Improvement in techniques for understanding the large scale structure of the Universe - Gagrani, Praful (Kansas State University, 2018)
Part 1: The redshift-space bispectrum (three point statistics) of galaxies can be used to measure key cosmological parameters. In a homogeneous Universe, the bispectrum is a function of five variables and unlike its two point statistics counterpart -- the power spectrum, which is a function of only two variables -- is difficult to analyse unless the information is somehow reduced. The most commonly considered reduction schemes rely on computing angular integrals over possible orientations of the bispectrum triangle thus reducing it to sets of functions of only three variables describing the triangle shape. We use Fisher information formalism to study the information loss associated with this angular integration. We find that most of the information is in the azimuthal averages of the first three even multipoles. This suggests that the bispectrum of every configuration can be reduced to just three numbers (instead of a 2D function) without significant loss of cosmologically relevant information. Part 2: One way of enhancing the cosmological information extracted from the clustering of galaxies is by weighting the galaxy field. The most widely used weighting schemes assign weights to galaxies based on the average local density in the region and their bias with respect to the dark matter field. They are designed to minimize the fractional variance of the galaxy power-spectrum. We demonstrate that the currently used bias dependent weighting scheme can be further optimized for specific cosmological parameters. Part 3: Choice of the box-size of a cosmological simulation involves a crucial trade-off between accuracy and complexity. We use Lagrangian perturbation theory to study the effects of box size on the predicted power spectrum and Baryon Acoustic Oscillation ruler. We find that although the optimal size depends on the final redshift of evolution, in general, the 2-point statistics of relevant scales is fairly accurate for a simulation box-size of length greater than 1000 Mpc.
Keywords: Cosmology; Large scale structure; Statistics