts for a Euclid-like and an
SKAII-like configuration, as examples. Particular focus is placed on the
dependence of the results on the size of the redshift bins and on the cutoff in
$\ell$ adopted in the analysis.
