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.

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京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第18795号 / 理博第4053号 / 新制||理||1583(附属図書館) / 31746 / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 嶺重 慎, 教授 太田 耕司, 准教授 樽家 篤史 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

>Magister Scientiae - MSc / The growth rate of large-scale structure is a key probe of gravity in the accelerating Universe. Standard models of Dark Energy within General Relativity predict essentially the same growth rate, whereas Modified Gravity theories without Dark Energy predict a different growth rate. Redshift-space distortions lead to anisotropy in the power spectrum, and extracting the monopole and quadrupole allows us to determine the growth rate and thus test theories of gravity. We investigate redshift-space distortions in the intensity maps of the 21cm emission line of neutral hydrogen (HI) in galaxies after the Epoch of Reionization: HI intensity mapping delivers very accurate redshifts. We first use the standard approach based on the Fourier power spectrum. Then we explored an alternative approach, based on the spherical-harmonic angular power spectrum. Fisher forecasting was used to make predictions of the accuracy with which MeerKAT will measure the growth rate parameter, via the proposed MeerKAT Large Area Synoptic Survey (MeerKLASS). Then we extend the forecasts to consider the planned HI intensity mapping survey in Phase 1 of the Square Kilometre Array. These forecasts enable us to predict at what level of accuracy General relativity and various alternative theories could be ruled out.

>Magister Scientiae - MSc / We begin by finding a system of differential equations for the background and linearly perturbed variables in the standard, ɅCDM model, using the Einstein Field Equations, and then solving these numerically. Later, we extend this to dynamical dark energy models parameterised by an equation of state, w, and a rest frame speed of sound, cs. We pay special attention to the large-scale behaviour of Δm, the gauge invariant, commoving matter density, since the approximation Δm ≃ δm, where δm is the longitudinal gauge matter density, is more commonly used, but breaks down at large scales. We show how the background is affected by w only, so measurements of perturbations are required to constrain cs. We examine how the accelerated expansion of the universe, caused by dark energy, slows down the growth rate of matter. We then show the matter power spectrum is not in itself useful for constraining dark energy models, but how redshift-space distortions can be used to extract the growth rate from the galaxy power spectrum, and hence how redshift-space power spectra can be used to constrain different dark energy models. We find that on small scales, the growth rate is more dependent on w, while on large scales, it depends more on cs.

Le modèle ΛCDM de la cosmologie repose sur l’existence d’une composante exotique, appelée énergie noire, pour expliquer l’accélération tardive de l’expansion de l’univers à z < 0.7. Des alternatives à cette constante cosmologique proposent de modifier la théorie de la gravitation basée sur la relativité générale aux échelles cosmologiques. Depuis l’automne 2014, le multi-spectrographe SDSS-eBOSS effectue un relevé de quasars dans un domaine en redshift peu exploré entre 0.8 ≤ z ≤ 2.2 dont l’un des objectifs majeurs est d’étendre les contraintes sur la nature de l’énergie noire et de tester la validité de la théorie de la relativité générale à plus haut redshift en utilisant les quasars comme traceurs de la matière.Dans cette thèse, nous mesurons et analysons la fonction de corrélation à deux points de l’échantillon de quasars obtenu après deux ans d'observation de eBOSS pour contraindre les distances cosmiques, à savoir la distance angulaire DA et le taux d'expansion H, ainsi que le taux de croissance des structures fσ8 à un redshift effectif Zeff = 1.52. Nous commençons par construire des catalogues des grandes structures qui prennent en compte la géométrie angulaire et radiale du relevé. Puis pour obtenir des contraintes robustes, nous identifions plusieurs sources d’effets systématiques, en particulier ceux liés à la modélisation et aux observations sont étudiées avec des « mock catalogues » dédiés qui correspondent à des réalisations fictives de l’échantillon de quasars eBOSS. Les paramètres cosmologiques de ces catalogues fictifs étant connus, ils sont utilisés comme référence pour tester notre procédure d’analyse. Les résultats de ce travail sur l’évolution des distances cosmiques sont compatibles avec les prédictions du modèle ΛCDM utilisant les paramètres de Planck et basé sur l’existence d’une constante cosmologique. La mesure du taux de croissance des structures est compatible avec la prédiction de ce modèle basé sur la relativité générale, ce qui étend ainsi la validité de la théorie aux échelles cosmologiques à grand redshift. Nous utilisons également notre mesure pour mettre à jour les contraintes sur les modèles d'extensions à ΛCDM et sur les scénarios de gravité modifiée. Ce travail de thèse constitue une première étude menée avec les données de quasars eBOSS et sera utilisée pour l’analyse de l’échantillon final à la fin 2019 ou l’on attend une amélioration de la précision statistique d’un facteur 2. Associé à BOSS, eBOSS ouvrira la voie pour les futurs programmes d’observation, comme le télescope au sol DESI et le satellite Euclid. Ces deux programmes sonderont intensivement l’époque de l’univers entre 1 < z < 2 en observant plusieurs millions de spectres, ce qui permettra d'améliorer d'un ordre de grandeur au moins les contraintes actuelles sur les paramètres cosmologiques. / The ΛCDM model of cosmology assumes the existence of an exotic component, called dark energy, to explain the late-time acceleration of the expansion of the universe at redshift z < 0.7. Alternative scenarios to this cosmological constant suggest to modify the theory of gravitation based on general relativity at cosmological scales. Since fall 2014, the SDSS-IV eBOSS multi-object spectrograph has undertaken a survey of quasars in the almost unexplored redshift range 0.8 ≤ z ≤ 2.2 with the key science goal to complement the constraints on dark energy and extend the test of general relativity at higher redshifts by using quasars as direct tracers of the matter field.In this thesis work, we measure and analyse the two-point correlation function of the two-year data taking of eBOSS quasar sample to constrain the cosmic distances, i.e. the angular diameter distance DA and the expansion rate H, and the growth rate of structure fσ8 at an effective redshift Zeff = 1.52. First, we build large-scale structure catalogues that account for the angular and radial incompleteness of the survey. Then to obtain robust results, we investigate several potential systematics, in particular modeling and observational systematics are studied using dedicated mock catalogs which are fictional realizations of the data sample. These mocks are created with known cosmological parameters such that they are used as a benchmark to test the analysis pipeline. The results on the evolution of distances are consistent with the predictions for ΛCDM with Planck parameters assuming a cosmological constant. The measurement of the growth of structure is consistent with general relativity and hence extends its validity to higher redshift. We also provide updated constraints on extensions of ΛCDM and models of modified gravity. This study is a first use of eBOSS quasars as tracers of the matter field and will be included in the analysis of the final eBOSS sample at the end of 2019 with an expected improvement on the statistical precision of a factor 2. Together with BOSS, eBOSS will pave the way for future programs such as the ground-based Dark Energy Spectroscopic Instrument (DESI) and the space-based mission Euclid. Both programs will extensively probe the intermediate redshift range 1 < z < 2 with millions of spectra, improving the cosmological constraints by an order of magnitude with respect to current measurements.