Title:

Geometric and growth rate tests of General Relativity with recovered linear cosmological perturbations

The expansion of the universe is currently accelerating, as first inferred by Efstathiou et al. (1990), Ostriker & Steinhardt (1995) and directly determined by Riess et al. (1998) and Perlmutter et al. (1999). Current constraints are consistent with a time independent equationofstate of w = 1, which is to be expected when a constant vacuum energy density dominates. But the Quantum Field Theory prediction for the magnitude of this vacuum energy is very much larger than that inferred (Weinberg, 1989; Koksma & Prokopec, 2011). It is entirely possible that the cause of the expansion has an alternative explanation, with both the inclusion of a quantum scalar field and modified gravity theories able to reproduce an expansion history close to, but potentially deviating from, that of a cosmological constant and cold dark matter. In this work I investigate the consistency of the VIMOS Public Extragalactic Redshift Survey (VIPERS) v7 census of the galaxy distribution at z = 0:8 with the expansion history and linear growth rate predicted by General Relativity (GR) when a Planck Collaboration et al. (2016) fiducial cosmology is assumed. To do so, I measure the optimally weighted redshiftspace power spectrum (Feldman et al., 1994), which is anisotropic due to the coherent infall of galaxies towards overdensities and outflow from voids (Kaiser, 1987). The magnitude of this anisotropy can distinguish between modified theories of gravity as the convergence (divergence) rate of the velocity field depends on the effective strength of gravity on cosmological scales (Guzzo et al., 2008). This motivates measuring the linear growth rate rather than the background expansion, which is indistinguishable for a number of modified gravity theories. In Chapter 6 I place constraints of fσ8(0:76) = 0:44 ± 0:04; fσ8(1:05) = 0:28 ± 0:08; with the completed VIPERS v7 survey; the combination remains consistent with General Relativity at 95% confidence. The dependence of the errors on the assumed priors will be investigated in future work. Further anisotropy is introduced by the AlcockPaczynski effect  a distortion of the observed power spectrum due to the assumption of a fiducial cosmology differing from the true one. These two sources of anisotropy may be separated based on their distinct scale and angular dependence with sufficiently precise measurements. Doing so degrades the constraints: fσ8(0:76) = 0:31 ± 0:10; fσ8(1:05) = 0:04 ± 0:26; but allows for the background expansion (FAP ≡ (1 + z)DAH=c) to be simultaneously constrained. Galaxy redshift surveys may then directly compare both the background expansion and linear growth rate to the GR predictions I find the VIPERS v7 jointposterior on (fσ8; FAP ) shows no compelling deviation from the GR expectation although the sizeable errors reduce the significance of this conclusion. In Chapter 4 I describe and outline corrections for the VIPERS spectroscopic selection, which enable these constraints to be made. The VIPERS selection strategy is (projected) density dependent and may potentially bias measures of galaxy clustering. Throughout this work I present numerous tests of possible systematic biases, which are performed with the aid of realistic VIPERS mock catalogues. These also allow for accurate statistical error estimates to be made { by incorporating the sample variance due to both the finite volume and finite number density. Chapter 5 details the development and testing of a new, rapid approach for the forward modelling of the power spectrum multipole moments obtained from a survey with an involved angular mask. An investigation of the necessary corrections for the VIPERS PDR1 angular mask is recorded. This includes an original derivation for the integral constraint correction for a smoothed, jointfield estimate of ¯n(z) and a description of how the mask should be accounted for in light of the Alcock Paczynski effect. Chapter 7 investigates the inclusion of a simple local overdensity transform: 'clipping' prior to the redshiftspace distortions (RSD) analysis. This tackles the root cause of nonlinearity and potentially extends the validity of perturbation theory. Moreover, this marked clustering statistic potentially amplifies signatures of modified gravity and, as a densityweighted twopoint statistic, includes information not available to the power spectrum. I show that a linear realspace power spectrum with a Kaiser factor and a Lorentzian damping yields a significant bias without clipping, but that this may be removed with a sufficiently strict transform; similar behaviour is observed for the VIPERS v7 dataset. Estimates of fσ8 for different thresholds are highly correlated due to the overlapping volume, but the bias for insufficient clipping can be calibrated and the correlation obtained using mock catalogues. A maximum likelihood value for the combined constraint of a number of thresholds is shown to achieve a ' 16% decrease in statistical error relative to the most precise singlethreshold estimate. The results are encouraging to date but represent a work in progress; the final analysis will be submitted to Astronomy & Astrophysics as Wilson et al. (2016). In addition to this, an original extension of the prediction for a clipped Gaussian field to a clipped lognormal field is presented. The results of tests of this model with a realspace cube populated according to the halo occupation distribution model are also provided.
