Les trous noirs supermassifs résident dans les centres de la plupart des galaxies massives et on observe des corrélations entre leurs masses et les propriétés de leurs galaxies hôtes. De plus, on observe des trous noirs de plus d’un milliard de masses solaires quelques centaines de millions d’années seulement après le Big Bang. Ces trous noirs supermassifs présents dans l’univers jeune ne sont que le sommet de l’iceberg de l’ensemble de la population de trous noirs, mais ils mettent en question notre compréhension de la formation et de la croissance des premiers trous noirs. Notre nouvelle méthode améliorant le calcul de la densité de colonne de H2 donne des probabilités pour former des graines massives de trous noirs qui sont plus d’un ordre de grandeur plus élevées que prédit précédemment. Nous trouvons que CR7 pourrait être le premier candidat à héberger un tel trou noir formé par effondrement direct et nous démentons l’existence initialement revendiquée d’une population stellaire massive primordial dans CR7. Nous calculons la densité des taux de fusion des trous noirs binaires des premières étoiles et leurs taux de détection avec aLIGO. Notre modèle démontre que les détections des ondes gravitationnelles à venir au cours des prochaines décennies permettront d’imposer des contraintes plus strictes sur les propriétés des premières étoiles et donc sur les scénarios de formation des premiers trous noirs. Nous développons un modèle analytique en 2D de la rétroaction des noyaux actifs de galaxie pour démontrer qu’un profil de disque plus réaliste réduit la quantité de gaz qui est éjectée du halo par rapport aux modèles 1D existants. La rétroaction empêche l’accretion de gaz sur le trou noir central pendant seulement ∼1 million d’année environ, ce qui permet une accretion de gaz presque continue dans le plan du disque. Avec cette thèse, je contribue à une meilleure compréhension de la formation et la croissance des premiers trous noirs supermassifs. / Supermassive black holes reside in the centres of most massive galaxies and we observe correlations between their mass and properties of the host galaxies. Besides this correlation between a galaxy and its central black hole (BH), we see BHs more massive than one billion solar masses already a few hundred million years after the Big Bang. These supermassive BHs at high redshift are just the tip of the iceberg of the entire BH population, but they challenge our understanding of the formation and growth of the first BHs. Our improved method to calculate H2 self-shielding yields probabilities to form massive seed BHs that are more than one order of magnitude higher, than previously expected. We find that CR7 might be the first candidate to host such a direct collapse BH and we disprove the initially claimed existence of a massive metal-free stellar population in CR7. We calculate the merger rate density of binary BHs from the first stars and their detection rates with aLIGO. Our model demonstrates that upcoming detections of gravitational waves in the next decades will allow to put tighter constraints on the properties of the first stars and therefore on formation scenarios of the first BHs. We develop a 2D analytical model of active galactic nuclei-driven outflows to demonstrate that a more realistic disc profile reduces the amount of gas that is ejected out of the halo, compared to existing 1D models. The outflow prevents gas accretion on to the central BH for only about ∼1Myr, which permits almost continuous gas inflow in the disc plane. With this thesis, I contribute to a better understanding of the formation and growth of the first supermassive BHs.

Le rayonnement fossile, ou CMB, est un sujet d’étude clé pour la cosmologie car il indique l’état de l’univers à une époque primordiale. Le CMB est observable dans le ciel dans la bande de fréquences des micro-ondes. Cependant, il existe des processus astrophysiques, les avant-plans, qui émettent dans les micro-ondes, et rendent indispensable le traitement des données avec des méthodes de séparation de composantes. J'utilisé la méthode aveugle SMICA pour obtenir une estimation directe du spectre de puissance angulaire du CMB. La détermination des petites échelles de ce spectre est limité par les avant-plans comme les galaxies lointaines, et par le biais du bruit. Dans cette analyse, ces deux limitations sont abordées. En ajoutant des hypothèses sur la physique des galaxies lointaines, il est possible de guider l’algorithme pour estimer leur loi d'émission. Un spectre de puissance angulaire obtenu d'une carte du ciel a un biais dû au bruit à petites échelles. Toutefois, les spectres obtenus en croisant différentes cartes n'ont pas ce biais. J'ai donc adapté la méthode SMICA pour qu'elle n'utilise que ces derniers, diminuant l'incertitude due au bruit dans l'estimation du CMB. Cette méthode a été étudiée sur des nombreuses simulations et sur les données Planck 2015, afin d'estimer des paramètres cosmologiques. Les résultats montrent que la contamination résiduelle des avant-plans présente dans le spectre CMB, même si fortement réduite, peut introduire des biais dans l'estimation des paramètres si la forme des résiduels n'est pas bien connue. Dans cette thèse, je montre les résultats obtenus en étudiant un modèle de gravité modifiée. / The Planck satellite observed the whole sky at various frequencies in the microwave range. These data are of high value to cosmology, since they help understanding the primordial universe through the observation of the cosmic microwave background (CMB) signal. To extract the CMB information, astrophysical foreground emissions need to be removed via component separation techniques. In this work I use the blind component separation method SMICA to estimate the CMB angular power spectrum with the aim of using it for the estimation of cosmological parameters. In order to do so, small scales limitations as the residual contamination of unresolved point sources and the noise need to be addressed. In particular, the point sources are modelled as two independent populations with a flat angular power spectrum: by adding this information, the SMICA method is able to recover the joint emission law of point sources. Auto-spectra deriving from one sky map have a noise bias at small scales, while cross-spectra show no such bias. This is particularly true in the case of cross-spectra between data-splits, corresponding to sky maps with the same astrophysical content but different noise properties. I thus adapt SMICA to use data-split cross-spectra only. The obtained CMB spectra from simulations and Planck 2015 data are used to estimate cosmological parameters. Results show that this estimation can be biased if the shape of the (weak) foreground residuals in the angular power spectrum is not well known. In the end, I also present results of the study of a Modified Gravity model called Induced Gravity.

L’étude des amas globulaires (AGs) nous offre une opportunité d’appréhender l’histoire de leurs galaxies hôtes et ainsi l’histoire de l’univers. Dans cette thèse, je me suis intéressé aux propriétés des AGs dans différents environnements. Tout d’abord, je me suis concentré sur les AGs de l’amas de la Vierge, un amas de galaxies très dense situé à environ 16,5 Mpc. J’ai utilisé les données observées par le relevé NGVS (Next Generation Virgo Survey) pour définir un échantillon qui contient 1846AGs. J’ai ensuite comparé les couleurs de ces amas avec celles d’autres AGs originaires de la Voie Lactée et j’ai remarqué des différences de couleurs encore jamais observées, dont la nature exacte est encore énigmatique. Pour comprendre ces différences, j’ai ensuite comparé les AGs observés avec des AGs synthétiques basés sur 10 modèles de synthèse de populations stellaires. J’ai aussi étudié les âges et les métallicités ressortant de la confrontation directe des couleurs des AGs à ces modèles. En conclusion, en l’état actuel, les modèles ne rendent pas compte de la diversité identifiée dans ma thèse. Finalement, j’ai effectué une brève étude des propriétés spatiales des AGs autour de M87 pour repérer des marques d’accrétion. / Through the study of the globular cluster (GC) properties, it is possible to unravel the history of their host galaxies and by extension the history of the universe. During this thesis, I was interested in the GC properties in different environments. First, I looked at the GCs in the Virgo cluster, a dense galaxy cluster located at 16.5 Mpc. I used data from the survey NGVS (Next Generation Virgo Survey) to define a sample of 1846 GCs. Then, I compared the colors of these GCs with those of Milky Way GCs and I noted color differences never yet observed, which are still enigmatic. In order to understand these differences, I compared the observed GCs with synthetic GCs obtained with 10 stellar population synthesis models. I also studied the age and metallicity predictions of those models. In the end, in their current status, the models do not account for the diversity highlighted in my thesis. Finally, I assessed the spatial properties of the GCs around M87 in order to find any signatures of a recent accretion.

One of the key goals of Milky Way science is measuring the distribution of dark matter in the Galaxy. Through the study of Galactic dynamics, inferences can be made about the structure of the Galaxy, and hence the dark matter distribution. To this end, we present a study of methods useful for modelling and understanding dynamical systems in the Galaxy. A natural choice of coordinate system when studying dynamical systems is the canonical system of angle-action coordinates. We present methods for estimating the angle-actions in both axisymmetric and triaxial potentials. These fall into two categories: non-convergent and convergent. The non-convergent methods are fast approaches, mostly based on approximations to Stäckel potentials. We investigate the accuracy of these methods for realistic Galactic potentials. The slower convergent methods operate by constructing generating functions to take us from simple analytically-tractable potentials to our target potential. Tidal streams should prove useful for constraining the large-scale dark matter distribution in the Galaxy. Armed with our new angle-action tools, we investigate the properties of known streams in a realistic Galactic potential. We present a simple algorithm for constraining the Galactic potential using a tidal stream, which exploits the expected structure of a stream in the angle-frequency space of the true potential. We expand this approach into a fully probabilistic scheme that allows for handling of large errors, missing data and outliers. We close by discussing another tool useful for modelling the dynamics of the Galaxy: extended distribution functions for the Galactic disc. We present a simple extension of an action-based distribution function from Binney (2010) that includes metallicity information, and compare the model predictions with current data. These models are essential for incorporating the selection effects of any survey, and reveal the important chemo-dynamic correlations that expose the history and evolution of the Galaxy.

Counting stars as a means of studying the structure of the Milky Way has a long history, which has progressed significantly with the undertaking of large-area surveys. Photographic surveys have been supplanted with the advent of CCD technology by digital surveys, which provide improved data quality allowing better calibration and fainter limits to be probed reliably. The INT/WFC Photometric H Survey of the Northern Galactic Plane (IPHAS) provides broad-band r0 and i0 photometry down to 20th magnitude at Galactic latitudes jbj < 5 . In this work I make use of the opportunity that IPHAS photometry provides to create stellar number density maps of the Northern Galactic Plane. I produce preliminary maps which are used to identify and exclude poor quality data during the preparation of the second data release of the survey (DR2). By crossmatching IPHAS against the AAVSO Photometric All-Sky Survey (APASS), I derive transformations between the two photometric systems, and measure the per-IPHAS- field magnitude shifts needed to bring the two surveys in line before a global calibration can be applied. Repeating the crossmatching approach between IPHAS and the Sloan Digital Sky Survey (SDSS), I derive transformations between the two surveys and assess their agreement before and after global photometric calibration, in order to gauge the improvement achieved. The effects of incompleteness begin to affect the fainter end of any photometric survey as a consequence of confusion and sensitivity limits. I present the application of artificial source insertion on every broad-band IPHAS DR2 image in order to measure the impact of incompleteness across the entire survey. These measurements are used to construct incompleteness-corrected density maps down to magnitude limits of r0 . 19 and i0 . 18 at an angular resolution of 1 arcminute. These maps represent a unique data product which has applications in studies of Galactic structure and extinction. I perform a cluster search on the i0-band density map, which in addition to returning 71 known clusters, identifies 29 overdensities unassociated with any known clusters. I compare the stellar densities given by my maps to those in simulated versions of the Milky Way generated by models of Galactic population synthesis. I examine the Gaia Universe Model Snapshot (GUMS), a catalogue which predicts the sky as may be observed by the Gaia mission. In order to make meaningful comparisons between GUMS and IPHAS I determine transformations between the two photometric surveys. The results of the comparison are mixed. I also make use of the 2003 Besan con model of Galactic population synthesis to generate catalogues of synthetic photometry along three sightlines in the IPHAS footprint in order to test different 3D extinction prescriptions. The lowest Galactic longitudes (` 30 ) prove to be particularly challenging to emulate, suggesting 3D mapping of optical extinction in the Galactic Plane is not yet a mature art. The main problem appears to be one of underprediction of the obscuration.

In this thesis, I use the new generation of radio interferometer along with X-ray observations to investigate the dynamics and energetics of radio-loud active galaxies which are key to understanding AGN feedback and the evolution of galaxies as a whole. I present new JVLA observations of powerful radio source and use innovative techniques to undertake a detailed analysis of JVLA observations of powerful radio galaxies. I compare two of the most widely used models of spectral ageing, the Kardashev-Pacholczyk and Jaffe-Perola models and also results of the more complex, but potentially more realistic, Tribble model. I find that the Tribble model provides both a good fit to observations as well as providing a physically realistic description of the source. I present the first high-resolution spectral maps of the sources and find that the best-fitting injection indices across all models take higher values than has previously been assumed. I present characteristic hot spot advance speeds and compare them to those derived from dynamical ages, confirming that the previously known discrepancy in speed remains present in older radio sources even when ages are determined at high spectral and spatial resolutions. I show that some previously common assumptions made in determining spectral ages with narrow-band radio telescopes may not always hold. I present results from a study of the powerful radio galaxy 3C223 at low frequencies with LOFAR to determine its spectrum on spatially small scales and tightly constrain the injection index, which I find to be consistent with the high values found at GHz frequencies. Applying this new knowledge of the low energy electron population, I perform synchrotron / inverse-Compton model fitting and find that the total energy content of the radio galaxy lobes increases by a factor greater than 2 compared to previous studies. Using this result to provide revised estimates of the internal pressure, I find the northern lobe to be in pressure balance with the external medium and the southern lobe to be overpressured. I go on to present the first large sample investigation of the properties of jets in Fanaroff and Riley type I radio galaxies (FR-I) at X-ray energies based on data from the Chandra archive. I explore relations between the properties of the jets and the properties of host galaxies in which they reside. I find previously unknown correlations to exist, relating photon index, volume emissivity, jet volume and luminosity, and find that the previously held assumption of a relationship between luminosities at radio and X-ray wavelengths is linear in nature when bona fide FR-I radio galaxies are considered. In addition, I attempt to constrain properties which may play a key role in determination of the diffuse emission process. I test a simple model in which large-scale magnetic field variations are primarily responsible for determining jet properties; however, we find that this model is inconsistent with our best estimates of the relative magnetic field strengths in my sample.

I have investigated the properties of the large scale structure of the nearby Universe using data from the Galaxy and Mass Assembly survey (GAMA). I generated complementary halo mass estimates for all groups in the GAMA Galaxy Group Catalogue (G³C) using a modified caustic mass estimation algorithm. On average, the caustic mass estimates agree with dynamical mass estimates within a factor of 2 in 90% of groups. A volume limited sample of these groups and galaxies are used to generate the large scale structure catalogue. An adapted minimal spanning tree algorithm is used to identify and classify structures, detecting 643 filaments that measure up to 200 Mpc/h, each containing 8 groups on average. A secondary population of smaller coherent structures, dubbed `tendrils,' that link filaments together or penetrate into voids are also detected. On average, tendrils measure around 10 Mpc/h and contain 6 galaxies. The so-called line correlation function is used to prove that tendrils are real structures rather than accidental alignments. A population of isolated void galaxies are also identified. The properties of filaments and tendrils in observed and mock GAMA galaxy catalogues agree well. I go on to show that voids from other surveys that overlap with GAMA regions contain a large number of galaxies, primarily belonging to tendrils. This implies that void sizes are strongly dependent on the number density and sensitivity limits of the galaxies observed by a survey. Finally, I examine the properties of galaxies in different environments, finding that galaxies in filaments tend to be early-type, bright, spheroidal, and red whilst those in voids are typically the opposite: blue, late-type, and more faint. I show that group mass does not correlate with the brightness and morphologies of galaxies and that the primary driver of galaxy evolution is stellar mass.

This thesis presents spectroscopic observations of z ≥ 7 galaxy candidates in the Hubble Ultra Deep Field, which were selected with HST WFC3 imaging, using the Lyman-Break technique. Four z-band (z ≈ 7) dropout galaxies were targeted with Gemini/GNIRS, one z-band dropout galaxy and three Y -band (z ≈ 8 − 9) dropout galaxies with VLT/XSHOOTER, and 22 z-band dropouts with VLT/FORS2, where 15 of the latter are strong candidates. No evidence of Lyman-α emission is found, and the upper limits on the Lyman-α flux and the broad-band magnitudes are used to constrain the rest-frame equivalent widths for this line emission. Amongst the targeted objects, observations were made of HUDF.YD3, a relatively bright Y -band dropout galaxy likely to be at z ≈ 8 − 9 on the basis of its colours in the HST ACS and WFC3 images. Lehnert et al. (2010) observed this galaxy using the VLT/SINFONI integral field spectrograph and claim that it exhibits Lyman-α emission at z = 8.55. In observations of this object described in this thesis, which were made with VLT/XSHOOTER and Subaru/MOIRCS, this line was not reproduced despite the expected signal in the combined MOIRCS & XSHOOTER data being 5σ. Hence it appears unlikely that the reported Lyman-α line emission at z > 8 is real. Accounting for incomplete spectral coverage, in total (across all spectro- graphs) 9.63 z-band dropouts and 1.15 Y -band dropouts are surveyed to a Lyman-α rest-frame Equivalent Width better than 75 ̊A. A model where the fraction of high rest-frame equivalent width emitters follows the trend seen at z = 3−6.5 is inconsistent with these non-detections at z = 7−9 at a confidence level of ∼ 91%, which may indicate that a significant neutral HI fraction (χHI) in the intergalactic medium suppresses the Lyman-α line at z > 7. In particular, the lack of detection of Lyman-α emission in this spectroscopy is compared with results at lower redshift by Stark et al. (2010), who derive a mapping between Lyman-α fractions and χHI based on radiative transfer simulations by McQuinn et al. (2007). These results suggest a lower limit of χHI ~ 0.5.

Avec l’essor actuel de la sophistication et de l’efficacité des codes de cosmologie hydrodynamique,il est devenu possible d’inclure le transfert radiatif (RT) des photons ionisants dansles simulations cosmologiques, soit en post-traitement, soit en simulations couplées rayonnement+hydrodynamique (RHD). Malgré de nombreux obstacles, il y a eu cette derniéredécennie beaucoup de recherches menées sur les différentes stratégies et implémentations,dû au fait qu’un nombre de problèmes intéressants peuvent être désormais abordés par laRT et RHD, par exemple comment et quand l’Univers s’est réionisé, comment l’émissionradiative des étoiles et des noyaux actifs de galaxies se comportent pour réguler la formationdes structures à des échelles petites et grandes, et quelles prédictions et interprétationsnous pouvons faire des phénomènes observés, tels que la forêt Lyman-alpha et des sourcesdiffuses de rayonnement.Cela coïncide avec l’avènement du télescope spatial James Webb (JWST) et d’autresinstruments de pointe qui sont sur le point de nous donner un aperçu sans précédent sur lafin des âges sombres de l’Univers, quand le cosmos est passé d’un état froid et neutre à unétat chaud et ionisé, à la suite de l’apparition des sources radiatives.Notre préoccupation principale étant les rétroactions radiatives des premieres structures,nous avons mis en place une version RHD du code cosmologique Ramses, que nous appelonsRamsesRT, basée sur la méthode des moments. Ce code nous permet d’étudier les effets durayonnement ionisant dans les simulations cosmologiques RHD qui tirent pleinement profitdes stratégies de raffinement adaptif de grille et de parallélisation de Ramses. Pour rendreauto-cohérent le RHD nous avons également mis en oeuvre une thermochimie hors-équilibreincluant des espèces de l’Hydrogène et de l’Hélium qui interagissent avec le rayonnementtransporté.Je présente dans cette thèse une description détaillée de RamsesRT et de nombreux testscontribuant à sa validation.Jusqu’à présent nous avons utilisé RamsesRT pour étudier l’émission Lyman-alpha decourants d’accrétion, qui sont prédits à grand redshift par les simulations cosmologiques,mais n’ont jamais été clairement identifiés par les observations. Nous avons également étudiéle chauffage gravitationnel dans ces courants pour déterminer si ce dernier pouvait être lasource motrice principale des Lyman-alpha blobs, un phénomène observé qui a été beaucoupétudié et débattu au cours de la dernière décennie. Cet étudie nous permet de conclure queles Lyman-alpha blobs peuvent, en principe, être alimentés par le chauffage gravitationnel,et que d’autre part, les courants d’accrétion sont sur le point d’être directement détectablesavec des instruments à venir.Mes intentions futures sont d’utiliser RamsesRT dans les simulations cosmologiques àhaute résolution, de la formation des premiéres galaxies jusqu’à l’époque de la réionisation,et ainsi étudier comment la rétroaction radiative affecte la formation et l’évolution de cesgalaxies et de faire des prévisions d’observation qui peuvent être testées avec des instrumentssophistiqués tels que le JWST. / With the increasing sophistication and efficiency of cosmological hydrodynamics codes, ithas become viable to include ionizing radiative transfer (RT) in cosmological simulations,either in post-processing or in full-blown radiation-hydrodynamics (RHD) simulations. Inspite of the many hurdles involved, there has been much activity during the last decade or soon different strategies and implementations, because a number of interesting problems canbe addressed with RT and RHD, e.g. how and when the Universe became reionized, howradiation from stars and active galactic nuclei plays a part in regulating structure formationon small and large scales, and what predictions and interpretations we can make of observedphenomena such as the Lyman-alpha forest and diffuse sources of radiation.This coincides with the advent of the James Webb space telescope (JWST) and otherstate-of-the-art instruments which are about to give us an unprecedented glimpse into theend of the dark ages of the Universe, when the cosmos switched from a cold and neutralstate to a hot and ionized one, due to the turn-on of ionizing radiative sources.With a primary interest in the problem of radiative feedback in early structure formation,we have implemented an RHD version of the Ramses cosmological code we call RamsesRT,which is moment based and employs the local M1 Eddington tensor closure. This code allowsus to study the effects of ionizing radiation on-the-fly in cosmological RHD simulationsthat take full advantage of the adaptive mesh refinement and parallelization strategies ofRamses. For self-consistent RHD we have also implemented a non-equilibrium chemistry ofthe atomic hydrogen and helium species that interact with the transported radiation.I present in this thesis an extensive description of the RamsesRT implementation andnumerous tests to validate it.Thus far we have used the RHD implementation to study extended line emission fromaccretion streams, which are routinely predicted to exist at early redshift by cosmologicalsimulations but have never been unambiguously verified by observations, and to investigatewhether gravitational heating in those streams could be the dominant power source ofso-called Lyman-alpha blobs, an observed phenomenon which has been much studied anddebated during the last decade or two. Our conclusions from this investigation are thatLyman-alpha blobs can in principle be powered by gravitational heating, and furthermorethat accretion streams are on the verge of being directly detectable for the first time withupcoming instruments.My future intent is to use RamsesRT for high-resolution cosmological zoom simulations ofearly galaxy formation, up to the epoch of reionization, to study how radiative feedbackaffects the formation and evolution of those galaxies and to make observational predictionsthat can be tested with upcoming instruments such as the JWST.

Le Modèle Standard de la cosmologie décrit la formation des structures à grande échelle dans l'Univers récent dans un cadre quasi–newtonien. Ce modèle requiert la présence de composantes inconnues, la Matière Noire et l'Énergie Noire, afin de vérifier correctement les observations. Ces deux quantités représentent à elles seules près de 95% du contenu de l'Univers. Bien que ces composantes sombres soient activement recherchées par la communauté scientifique, il existe plusieurs alternatives qui tentent de traiter le problème des structures à grande échelle. Les théories inhomogènes décrivent l'impact des fluctuations cinématiques sur le comportement global de l'Univers. D'autres théories proposent également d'aller au-delà de la relativité générale. Durant cette thèse, j'ai mis au point des éléments clés d'une théorie lagrangienne totalement relativiste de la formation des structures. Supposant un feuilletage particulier de l'espace–temps j'ai résolu le système d'équations du premier ordre afin d'obtenir des solutions décrivant l'évolution de la matière dans un espace à la géométrie perturbée. J'ai également développé un schéma de résolution pour les ordres supérieurs de perturbation ainsi que leurs équivalent newtoniens. Une autre partie de ce travail de thèse consiste en le développement de quelques applications directes : la description d'un Univers silencieux ou l'hypothèse de courbure de Weyl et le problème de 'entropie gravitationnelle. Les objectifs à plus ou moins court terme seraient d'obtenir la description d'observables physiques and le développement d'autres applications. Cette étape de développement sera une interaction entre approches théorique et numérique et requerra de se rapprocher fortement des observateurs / The standard model of cosmology describes the formation of large scale structures in the late Universe within a quasi–Newtonian theory. This model requires the presence of unknown compounds of the Universe, Dark Matter and Dark Energy, to properly fit the observations. These two quantities, according to the Standard Model, represent almost 95% of the content of the Universe. Although the dark components are searched for by the scientific community, there exist several alternatives which try to deal with the problem of the large scale structures. Inhomogeneous theories describe the impact of the kinematical fluctuations on the global behaviour of the Universe. Or some theories proposed to go beyond general relativity. During my Ph.D. thesis, I developed key–elements of a fully relativistic Lagrangian theory of structure formation. Assuming a specific space–time slicing, I solved the first order system of equations to obtain solutions which describe the matter evolution within the perturbed geometry, and I developed higher order schemes and their correspondences with the Lagrangian perturbation solutions in the Newtonian approach. I also worked on some applications of these results like the description of a silent Universe or the Weyl curvature hypothesis and the problem of gravitational entropy. Further objectives are the description of physical observables and the development of direct applications. Next step of the development is an interaction between theoretical and numerical approaches, a study which would require strong cooperation with observers