The first billion years from the beginning of the Universe is the focus of multiple astronomical facilities in the upcoming decade. This unique era is marked by the formation of the first stars and galaxies, which release ionising radiation into the intergalactic medium(IGM). As a result, these sources initiate a period during which the cold and dense IGM, primarily consisting of neutral hydrogen (HI ), is heated and ionised. We refer to this era as the Epoch of Reionisation (EoR). How the EoR transpired hence depends on the properties of these ionising sources, and this forms a vital piece to the puzzle of understanding the early Universe. This licentiate thesis aims to educate the reader on the power spectrum (PS) statistic of the 21-cm signal from HI during the EoR. The PS is a prospective observable by radio interferometers, such as the Low-Frequency Array (LOFAR) and the future Square Kilometre Array (SKA). It is an essential stepping stone in comprehending the dominant physical processes affecting the IGM at a given length scale during the EoR. In Paper I, we analyse the decomposition of the 21-cm PS from Lidz et al. (2007) (eq. 2)and study the evolution of its terms. We conduct our investigation for a set of C 2 -Ray and 21cmFAST simulations with volumes of (714 cMpc)3, concentrating on large-scales (k < 0.3 Mpc−1 ) as the signal-to-noise ratio of observing these scales will be high. We find that the 21-cm PS tracks the PS of neutral hydrogen fluctuations, which itself past a certain scale tracks the matter PS after a global ionisation fraction of x̄HII∼ 0.1. Hence, the 21-cm PS possesses a two-regime form for which the large-scale PS is a biased version of the cosmological density field and the small-scale PS depends on the astrophysics of the EoR. We construct a bias parameter to explore whether the 21-cm PS can be used as a probe of cosmology on large k-scales. We discover a transition feature for both simulations, following the ktrans ≈ 2/λMFP empirical formula. The transition scale between the scale-independent and scale-dependent bias regimes is directly related to the value of the mean free path of ionising photons (λMFP ).

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Béla Bartók's Piano Sonata Sz.80 is known for its integration of modernist language with traditional elements. However, due to Bartók's radical style of writing, it remains challenging to precisely define the piece's motives, voice-leading, and structure, even though pianists who perform it may intuitively comprehend them. Therefore, this study aims to elucidate the Piano Sonata's motivic and tonal structure, genesis and development. First, this study demonstrates Bartók's use of linear motives and progressions to elucidate the Piano Sonata's large-scale structure and demonstrate its internal coherence. Second, by comparing the published score with the facsimile of the Budapest Manuscript, it is possible to shed light on the significance of the changes that Bartók made, facilitating a better understanding of his intentions. Lastly, this study suggests interpretive decisions based on the analysis and manuscripts, thus providing performers with a more thorough understanding of the piece.

<p>We investigate the clustering of HI-selected galaxies in the ALFALFA survey and compare results with those obtained for HIPASS. Measurements of the angular correlation function and the inferred 3D-clustering are compared with results from direct spatial-correlation measurements. We are able to measure clustering on smaller angular scales and for galaxies with lower HI masses than was previously possible. We calculate the expected clustering of dark matter using the redshift distributions of HIPASS and ALFALFA and show that the ALFALFA sample is somewhat more anti-biased with respect to dark matter than the HIPASS sample. We are able to conform the validity of the dark matter correlation predictions by performing simulations of the non-linear structure formation. Further we examine how the bias evolves with redshift for radio galaxies detected in the the first survey.</p>

<p>We investigate the clustering of HI-selected galaxies in the ALFALFA survey and compare results with those obtained for HIPASS. Measurements of the angular correlation function and the inferred 3D-clustering are compared with results from direct spatial-correlation measurements. We are able to measure clustering on smaller angular scales and for galaxies with lower HI masses than was previously possible. We calculate the expected clustering of dark matter using the redshift distributions of HIPASS and ALFALFA and show that the ALFALFA sample is somewhat more anti-biased with respect to dark matter than the HIPASS sample. We are able to conform the validity of the dark matter correlation predictions by performing simulations of the non-linear structure formation. Further we examine how the bias evolves with redshift for radio galaxies detected in the the first survey.</p>

Absorption profiles are found in the observed spectra from quasars, and the most prominent of these are the Damped Lyman-alpha Absorbers (DLAs). They are caused by large collections of neutral hydrogen (HI) gas, which are thought to be housed in galaxies that lie along the line-of-sight to quasars. HI gas associated with DLAs contains most of the HI gas in the Universe during 2 < z < 5, and hence details about DLAs are important for understanding the history of star formation, as well as the formation and evolution of galaxies. Wyithe (2008) proposed a method of determining the characteristic mass of dark matter haloes that host DLAs. This involves generating an analytic power spectrum of the fluctuations in 21cm brightness temperature caused by the HI gas in the Universe. Calculating this analytic 21cm power spectrum requires a formalism for the HI mass weighted clustering bias of DLAs on both large and small scales. We include this DLA clustering bias by firstly generating an analytic galaxy power spectrum using the halo model of Peacock & Smith (2000), as well as including the occupation of haloes by galaxies -- using the Halo Occupation Distribution (HOD) weighting of Peacock (2003). This weighting is then adapted to account for the occupation of haloes by HI gas. / We then fit the analytic 21cm power spectrum generated using this formalism to a simulated 21cm power spectrum, with the characteristic mass of DLA host haloes being used as a fitting parameter. The DLA host halo mass is in turn dependent upon two parameters in our model: the minimum mass of haloes M_{min} included in our formalism, and the HI weighting index alpha_{HI}. The neutral hydrogen fraction is another parameter, which we can choose to be the same as that from our simulation volume. If we also choose a value for alpha_{HI} that is motivated by analysis of the dark matter and HI gas content of the haloes in the simulation, then we are able to fit the 21cm power spectrum at both large and small scales, with an M_{min} that is the same or similar to the lowest mass in the simulation's halo catalogue. This in turn gives a similar value for the DLA host halo mass that is known to be the case in the simulation. This demonstrates the viability of the Wyithe (2008) method for determining the DLA host halo mass using observations of 21cm fluctuations. However, degeneracies in the free parameters of our analytic formalism would hinder an accurate determination of the DLA host halo mass from actual future observations. This is due to the fact that the real space, spherically averaged 21cm power spectrum is used throughout this thesis. However, extending our analytic formalism to the redshift space, angular-dependent 21cm power spectrum should be capable of breaking the degeneracy between DLA host halo mass and neutral hydrogen fraction.

Dans cette thèse sur articles, nous nous intéressons aux grandes structures de l’Univers et à leur rôle fondamental pour la cosmologie et la formation des galaxies. Les galaxies naissent et grandissent au sein des filaments de la toile cosmique soulevant la question de l’impact de ces filaments sur les propriétés galactiques telles que la morphologie. Pour étudier cette question fondamentale, nous allons dans un premier temps montrer que dans les simulations numériques de l’Univers, le spin des galaxies est fortement lié à la direction de leur filament hôte avec un comportement qui dépend de leur masse. Ces corrélations spin-filament seront expliquées qualitativement dans le contexte de la formation hiérarchique des structures cosmologiques. Un modèle analytique tenant compte de l’anisotropie de la toile cosmique complètera ce tableau en reproduisant les corrélations observées. Ces idées sont importantes pour comprendre la morphologie des galaxies mais aussi les alignements intrinsèques qui peuvent certaines sondes cosmologiques basées sur la mesure de l’astigmatisme cosmique. Nous allons en particulier mesurer cette contamination dans une simulation hydrodynamique. Dans la seconde partie de ce manuscrit, nous nous poserons la question de comment extraire efficacement de l’information de la toile cosmique en mesurant sa topologie et sa géométrie et en utilisant la théorie perturbative dans un régime quasi-linéaire, la pierre angulaire de ce travail reposant sur l’étude analytique de l’impact de l’effondrement non-linéaire des structures et des distorsions en espace des redshifts sur la statistique du champ de densité cosmique. / This thesis by publication is devoted to the theoretical understanding of the large-scale structure of the Universe and its role in the context of cosmology and galaxy formation. The birth and evolution of galaxies occur within the large cosmic highways drawn by the cosmic web and the natural question which arises is whether galaxies retain a memory of the large-scale cosmic flows from which they emerge. To address this key question, we will first show that in cosmological simulations, the spin of galaxies and the direction of their host filament are correlated in a mass-dependent way. This signal will be shown to be qualitatively understood in the context of hierarchical structure formation. An analytic model which explicitly takes into account the anisotropy of the cosmic web will complement this qualitative understanding by reproducing the measured correlations. Those ideas are important to understand the evolution of galaxy morphology but also to understand the intrinsic alignments of galaxies that contaminate cosmological probes like cosmic shear experiments. We will in particular measure this contamination directly from a state-of-the-art hydrodynamical simulation. In a second part, we will address the question of how to efficiently use large-scale structure data to probe the cosmological model describing our Universe by measuring its topology and geometry and using perturbation theory in the weakly and even mildly non-linear regime. The major contribution of this work is to analytically study the effect of redshift space distortions and non-linear collapse of structures on the topology, geometry and statistics of the cosmic density field.

Philosophiae Doctor - PhD / We investigate the clustering of HI-selected galaxies in the ALFALFA survey and compare results with those obtained for HIPASS. Measurements of the angular correlation function and the inferred 3D-clustering are compared with results from direct spatial-correlation measurements. We are able to measure clustering on smaller angular scales and for galaxies with lower HI masses than was previously possible. We calculate the expected clustering of dark matter using the redshift distributions of HIPASS and ALFALFA and show that the ALFALFA sample is somewhat more anti-biased with respect to dark matter than the HIPASS sample. We are able to conform the validity of the dark matter correlation predictions by performing simulations of the non-linear structure formation. Further we examine how the bias evolves with redshift for radio galaxies detected in the the first survey. / South Africa

>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.