Fisher matrix for the angular power spectrum of multi-tracer galaxy surveys

Abstract Redshift evolution and peculiar velocities break the isotropy of cosmological surveys with respect to directions parallel transverse line sight, limiting accuracy Fourier representation small areas redshift ranges. In contrast space power spectrum, full information about two-point function tracers large-scale structure is encapsulated in redshift-dependent angular spectrum C ij ℓ ( z i , j ) for tracer species at slices expressed harmonic space. this paper we derive semi-analytical expressions multi-tracer Fisher matrix spectra, real space, which are exact linear regime formation. Our can be used forecast constraining galaxy many a large number slices, derivation from numerically evaluated covariance matrices may not feasible or practical.