High resolution tomography for galaxy spectroscopic surveys with angular redshift fluctuations

In the context of next-generation spectroscopic galaxy surveys, new statistics of the distribution of matter are currently being developed. Among these, we investigated the angular redshift fluctuations (ARF), which probe the information contained in the projected redshift distribution of galaxies. Relying on the Fisher formalism, we show how ARF will provide complementary cosmological information compared to traditional angular galaxy clustering. We tested both the standard $\mathrm{\Lambda CDM}$ model and the $\mathrm{wCDM}$ extension. We find that the cosmological and galaxy bias parameters express different degeneracies when inferred from ARF or from angular galaxy clustering. As such, combining both observables breaks these degeneracies and greatly decreases the marginalised uncertainties by a factor of at least two on most parameters for the $\mathrm{\Lambda CDM}$ and $\mathrm{wCDM}$ models. We find that the ARF combined with angular galaxy clustering provide a great way to probe dark energy by increasing the figure of merit of the $w_0$-$w_{\rm a}$ parameter set by a factor of more than ten compared to angular galaxy clustering alone. Finally, we compared ARF to the CMB lensing constraints on the galaxy bias parameters. We show that a joint analysis of ARF and angular galaxy clustering improves constraints by $\sim 40\%$ on galaxy bias compared to a joint analysis of angular galaxy clustering and CMB lensing.