Cosmology is one of the best tools to understand the physics that governs the universe at high energies. On one hand, inflation is a very robust mechanism to explain the initial conditions of the universe. On the other hand general relativity provides a solid framework for the formation of cosmic structures at cosmological scales. Nevertheless, there are still important issues that remain without a clear answer. For example, inflation still lacks of a concrete microphysical description, and also there is still no satisfactory mechanism to explain the late time acceleration of the universe. This thesis addresses these two topics. In the first part we discuss the effects of heavy degrees of freedom coupled to inflation. This has been an important topic over the years, because the experimental success might make it possible to detect new degrees of freedom in inflation. In chapter two we discuss the case when non relativistic heavy fields are coupled to the inflaton through a non minimal gravitational coupling. Here we find that, for certain geometries, the heavy field can modify the potential for a few e-folds, either stopping inflation, or setting its initial conditions. In chapter 3 we study the dynamics of fluctuations in holographic inspired models of multi-field inflation. We find that the entropy mass $\mu$ (the mass of the fluctuation orthogonal to the trajectory of inflation) satisfies an universal upper bound given by $\mu \leq 3 H / 2$. This bound coincides with the requirement of unitarity of conformal operators living on the boundary of the theory. In the second part of the thesis we study high energy effects on the Cosmic Microwave Background (CMB). In the fourth chapter we study the role of disformal transformation on cosmological backgrounds and its relation to the speed of sound for tensor modes. A speed different from one for tensor modes can arise in several contexts such as Galileons theories, or massive gravity. Nevertheless the speed is very constrained to be one by observations of gravitational wave emission. It has been shown that in inflation a disformal transformation allows the speed for tensor modes, to be set to one without making changes to the curvature power spectrum. We show that on the CMB, after doing the transformation, there is an imprint on the acoustic peaks, and the diffusion damping. This has interesting consequences: for a particular class of theories the transformation can be used to constrain the parameter space in different regimes. In chapter five we study the impact of gravitons with non-vanishing masses on the polarisation of th CMB . We also focus on putative modifications to the speed of the gravitational waves. We find that a change of the graviton speed shifts the acoustic peaks of the B-mode polarization and then could be easily constrained. In all cases when both massless and massive gravitons are present, we find that the B-mode CMB spectrum is characterised by a low $l$ plateau together with a shifted position for the first few peaks compared to a massless graviton spectrum. This shift depends on the mixing between the gravitons in their coupling to matter and could serve as a hint in favour of the existence of multiple gravitons.

In this thesis we present work done in an analysis of models of brane induced gravity. These are higher dimensional generalizations of Einstein's General relativity where our universe is considered as a brane in a higher dimensional bulk and where the gravitational dynamics on the brane is enhanced. This provides a modification of gravity on the brane as compared to ordinary general relativity, primarily at very large distances. These models are therefore very interesting for adressing the cosmological constant problem. Even though the basic setup is natural to consider from the perspective of effective field theory and also follow from certain string theoretical considerations, the models have been plagued by inconsistencies in the form of unstable modes. In particular, a ghostlike and tachyonic scalar mode appears already at the linear level in a perturbative treatment. In order to gain a deeper insight into the nature of these consistency problems we have revisited the models, performing a more extensive analysis of the generic models than has previously been done. We have worked entirely in a gauge invariant formalism in order not to be obscured by gauge issues. We have also incorporated an effective thickness of the brane in our analysis and performed an explicit analysis of the effect of contributions from the extrinsic geometry. Although our analysis has been carried out at the linear level in a perturbative treatment we are able to get a deeper understanding of the unstable mode and illuminate some of the difficulties of these models that would likely persist even in a full nonlinear analysis.

This thesis attempts to test several frameworks of non-Newtonian gravity in the context of galaxies and galaxy clusters. The theory most extensively discussed was that of Modified Newtonian Dynamics (MOND) with Galileon gravity, Emergent Gravity (EG) and Modified Gravity (MOG) mentioned to a lesser extent. Specifically, the main focus of this thesis was to determine whether MOND and MOND-like theories were compatible with galaxy cluster data, without the need to include cold dark matter. To do this, the paradigms of Extended MOND (EMOND), Generalised MOND (GMOND) and superfluid dark matter were investigated. The theories were outlined and applied to galaxy cluster data. The main findings of this were that EMOND and GMOND had some success with explaining galaxy cluster mass profiles, without requiring an additional dark matter component. The superfluid paradigm also enjoyed some success in galaxy clusters, which was expected as it behaves in a similar manner to the standard cold dark matter paradigm in cluster environments. However, the superfluid paradigm may have issues in the very centre of galaxy clusters due to the theory predicting constant density cores, whereas the cold dark matter paradigm predicts density cores which are cuspier. The EMOND paradigm was also tested against ultra-diffuse galaxy (UDGs) data as they appear in cluster environments, where EMOND becomes important. It was found that EMOND can reproduce the inferred mass of the UDGs, assuming they lie on the fundamental manifold (FM). The validity of the assumptions used to model the UDGs are discussed in the text. A two-body problem was also conducted in the Galileon gravity framework. The amount of additional gravitational force, compared to Newtonian was determined for a small galaxy at the edge of a galaxy cluster.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20177号 / 理博第4262号 / 新制||理||1613(附属図書館) / 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 佐々木 節, 教授 田中 貴浩, 教授 川合 光 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

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京都大学 / 新制・課程博士 / 博士(理学) / 甲第23453号 / 理博第4747号 / 新制||理||1680(附属図書館) / 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 向山 信治, 准教授 De Felice Antonio , 教授 萩野 浩一 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

京都大学 / 新制・課程博士 / 博士(理学) / 甲第24869号 / 理博第4979号 / 新制||理||1711(附属図書館) / 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 向山 信治, 准教授 樽家 篤史, 教授 橋本 幸士 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

We begin by reviewing special and general relativity in such a way as to smoothly transition into current research. We present the variational formalism of general relativity as well as the extension into the palatini formalism. This allows us to develop a theory on a metric affine manifold rather than the standard manifold in general relativity. We present a generalized action intended to replace the Einstein Hilbert action in general relativity and derive some consequences thereof. The modified field equations are derived by varying this action using the Palatini approach. The corresponding differential equations are solved thereby establishing the equivalence between the modified action and the standard action with a cosmological constant. Furthermore the metric due to a spherically symmetric distribution of mass is found and applied in calculating the bending of light in the curved space. It is deduced that no difference between the modified action and the original Einstein Hilbert action is observed thereby implying that the experiment involving the bending of light around the sun in 1919 in no way distinguishes between our modification and the original approach by Einstein and Hilbert.

Bimetric theory is an extension to general relativity that introduces a secondary symmetric rank-two tensor field. This secondary spin-2 field is also dynamical, and to avoid the Boulware-Deser ghost issue, the interaction between the two fields is obtained through a potential that involes the matrix square-root of the tensors. This square-root “quantity” is a linear transformation, herein referred to as the square-root isometry. In this work we explore the conditions for the existence of the square-root isometry and its group properties. Morever we study the conditions for the simultaneous 3+1 decomposition of two fields, and then, in terms of null-cones, give the (local) causal relations between fields coupled by the square-root isometry. Finally, we show the algebraic equivalency of bimetric theory and its vielbein formulation up to a one-to-one map relating the respective parameter spaces over the real numbers. / Den bimetriska teorin är en utökning av den allmänna relativitetsteorin som introducerar ett sekundärt symmetriskt tensorfält av rang-två. Det här sekundära spin-2 fältet är också dynamiskt, och för att undvika Boulware-Deser spöke, erhålls vaxelverkan mellan de två fältena genom en potential som er baserad på kvadratrotsmatris av två tensorfält. Den “kvadratroten” är en linjär avbildning som kallas kvadratrotsisometri. I detta arbete utforskas förutsättningar för existensen av kvadratrotsisometrin och ges dess egenskaper i termer av gruppteori. Därutöver utforskas förutsättningarna för den samtidiga 3+1 dekompositionen av två tensorfält och sedan, i termer av ljuskoner, ges de (lokala) kausala relationerna för tensorfält kopplade genom kvadratrotsisometrin. Slutligen bevisas den algebraiska ekvivalensen mellan den bimetriska teorin och dess vielbein formulering upp till en bijektiv relation mellan respektive parameterutrymmen över de reella talen. / <p>Summarizes the results from the project done between March 2014 and November 2014.</p>

This thesis explores topics related to the formation and development of the large-scale structure in the Universe, with the focus being to compute properties of the evolved non-linear density field in an approximate way. The first three chapters form an introduction: Chapter 1 contains the theoretical basis of modern cosmology, Chapter 2 discusses the role of N-body simulations in the study of structure formation and Chapter 3 considers the phenomenological halo model. In Chapter 4 a novel method of computing the matter power spectrum is developed. This method uses the halo model directly to make accurate predictions for the matter spectrum. This is achieved by fitting parameters of the model to spectra from accurate simulations. The final predictions are good to 5% up to k = 10 hMpc-1 across a range of cosmological models at z = 0, however accuracy degrades at higher redshift and at quasi-linear scales. Chapter 5 is dedicated to a new method of rescaling a halo catalogue that has previously been generated from a simulation of a specific cosmological model to a different model; a gross rescaling of the simulation box size and redshift label takes place, then individual halo positions are modified in accord with the large scale displacement field and their internal structure is altered. The final power spectrum of haloes can be matched at the 5% level up to k = 1 hMpc-1, as can the spectrum of particles within haloes reconstituted directly from the rescaled catalogues. Chapter 6 applies the methods of the previous two chapters to modified gravity models. This is done in as general a way possible but tests are restricted to f(R) type models, which have a scale-dependent linear growth rate as well as having 'chameleon screening' - by which modifications to gravity are screened within some haloes. Taking these effects into account leads to predictions of the matter spectrum at the 5% level and rescaled halo distributions that are accurate to 5% in both real and redshift space. For the spectrum of halo particles it is demonstrated that accurate results may be obtained by taking the enhanced gravity in some haloes into account.