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

##### Abstract

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 equation-of-state 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 redshift-space 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 Alcock-Paczynski 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 joint-posterior 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 PDR-1 angular mask is recorded. This includes an original derivation
for the integral constraint correction for a smoothed, joint-field 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 redshift-space distortions (RSD)
analysis. This tackles the root cause of non-linearity and potentially extends
the validity of perturbation theory. Moreover, this marked clustering statistic
potentially amplifies signatures of modified gravity and, as a density-weighted two-point statistic, 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 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 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). 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 real-space cube populated according to
the halo occupation distribution model are also provided.