Large scale structure cosmology on the light cone

The power spectrum is a very successful statistic for extracting cosmological information from the large-scale structure of the universe. When applied to data provided by galaxy redshift surveys, one of the key strengths of the power spectrum is its ability to determine the growth rate of structure and the expansion history of the universe, two important probes of cosmological models. Upcoming and future surveys will provide a higher number density of targets over a much greater volume than previously attainable, enabling the power spectrum to test cosmological models with more precision. Consequently, these large-volume surveys will require modelling of the power spectrum to a high degree of accuracy over a wider range of scales, and any previous modelling assumptions should be tested to assess their validity in this new regime. The main task of this work is to address some of these challenges posed when modelling the galaxy power spectrum for very deep and wide-angle redshift surveys. Working with these conditions presents two problems that many previous smaller surveys did not necessarily have to address. Firstly, the distant observer approximation is no longer valid, and so working in spherical coordinates is required to properly model the survey window function that becomes convolved with the power spectrum in any volume or magnitude-limited sample. This choice of coordinate system introduces spherical Bessel functions into the integrals of the model equations, which can be notoriously difficult to evaluate. Secondly, when working with very deep surveys, the pair counting of objects that exist at significantly different redshifts from one another requires the use of unequal-time correlators for a full treatment of the modelling, otherwise this may introduce systematic errors when trying to recover cosmological parameters. We start off by reviewing the existing model for the power spectrum on the past lightcone, working in the simple case of unbiased tracers on the full sky, and extend this model further into the non-linear regime. We develop numerical code in C++ that is able to compute the model in an accurate and timely manner, and test the validity of the standard mean-redshift approximation to the unequal-time correlator. We find this to cause a significant bias in the expected power spectrum amplitude, particularly for deep surveys. Following from this, we show that an effective fixed-time redshift can be easily determined that gives a good approximation to the unequal-time case, over a wide range of scales and redshifts. We then test the model against mock lightcone catalogues, created from large-volume N-body simulations, and find excellent agreement between our measurements and the theory, to within ±5%, over a range of magnitude-limited samples, and for the scales 4 × 10-3 = k = 0.5 [h Mpc-1 ]. We also tested how well the commonly used FKP weights effected the measurements, for various values of fiducial power P0 and over the range of magnitude cuts, finding they could boost the signal-to-noise by factors of a few. Using the mock lightcone catalogues, we then forecast the probability of upcoming and future galaxy redshift surveys being able to robustly detect the turnover-scale in the power spectrum. We found that a turnover was detectable with a probability of P = 95% in an all-sky catalogue, limited to an apparent magnitude of mlim ~ 21, with this probability remaining high for surveys with mlim ~ 22 at 20% sky coverage. We then extend the model of the power spectrum on the past lightcone to make it more applicable to realistic surveys, by including terms for galaxy bias and a survey mask that is not necessarily isotropic. As accounting for these effects produces a more mathematically complicated model, we look for new methods to make numerical evaluation more feasible. We find that as long as time-separability of the unequal-time correlator holds, an approximation that was employed for the previous full-sky case can still be used to make the calculation of the model at small-scales a trivial task. For evaluation of the model at large scales, we apply the FFTLog method in conjunction with analytic transforms of Bessel integrals, deriving expressions for our specific case and listing an example of a step-by-step algorithm for implementing this numerically. Finally, we give an overview of the 4MOST Cosmology Redshift Survey, an upcoming spectroscopic survey in the southern hemisphere which aims to synergize with weak lensing and CMB surveys to better constrain the late-time universe. We detail the clustering pipeline that we have developed in Python for this survey, which utilises existing libraries to compute two-point statistics in both configuration and Fourier space. This can be used for for assessing the quality of the mock catalogues being generated in advance of the survey going live, as well as for survey design optimisation. We end by briefly reviewing some of the results produced by the pipeline when being run on the most up-to-date mocks from the 4MOST simulation team.