Geometric and growth rate tests of General Relativity with recovered
  linear cosmological perturbations
  I investigate the consistency of the VIMOS Public Extragalactic Redshift
Survey v7 galaxy sample with the expansion history and linear growth rate
predicted by General Relativity (GR) and a Planck (2015) cosmology. To do so, I
measure the redshift-space power spectrum, which is anisotropic due to both
redshift-space distortions (RSD) and the Alcock-Paczynski (AP) effect. In
Chapter 6, I place constraints of $f \sigma_8(0.76) = 0.44 \pm 0.04$ and $f
\sigma_8(1.05) = 0.28 \pm 0.08$, which remain consistent with GR at 95%
confidence. Marginalising over the anisotropic AP effect degrades the
constraints by a factor of three but allows $F_{AP} \equiv (1+z) D_A H/c$ to be
simultaneously constrained. The VIPERS v7 joint-posterior on $(f \sigma_8,
F_{AP})$ shows no compelling deviation from GR.
  Chapter 7 investigates the inclusion of a simple density transform:
`clipping' prior to the RSD analysis. This tackles the root-cause of
non-linearity and may extend the validity of perturbation theory. Moreover,
this marked statistic would amplify signatures of shielded modified gravity
models and includes information not available to the power spectrum. I show
that a linear real-space power spectrum with a Kaiser factor and a Lorentzian
damping yields a significant bias without clipping, but that this may be
removed with a strict threshold; similar behaviour is observed for the data.
Estimates of $f \sigma_8$ for different thresholds are highly correlated, but
this may be obtained using mocks. A maximum likelihood estimate from a
combination of thresholds is shown to achieve a 16% decrease in statistical
error relative to a single-threshold 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).
