String theory imposes slight modifications to Einstein's equations of general relativity (GR). In (4), the authors claim that the gravitational field equations in empty space, which in GR are just R [subscript greek letters mu nu ] = 0, should hold one extra term which is first order in the string constant [alpha'] and proportional to the Riemann curvature tensor squared. They do admit, however, that this simple modification is just schematic. In (1) the authors use modified equations which are coupled to the dilation field. We show that equations given in (4) do not admit an isotropic solution; justification of these equations would require sacrificing isotropy. We thus investigate the consequences of the coupled equations from (1) and the black-hole solution they give there. We calculate the additional perihelion precession of Mercury, the added deflection of photons by the sun, and the extra gravitational redshift which should be present if these equations hold. We determine that additional effects due to string theory in each of these cases are quite minuscule.

This thesis explores the spherically symmetric gravitational collapse of a massless scalar field in a minimally modified gravity theory denoted VCDM (V replaces $\Lambda$ in the $\Lambda$CDM abbreviation), a class of theories propagating the same degrees of freedom as general relativity at the expense of broken 4D diffeomorphism invariance. Numerical evolution of the equations of motion reveals that for small initial scalar profile amplitudes, no black hole forms from the collapse. However, for larger amplitudes, collapse leads to an apparent horizon's formation in finite time. Outside the horizon, the solution resembles the Schwarzschild geometry, while inside, the lapse function continues to decrease toward zero, implying the formation of a singularity/foliation breakdown. This suggests a need for a UV completion for the theory inside the horizon. Despite this, VCDM can describe the entire time evolution of the universe outside the black hole horizon without requiring knowledge of such a UV completion. / Denna uppsats undersöker den sfäriskt symmetriska gravitationskollapsen av ett masslöst skalärfält inom en minimalt modifierad gravitationsteori betecknad VCDM (där V ersätter $\Lambda$ i $\Lambda$CDM-förkortningen), en klass av teorier som propagerar samma frihetsgrader som den allmäna relativitetsteorin på bekostnad av bruten fyrdimensionell diffeomorfiinvarians. Numerisk utveckling av rörelseekvationerna visar att ett svart hål inte kan bildas om begynnelseamplituden hos den initiala skalärfältsprofilen är liten. För större amplituder bildas en uppenbar horisont på en ändlig tid. Utanför horisonten sammanfaller lösningen med Schwarzschildgeometrin, medan inuti horisonten fortsätter lapsefunktionen att falla mot noll, vilket implicerar formationen av en singularitet/sönderfall av rumtidsfolieringen. Detta tyder på att teorin är i behov av en UV-komplettering innanför horisonten. Trots detta kan VCDM beskriva hela universums tidsutveckling utanför det svarta hålet utan vetskap om en sådan UV-komplettering.

Galaxies are natural laboratories for testing fundamental physics on the nature of the dark matter. MOdified Newtonian Dynamics (MOND) has been tested for over 20 years on small and large scales. While there are several versions of how MOND extrapolates to the large scales, and these versions are not yet fully successful, the original Bekenstein-Milgrom version of MOND is fully predictive and works very well on galaxy scales. However, little work has been done to explore this theory beyond fitting the rotation curves and Tully-Fisher relation of isolated disc galaxies. So far little is known of MONDian elliptical galaxies accelerating in any galaxy cluster. A defining feature of MOND is that internal dynamics of the galaxy depends on the overall acceleration of the galaxy. The existence of cuspy triaxial equilibria for elliptical galaxies is the minimal requirement to MOND. With the PhD project here, I constructed and then further studied the evolution and stability of gravitationally bound systems resembling like cuspy elliptical galaxies, both in isolation and when embedded in a uniform external field. I also studied the escape speeds from spiral galaxies, in particular by comparing the potentials of the Milky Way Galaxy in the Cold Dark Matter (CDM) and MOND frameworks.

Nós investigamos o raio de turnaround, a distância do centro da estrutura cósmica até a casca que está se descolando do fluxo de Hubble em um dado tempo, no contexto do modelo de colapso esférico, tanto em Relatividade Geral e em Gravidade Modificada, em particular no cenário f(R) chamado de modelo de Hu-Sawicki. O próximo passo foi investigar a relação entre este raio e a massa de virial de estruturas cósmicas no contexto do modelo LCDM e no modelo f(R) de gravidade modificada. / We investigate the turnaround radius, the distance from the center of the cosmic structure to the shell that is detaching from the Hubble flow at a given time, in the context of the spherical collapse model, both in General Relativity and in modified gravity, in particular f(R) scenarios -- namely the Hu-Sawicki model. The next step was to investigate the relationship between that radius and the virial mass of cosmic structures in the context of LCDM model and in an f(R) model of modified gravity.

Nós investigamos o raio de turnaround, a distância do centro da estrutura cósmica até a casca que está se descolando do fluxo de Hubble em um dado tempo, no contexto do modelo de colapso esférico, tanto em Relatividade Geral e em Gravidade Modificada, em particular no cenário f(R) chamado de modelo de Hu-Sawicki. O próximo passo foi investigar a relação entre este raio e a massa de virial de estruturas cósmicas no contexto do modelo LCDM e no modelo f(R) de gravidade modificada. / We investigate the turnaround radius, the distance from the center of the cosmic structure to the shell that is detaching from the Hubble flow at a given time, in the context of the spherical collapse model, both in General Relativity and in modified gravity, in particular f(R) scenarios -- namely the Hu-Sawicki model. The next step was to investigate the relationship between that radius and the virial mass of cosmic structures in the context of LCDM model and in an f(R) model of modified gravity.

General relativity (GR) has stood as the most accurate description of gravity for the last 100 years, weathering a barrage of rigorous tests. However, attempts to derive GR from a more fundamental theory or to capture further physical principles at high energies has led to a vast number of alternative gravity theories. The individual examination of each gravity theory is infeasible and as such a systematic method of examining modified gravity theories is a necessity. Studying generic classes of gravity theories allows for general statements about observables to be made independent of explicit models. Take, for example, those models described by the Horndeski action, the most general class of scalar-tensor theory with at most second-order derivatives in the equations of motion, satisfying theoretical constraints. But these constraints alone are not enough for a given modified gravity model to be physically viable and hence worth studying. In particular, observations place incredibly tight constraints on the size of any deviation in the solar system. Hence, any modified gravity would have to mimic GR in such a situation. To accommodate this requirement, many models invoke screening mechanisms which suppress deviations from GR in regions of high density. But these mechanisms really upon non-linear effects and so studying them in complex models is mathematically complex. To constrain the space of actions of Horndeski type to those which pass solar-system tests, a set of conditions on the four free functions of the Horndeski action are derived which indicate whether a specific model embedded in the action possesses a GR limit. For this purpose, a new and surprisingly simple scaling method is developed, identifying dominant terms in the equations of motion by considering formal limits of the couplings that enter through the new terms in the modified gravity action. Solutions to the dominant terms identify regimes where nonlinear terms dominate and Einstein's field equations are recovered to leading order. Together with an efficient approximation of the scalar field profile, one can determine whether the recovery of Einstein's field equations can be attributed to a genuine screening effect. The parameterised post-Newtonian (PPN) formalism has enabled stringent tests of static weak-field gravity in a theory-independent manner. This is through parameterising common perturbations of the metric found when performing a post-Newtonian expansion. The framework is adapted by introducing an effective gravitational coupling and defining the PPN parameters as functions of position. Screening mechanisms of modified gravity theories can then be incorporated into the PPN framework through further developing the scaling method into a perturbative series. The PPN functions are found through a combination of the scaling method with a post-Newtonian expansion within a screened region. For illustration, we show that both a chameleon and cubic galileon model have a limit where they recover GR. Moreover, we find the effective gravitational constant and all PPN functions for these two theories in the screened limit. To examine how the adapted formalism compares to solar-system tests, we also analyse the Shapiro time delay effect for these two models and find no deviations from GR insofar as the signal path and the perturbing mass reside in a screened region of space. As such, tests based upon the path light rays such as those done by the Cassini mission do not constrain these theories. Finally, gravitational waves have opened up a new regime where gravity can be tested. To this end, we examine how the generation of gravitational waves are affected by theories of gravity with screening to second post-Newtonian (PN) order beyond the quadrupole. This is done for a model of gravity where the black hole binary lies in a screened region, while the space between the binary's neighbourhood and the detector is described by Brans-Dicke theory. We find deviations at both 1.5 and 2 PN order. Deviations of this size can be measured by the Advanced LIGO gravitational wave detector highlighting that our calculation may allow for constraints to be placed on these theories. We model idealised data from the black hole merger signal GW150914 and perform a best fit analysis. The most likely value for the un-screened Brans-Dicke parameter is found to be ω = -1:42, implying on large scales gravity is very modified, incompatible with cosmological results.

Submitted by Leonardo Cavalcante (leo.ocavalcante@gmail.com) on 2018-04-30T14:18:12Z No. of bitstreams: 1 Arquivototal.pdf: 1310917 bytes, checksum: 54733929b9cb3c26ca0a0dc1adb0ae42 (MD5) / Made available in DSpace on 2018-04-30T14:18:12Z (GMT). No. of bitstreams: 1 Arquivototal.pdf: 1310917 bytes, checksum: 54733929b9cb3c26ca0a0dc1adb0ae42 (MD5) Previous issue date: 2015-02-27 / Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / Modifed theories of gravity has the objective to elucidate some open issues in the context of general relativity. From this perspective many theories have been proposed over the years. In this paper we deal with some of these theories and, for each of them, we gave our contribution proposing new scenarios that showed promise. So in the context of braneworld theory we held the first studies in three dimensional DGP theory, with terms of induced gravity of the new massive gravity type. The study of the propagators of disturbed theory showed unit propagation modes without the presence of tachyons. As regards to the Horava-Lifshitz theory, we studied the structure of membranes with scalar fields in 4+1 dimensions and the formation of black holes in 1+1 dimensions has been obtained for the first time. In the two previous cases we deal with nonprojectable version of this theory. Have also studied braneworld models in a bimetric theory where gravity is coupled to the scalar field that connects the two metrics. Although the scalar field having a linear term kinetic the theory remained stable and gravity localization was obtained. Finally, we apply the theory of gravitation with nondynamical fields to a cosmological model and found that for a certain specific stage of the Universe Expansion is possible to have a mechanism that generates a self tuning of the cosmological constant problem. / Teorias de gravidade modificada tem como objetivo elucidar alguns problemas em aberto no âmbito da Relatividade Geral. Dentro desta perspectiva muitas teorias foram propostas ao longo dos anos. Neste trabalho abordamos algumas destas teorias e, para cada uma delas, demos a nossa contribuição propondo novos cenários que se mostraram promissores. Assim, no contexto das teorias de mundo-brana estudamos pela primeira vez teorias do tipo DGP em 2+1 dimensões, com termos de gravidade induzida do tipo nova gravidade massiva. O estudo dos propagadores da teoria perturbada mostrou a propagação de modos unitários e sem a presença de táquions. No que diz respeito à teoria de Horava-Lifshitz, estudamos a estrutura de branas com campos escalares em 4+1 dimensões e a formação de buracos em 1+1 foi obtida pela primeira vez. Nos dois casos anteriores tratamos da versão não projetável desta teoria. Estudamos ainda modelos de mundo-brana em uma teoria com bimétrica onde a gravidade se acopla ao campo escalar que conecta as duas métricas. Apesar de o campo escalar possuir um termo cinético linear a teoria se mostrou estável e localização da gravidade foi obtida. Por fim, aplicamos a teoria da gravitação com campos não dinâmicos a um modelo cosmológico e constatamos que para certa fase específica da expansão do Universo é possível termos um mecanismo que gera um auto ajuste da constante cosmológica.

La description actuelle des interactions fondamentales repose sur deux théories ayant le statut de modèle standard. Les interactions électromagnétiques et nucléaires sont décrites à un niveau quantique par le Modèle Standard de la physique des particules, alliant théories de jauge et brisures spontanées de symétrie par le mécanisme de Higgs. À l'opposé, l'interaction gravitationnelle est décrite par la relativité générale,basée sur une description dynamique de l'espace-temps dans un cadre classique.Bien que ces deux modèles soient vérifiés avec une grande précision dansle système solaire, ils sont affligés d’un certain nombre de problèmes théoriques et manquent de force prédictive aussi bien à l'échelle de Planck qu’à l'échelle cosmologique ;ils ne sont par conséquent plus perçus comme fondamentaux. La cosmologie, dont la phénoménologie fait apparaitre ces deux échelles extrêmes, apparaît alors comme un laboratoire privilégié pour tester les théories au delà de ces modèles standards.La première partie de cette thèse concerne l'étude des cordes cosmiques, défauts topologiques se formant lors de la brisure spontanée de théories de grande unification dans l'univers primordial.J’y montre notamment comment étudier ces défauts en prenant en compte la structure complète des théories de physique des particules dont ils sont issus, ce qui représente une avancée importante par rapport à la description courante en termes de modèles ”jouets”très simplifiés. La deuxième partie de cette thèse consiste en la construction et l'étude de différentes théories de gravité modifiée liées au modèle de Galiléon, un modèle tentant notamment d'expliquer la phénoménologie liée à l'énergie noire. / The current description of fundamental interactions is based on two theories with the status of standard models. The electromagnetic and nuclear interactions are described at a quantum level by the Standard Model of particle physics, using tools like gauge theories and spontaneous symmetry breaking by the Higgs mechanism. The gravitational interaction is described on the other hand by general relativity, based on a dynamical description of space-time at a classical level.Although these models are verified to high precision in the solar system experiments, they suffer from several theoretical weaknesses and a lack of predictive power at the Planck scale as well as at cosmological scales; they are thus not viewed anymore as fundamental theories. As its phenomenology involves both these extreme scales, cosmology is then a good laboratory to probe theories going beyond these standard models.The first part of this thesis focus on cosmic strings, topological defects forming during the spontaneous symmetry breaking of grand unified theories in the early universe. I show especially how to study these defects while taking into account the complete structure of the particles physics models leading to their formation, going beyond the standard descriptions in terms of simplified toy-models. The second part is devoted to the construction and the examination of different theories of modified gravity related to the Galileon model, a model which tries in particular to explain the dark energy phenomenology.

Temnáenergietvořícípřibližně70%hmotyvesmíruz·stávájednouznejvětšch záhad moderní fyziky. K pochopení její podstaty jsou potřeba přesná kosmolog- ická měření. Jedním z projekt· zkoumající tuto exotickou formu hmoty bude i Large Synoptic Survey Telescope, který pom·že potvrdit či vyvrátit standardní kosmologický model (ΛCDM). Pro úspěch projektu je potřeba prozkoumat r·zné teorie temné energie. Jednou z alternativních teoríí vysvětlujících urychlenou expanzi vesmíru je tzv. chameleoní gravitace. Chameleon je nové skalární pole s hmotou závisející na okolní hustotě. V hustých prostředích jako je například Sluneční soustava získává pole velkou hmotu a propaguje se pouze na malých vzdálenostech díky čemuž m·že uniknout standardním test·m gravitace. V prá- ci mimo jiné studujeme chování chameleoního pole v okolí hvězd a v galaxiích. Ukazujeme také za jakých okolností je toto pole možné detekovat pomocí spek- troskopických měření a slabého čočkování.

Title: Study of dark energy and modified gravity and their influence on the cosmological parameters of the universe Author: Michal Vraštil Institute: Institute of Physics of the Czech Academy of Sciences Supervisor: RNDr. Michael Prouza, Ph.D., Institute of Physics of the Czech Academy of Sciences Abstract: Discovery of the accelerated expansion of the Universe poses a major theoretical puzzle. Although the assumption of a non-zero cosmological constant provides a minimal extension of general relativity that is consistent with observational data, many theories of modified gravity have been suggested as possible alternatives due to serious problems connected with the cosmological constant. Numerical predictions of structure formation for these models in the fully non-linear regime are very expensive and it is difficult, if not impossible, to explore such a huge space of models and parameters using high-resolution N-body simulations. Even in the mildly nonlinear regime, perturbative methods can become extremely complex. We explore whether simplified dynamical approximations, applicable for a certain set of cosmological probes, can be used to investigate models of modified gravity with acceptable accuracy in the latter instance. For the case of chameleon gravity, we found that it is screened away on scales...