Future galaxy surveys (whether space-based, like Euclid and the Roman Space Telescope, or ground-based like the Rubin Observatory’s LSST) will provide an unprecedented amount of data regarding the distribution of galaxies. This distribution encodes significant cosmological information, including neutrino mass and the nature of dark energy. However, the very power of these surveys can become problematic, in that they will probe scales (below 10 Mpc/h) on which the standard analysis techniques (using the galaxy power spectrum) are blind to significant portions of the cosmological information inherent in the data. This work develops two categories of tools for decoding this hidden information.
First, it applies the theory of sufficient statistics to galaxy surveys, providing prescriptions for these statistics, which one can then fit to observations. In particular, it provides, for any near-concordance cosmology, prescriptions for (a) the sufficient-statistics dark matter power spectrum, (b) the matter probability distribution function, and (c) the sufficient statistics galaxy power spectrum. Second, it pioneers techniques for fitting cosmological models to counts-in-cells (CIC) galaxy probability distributions; in particular, it (a) proposes and validates a galaxy bias model applicable to scales as small as 2 Mpc/h, (b) determines values for otherwise-degenerate parameters (sigma8 and galaxy bias) by fitting to observed CIC in SDSS data, and (c) derives and verifies formulae for the CIC covariance matrix.
Together, these tools allow maximally efficient extraction of cosmological information from the data returned by future galaxy surveys.