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

Minor changes. Matches version published in JCAP

References in corpus (11)

• The imprints of primordial non-gaussianities on large-scale structure: scale dependent bias and abundance of virialized objects
• Extended Limber Approximation
• Cosmological baryonic and matter densities from 600,000 SDSS Luminous Red Galaxies with photometric redshifts
• Spectral estimation on a sphere in geophysics and cosmology
• Shear Power Spectrum Reconstruction using Pseudo-Spectrum Method
• Lifting weak lensing degeneracies with a field-based likelihood
• Disantangling the effects of Doppler velocity and primordial non-Gaussianity in galaxy power spectra
• Extracting cosmological information from the angular power spectrum of the 2MASS Photometric Redshift catalogue
• On the accuracy and precision of correlation functions and field-level inference in cosmology
• SuperFaB: a fabulous code for Spherical Fourier-Bessel decomposition
• Euclid: Covariance of weak lensing pseudo-$C_{\ell }$ estimates. Calculation, comparison to simulations, and dependence on survey geometry