### Abstract

General relativity has proved itself to be an incredibly robust theory having passed many high precision solar system tests as well as being able to describe the evolution of the universe and its constituents. Its cosmological application necessarily requires large and mysterious energy components to match observations. In particular, the observation of cosmic acceleration forces general relativity to adopt a dominant dark energy component. This has prompted aurry of investigation into alternatives to the concordance model of gravity which can offer self-acceleration. These alternatives must deal with strong priors coming from the local tests of gravity. This has lead to the development of theories that exhibit so called screening mechanisms which allow them to be observationally equivalent to general relativity at small scales. On the other hand, these theories generically predict distinguishing phenomena at larger scales such as an enhanced gravitational force. This makes galaxy clusters and the LSS of the universe a great testbed for modifcations to gravity.

In particular, the anisotropy of galaxy clustering in redshift space, which arises due to the peculiar velocities of galaxies, offers a promising means of testing gravity. These so called redshift space distortions involve the velocity components of galaxies which in turn strongly involves the gravitational force and the growth rate of structure. This links us up with the fundamental laws of nature at large scales. As astronomical surveys become more and more precise, our measurements of the growth of structure become ever more powerful to detect departures from general relativity. This is true only if our theoretical modelling is up to the challenge these surveys propose. Specifically, with upcoming large volume, spectroscopic surveys such as Euclid and DESI, statistical errors will become tiny leaving room for various theoretical biases to enter the game. One such bias is that from using general relativity as a standard in data comparisons. Put in other words, the next era of astronomy will put us in a position to move beyond consistency tests of general relativity.

In this thesis we develop a c++ code that numerically and consistently constructs LSS observables, accounting for the redshift space distortion phenomenon. By consistently we mean that this can be done for a large class of alternative theories of gravity and dark energy models. This is done using perturbation theory which treats over-densities and velocities as small perturbations upon a homogeneous and isotropic expanding background spacetime. The construction provides the first order contribution in non-linear dynamics which gives a more accurate description of the observables, an ever growing necessity when looking to extract the most information in data comparisons. We focus on the redshift space power spectrum and correlation function, two commonly used statistics that are measured from galaxy surveys. Specifically, we adopt the Taruya, Nishimichi and Saito redshift space power spectrum model and Gaussian streaming model redshift space correlation function, which both employ beyond-linear treatments of the redshift space distortions. The perturbative approach makes the pipeline ideal for statistical inference analyses that require very quick model computations.

We test this framework against suites of numerical simulations that by and large describe the full dynamics of structure growth. Specifically, we make use of simulations within three models of gravity : general relativity, the 5-dimensional DGP brane world model and an f(R) model. The two latter models both exhibit screening which makes them viable contenders to the former. Comparing the perturbative approach to these simulations gives us a handle on its accuracy in modelling the dynamics of the perturbations. We also validate the pipelines' numerical predictions against well established analytic forms for DGP and general relativity. We find very good agreement in all comparisons and a significant improvement in accuracy over the linear treatment.

This is followed by a comparison of different approaches to the redshift space correlation function, specifically the Gaussian streaming model and the Fourier transform of the Taruya, Nishimichi and Saito spectrum. We find that these two approaches are consistent to within a few percent at scales around the baryon acoustic oscillation.

Finally, we use dark matter simulation data to perform a test for bias introduced

by incorrectly modelling gravity. This is done by using DGP simulation data in a

Markov Chain Monte Carlo analysis for two different templates for the redshift space power spectrum. The first template employs general relativity to model the perturbations while the second models them within the DGP model. We fit next generation like survey error bars on the data to put the analysis in that context. It is then found that for upcoming surveys, using general relativity as a benchmark model may only safely be used in consistency tests of general relativity but not to infer constraints on alternative models.

Date of Award | Jan 2018 |
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Original language | English |

Supervisor | Kazuya Koyama (Supervisor) & Gong-Bo Zhao (Supervisor) |