Using galaxy surveys to understand the cosmological evolution

Forthcoming galaxy redshift surveys are to a large extent motivated by the desire to obtain data on galaxy clustering so as to more accurately quantify the accelerating expansion of the Universe and thereby provide insight into the mechanism responsible for acceleration. Currently suggested mechanisms are: a cosmological constant, a new scalar field that contributes to the energy budget of the Universe as dark energy, and modification on the cosmological scale of the law of gravitation. It is also possible that the accelerating expansion of the Universe may only be properly understood by an as yet undeveloped alternative to the standard cosmological model. Because the large-scale distribution of galaxies is expected to follow a gaussian random field - for which statistical information is fully encoded in 2-point statistics, the key quantities provided by redshift surveys are the correlation function and its Fourier space analogue, the power spectrum. The detection of features due to baryonic acoustic oscillations (BAO) in these data will allow them to be used as standard rulers to reconstruct the expansion history of the Universe. In addition, the anisotropies (redshift-space distortions) induced by the velocities of galaxies on these correlators will provide a measurement of the growth rate of cosmic structures, and hence an independent probe of possible departures from the standard model. The power and scope of the forthcoming surveys (DESI and Euclid) will push measurements at least an order of magnitude beyond what is currently available, to provide unprecedented constraints on cosmological models. It is important therefore to refine the methods used to analyze the large data-sets being produced by these surveys. The investigations reported in this thesis contribute to this goal in several ways. The first part of this thesis describes the development of a faster method to measure the anisotropic clustering signal so as reduce computational load. In particular the measurement of line-of-sight-dependent clustering using fast Fourier transform routines is described, that results in an impressive increase in efficiency compared to standard pair-counting approaches. The second part is concerned with how best to combine data from different volumes within the surveys. Current analyses split the redshift range into separate bins and repeat the traditional analysis within each bin. However, this method is not only computationally expensive but also results in loss of information (ignoring galaxy pairs across different bins), and increased edge effects on large scales. An alternative approach is presented that applies weighting schemes to account for the redshift evolution of clustering. It is shown that the weightings act as a smooth window on the data, compressing the signal in the redshift direction with no theoretical loss of information. Subsequent development derived and optimum set of weightings to constrain the growth of structure from the redshift space distortions signal. The weighting technique was also applied to improve constraints on primordial non-gaussianity at large scales. The third part of this work describes the development and testing of an efficient algorithmic pipeline, developed to performthe analyses, including the development of faster new algorithms (incorporating the new weighting schemes) to measure the anisotropic signal. This part also discusses how to deal with survey geometry when considering redshift evolution in clustering. The final part describes the application of the pipeline to analyze eBOSS data. In particular the first constraint on growth rate evolution over an unprecedented volume (1 < z < 2), as covered by the DR14 quasars, is presented.