Projected Angular Statistics for Large-scale Structure Cosmology

Abstract

The large-scale structure (LSS) in the distribution of matter is an important probe for us to understand the universe. Being complementary to the cosmic microwave background (CMB) radiation, the LSS enhances the constraints on the properties of dark matter and dark energy, modified gravity and primordial non- Gaussianity. Galaxy surveys measure (sometimes approximate) redshifts and angular positions of galaxies, which trace the LSS. The natural observables are maps of the galaxy overdensity, projected in redshift bins. Similarly, line-intensity mapping (LIM) surveys measure fluctuations in the sky brightness in narrow frequency bands. This thesis considers the statistics of such projected observables, spanning theoretical modelling, simulation and data analysis. In the first original chapter, we develop a novel approach to approximate the calculation of the full-sky angular power spectra of galaxy clustering (with or without redshift-space distortions) and the weak lensing of galaxies and the CMB. The method makes use of flat-sky methods but includes integration over all line-of-sight wave-modes. With suitable geometrical recalibration, it is shown that this approach is highly accurate even at low spherical multipoles. The integration over the line-of-sight wave-modes is accelerated by applying the FFTLog algorithm to the 3D matter power spectrum; the resulting integrals can be evaluated analytically in terms of modified Bessel functions. We develop a Python code for computation of the angular power spectra with these techniques, which is substantially more efficient than any existing full-sky approach. We also carefully discuss the correspondence between our flat-sky approach and the full-sky methodology. In the second original chapter, we extend the flat-sky approach to the calculation of the tree-level angular bispectrum (or three-point function) of galaxy clustering, including redshift-space distortions. We extend the full-sky to flat-sky correspondence and derive approximate formulae for the angular bispectrum, which can be evaluated efficiently. On test cases, we find very good agreement with exact full-sky results, even at low multipoles, but with much-reduced computation times. In the final original chapter, we turn to LIM, specifically in the context of the SPHEREx mission. In the limit that the emission of the source galaxies in the relevant frequency range is dominated by a single line, LIM observations in a narrow frequency band can be related to the clustering of source galaxies in the corresponding narrow redshift interval. Our goal is to investigate the complications for cosmological interpretation of line-intensity mapping due to contamination from the continuum emission and other (interloper) lines of the source galaxies. To do so, we create a realistic simulation including all the signals and contaminants and to mimic the observed intensity maps from SPHEREx. We analyse these simulated data, finding that a principal component analysis effectively removes the continuum contamination to the angular power spectra allowing accurate recovery of the baryon-acoustic-oscillation features, which are important for constraining the properties of dark energy at high redshift.