### Abstract

Robust measurements of the large scale structure of the universe allow for precise characterisation of its low redshift behaviour and its late time accelerating expansion rate.In particular, Baryon Acoustic Oscillations (BAO) provide a standard ruler with which to measure the expansion rate, whilst Redshift Space Distortions (RSD) allow for tests of General Relativity on cosmological scales. In recent years many surveys have used these probes to investigate the nature of dark energy across a wide range of redshifts with increasing accuracy, culminating in a recent 1% measurement of the BAO scale by Anderson et al. (2014b). Current measurements point towards a consensus cosmological model where dark energy is described only by a Cosmological Constant. However, much of the parameter space available for dark energy models remains unexplored, a point that future surveys such as Euclid (Laureijs et al., 2011), DESI (Levi et al., 2013), LSST (Ivezic etal., 2008) and SKA (Maartens et al., 2015) will attempt to rectify.This thesis presents work that further confirms the consensus cosmological model using a set of new BAO and RSD measurements at low redshift, whilst also providing tools and techniques to aid in the analysis of next generation datasets.

To begin with, a new code for fast dark matter simulation is presented that can be used to generate large ensembles of accurate mock galaxy catalogues for use in estimating the statistical and systematic errors inherent within large scale structure measurements. The accuracy and speed of this code are tested, where it is found that the new code can reproduce the real-space 2- and 3-point dark matter clustering from a full non-linear N-Body simulation to within 2% and 5% on all scales of interest to BAO and RSD measurements.However each simulation can be run 3 orders of magnitude faster than the corresponding non-linear N-Body run. Several new features are also implemented that will be ofuse in constructing mock galaxy catalogues for next generation surveys. This code, the algorithms involved and its testing are published in Howlett et al. (2015b).

New measurements of the BAO and RSD signals in a low redshift galaxy sample drawn from the Sloan Digital Sky Survey Data Release 7 are also presented, along with their subsequent cosmological constraints. The simulation code above is first used to generate a set of mock galaxy catalogues based on the low redshift sample, before the sample and simulations are analysed using the most up-to-date BAO and RSD analysis methods. The procedure for generating the mock catalogues is tested and the clustering of the simulations is found to match that of the data extremely well, even down to scales of 5 h

^{−1}Mpc. Using the mock catalogues, the BAO and RSD fitting methods are checked for robustness before being used on the data set to obtain a new set of constraints on the expansion rate, equation of state of dark energy and growth rate of structure. In particular,the new BAO measurement completes the low redshift BAO distance ladder and improves current BAO and CMB constraints on the equation of state of dark energy by ⇠ 15%, to w

_{0}= −1.010 ± 0.081. This work is published in Ross et al. (2015) and Howlett et al.(2015a).

Finally, a new optimal method for estimating the covariance matrix of the two point clustering of matter is presented, based on a combination of analytic and simulation approaches.This new method can reproduce the covariance matrix estimated from the mock galaxy catalogues simulations used in the rest of this work very well on small scales, in a regime where theoretical estimates of the covariance matrix are extremely difficult to obtain accurately. The benefit of this method is that only simulations that are a fraction of the volume of the full mock galaxy catalogues are required, which in turn means fewer particles are needed to reach the same mass resolution and more simulations (and hence a more precise estimate of the covariance matrix) can be obtained for the same computational cost. The combination of this work and the new fast simulation code presents a much more practical and cost effective way of estimating the covariance matrix.

Date of Award | 21 Mar 2016 |
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Original language | English |

Supervisor | Will Percival (Supervisor), Marc Manera (Supervisor) & Robert Crittenden (Supervisor) |