Doutorado em Astrofísica, Cosmologia e Gravitação

URI Permanente para esta coleção

http://repositorio.ufes.br/handle/10/17489

Nível: Doutorado
Ano de início: 2016
Conceito atual na CAPES: 5
Ato normativo: Parecer 487/2018
Periodicidade de seleção: Semestral
Área(s) de concentração: Astronomia e Física
Url do curso: https://cosmologia.ufes.br/pt-br/pos-graduacao/PPGCosmo/detalhes-do-curso?id=1453

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Accelerated expansion as manifestation of gravity: when dark energy belongs to the left
(Universidade Federal do Espírito Santo, 2020-10-23) Giani, Leonardo; Amendola, Luca; Piattella, Oliver Fabio; https://orcid.org/0000000345580574; http://lattes.cnpq.br/5707156831919279; Fabris, Julio Cesar; https://orcid.org/000000018880107X; http://lattes.cnpq.br/5193649615872035; Velten, Hermano Endlich Schneider; https://orcid.org/0000000251557998; http://lattes.cnpq.br/0282590467459210; Silva, Saulo Carneiro de Souza; https://orcid.org/000000017098383X; http://lattes.cnpq.br/5571527465158124; Iglesias, Jorge Antonio Zanelli; Kamenchtchik, Alexandre
In order to explain the Late-times accelerated expansion of the Universe we must appeal to some form of Dark Energy. In the standard model of cosmology, the latter is interpreted as a Cosmological Constant . However, for a number of reasons, a Cosmological Constant is not completely satisfactory. In this thesis we study Dark Energy models of geometrical nature, and thus a manifestation of the underlying gravitational theory. In the rst part of the thesis we will review the CDM model and give a brief classi cation of the landscape of alternative Dark Energy candidates based on the Love lock theorem. The second part of the thesis is instead devoted to the presentation of our main results on the topic of Dark Energy. To begin with, we will report our studies about nonlocal modi cations of gravity involving the differential operator 1R, with emphasis on a speci c model and on the common behavior shared by this and similar theories in the late stages of the evolution of the Universe. Then we introduce a novel class of modi ed gravity theories based on the anticurvature tensor A (the inverse of the Ricci tensor), and assess their capability as source of Dark Energy. Finally, we will discuss a type of drift e ects which we predicted in the contest of Strong Gravitational Lensing, which could be employed both to study the e ective equation of state of the Universe and to constrain violations of the Equivalence Principle.
An analytic study of lensing by black holes in Kerr-de Sitter spacetimes
(Universidade Federal do Espírito Santo, 2023-08-11) Omwoyo, Eunice Monyenye; Belich Junior, Humberto; https://orcid.org/0000-0002-8795-1735; http://lattes.cnpq.br/3879935393431243; https://orcid.org/0000-0003-4660-8161; http://lattes.cnpq.br/5310812834959626; Fabris, Julio Cesar; https://orcid.org/000000018880107X; http://lattes.cnpq.br/5193649615872035; Falciano, Felipe Tovar; https://orcid.org/0000000322631252; http://lattes.cnpq.br/7214193952056222; Velten, Hermano Endlich Schneider; https://orcid.org/0000000251557998; http://lattes.cnpq.br/0282590467459210; Stuchilk, Zdenek; Dotti, Gustavo
The recent release of the images of M87 and Sagittarius A∗ (SgrA∗ ) black holes by the Event Horizon Telescope (EHT) collaboration has provided unprecedented insights into the emission structure on horizon scales. As technology advances, the aim is to capture even sharper and more detailed images which is among the main aims of the next generation Event Horizon Telescope (EHT). This raises the question of what can be expected and learned from highly resolved black hole images. In-depth studies using general relativistic magnetohydrodynamics simulations reveals that a highly resolved black hole image exhibits a distinct feature called the photon ring. This feature persists in the simulations, regardless of the nature of the astrophysical source profile surrounding the black hole. The photon ring is generated by photons on trajectories that have undergone extreme bending due to the strong gravity of the black hole, causing them to execute multiple orbits. As such, it is intricately connected to the specific properties and spacetime geometry in the vicinity of the black hole and is less sensitive to the astrophysical source profile around the black hole. Besides, the photon ring exhibits a nested sequence of self similar subrings that exponentially converge to the critical curve. The critical curve is purely a theoretical entity whose shape directly follows from General Relativity (GR) but is not in itself observable. However, the photon ring is in principle detectable in the near future observations. Given that this feature is contingent on spacetime geometry and black hole properties, its detection presents the potential for more robust tests of General Relativity (GR) and the Kerr hypothesis. Given the significance thereof, it is vital to conduct an extensive study and make predictions about the explicit nature of the photon ring in various black hole spacetimes. In this thesis, we present the photon ring structure in asymptotically de Sitter spacetimes, with emphasis on the Kerr-de Sitter (KdS) and Kerr-de Sitter Revisited (RKdS) spacetimes. Our analytical approach begins by obtaining solutions to the null geodesic equations in these spacetimes in terms of the Jacobi elliptic functions. These solutions shed light on the overall structure of bound and nearly bound photon orbits, which are the orbits central to this thesis. Subsequently, we delve into the analysis of the critical curve, for which we focus on observers located in the vicinity of the static radius. Moreover, utilizing the solutions we conduct an analytical ray-tracing to explore the properties of direct images, lensed rings, and photon rings. We also consider the special case of zero spin and zero cosmological constant. Our analysis takes into account locally static observers and assumes equatorial disks around the black holes. We compare the various images to the corresponding critical curves. Images arising from photons that have made 2 or more half orbits around the black hole exhibit a remarkable resemblance to the critical curve and are located in close proximity to this curve. Furthermore, these images demonstrate the same universal behavior as the critical curve, such as a more circular shape for small black hole spin and observer inclination angles, as well as a flattened appearance on one side for larger spin and inclination angles. From our study, these images demonstrate a more promising arena for tests of General Relativity (GR) than images arising from photons that have executed one half orbit around the black hole. Besides, we investigate the parameters that govern the subsequent rings’ exponential demagnification, rotation, and detection delay. These parameters are the Lyapunov exponent, the azimuthal angle change, and the time delay.
Black hole ringdown, and theoretical considerations concerning k-essence, Rastall and entangled gravity
(Universidade Federal do Espírito Santo, 2021-09-24) Santos, Edison Cesar de Oliveira; Fabris, Júlio César; https://orcid.org/000000018880107X; http://lattes.cnpq.br/5193649615872035; https://orcid.org/0000000261611804; http://lattes.cnpq.br/6514257640588577; Zanchin, Vilson Tonin; https://orcid.org/0000-0001-8499-1515; http://lattes.cnpq.br/2262120637290369; Aguiar, Odylio Denys de; https://orcid.org/0000-0002-2139-4390; http://lattes.cnpq.br/3325984959083987; Ricaldi, Wiliam Santiago Hipolito; https://orcid.org/000000021748553X; http://lattes.cnpq.br/0293080746483402; Sturani, Riccardo; https://orcid.org/0000000321574401; http://lattes.cnpq.br/9771195169911237; Christensen, Nelson; https://orcid.org/0000-0002-6870-4202; Moreschi, Osvaldo Mario; https://orcid.org/0000-0001-9753-3820
While the detection of gravitational waves was an outstanding achievement in theo- retical and observational physics, data science, computer science and engineering on their own merit, it also allowed us to observe black holes for the first time. Black hole physics had a tumultuous research history, from a nearly non-existent field to work, in the first years of general relativity, culminating in the golden age of general relativity in the sixties and mid-seventies, where black holes entered the mainstream theoretical physics. We could be arguably living in the second golden age of general relativity, but this time around black holes entered the mainstream observational physics. In light of this, this thesis tackle some problems in black hole physics, or in a broader sense, the current understanding of gravity. The first part of this thesis is devoted to developing the machinery of first-order perturbation theory in order to obtain the quasi-normal modes from both singular and non-singular black holes, that is, the frequencies related to the oscillation of a black hole after its merging. In the next section we contrast how a particular analytical model, that works from the merger up to the ringdown phase, constrains both the final mass and spin parameter when compared to the published results. In the second part, we investigate a series of works related to spherically-symmetric solutions of both k-essence and Rastall theories, where a possible solution to what seems a coincidence in both theories, might be related to a formulation of a lagrangian formalism for the latter theory. We end this thesis finding black hole solutions to a novel theory of gravity, entangled gravity. This model is not defined in the absence of any matter field, but we argue that black hole solutions satisfying the near vacuum condition resembles solutions obtained in standard general relativity.
Cosmological model with running vacuum energy and warm dark matter
(Universidade Federal do Espírito Santo, 2021-01-28) Ruiz, Jhonny Andres Agudelo; Chapiro, Ilia; https://orcid.org/0000-0001-6971-9409; http://lattes.cnpq.br/2644217574349073; https://orcid.org/0000-0002-8918-5835; http://lattes.cnpq.br/3039931513015232; Fabris, Júlio César; https://orcid.org/000000018880107X; http://lattes.cnpq.br/5193649615872035; Toribio, Alan Miguel Velasquez; https://orcid.org/0000-0002-2345-3999; http://lattes.cnpq.br/1885284194756497; Piattella, Oliver Fabio; https://orcid.org/0000000345580574; http://lattes.cnpq.br/5707156831919279; Rivera, Celia Del Carmen Escamilla; https://orcid.org/0000-0002-8929-250X; http://lattes.cnpq.br/6858596344111096; Peter, Patrick; https://orcid.org/0000-0002-7136-8326; http://lattes.cnpq.br/4674461245456989; Carballeira, Manuel Asorey; https://orcid.org/0000-0003-3669-6241
The core of the present thesis is the possibility of the change with the energy scale (running) of the cosmological constant. Theoretically, this running in the IR region is not ruled out. On the other hand, from the Quantum Field Theory (QFT) viewpoint, the energy released due to the variation of the cosmological constant in the late Universe cannot go to the matter sector. For this reason, the phenomenological bounds on such a running are not sufficiently restrictive. The situation can be different in the early Universe when the gravitational field was sufficiently strong to provide an efficient creation of particles from the vacuum. We develop a framework for systematically exploring this possibility. It is supposed that the running occurs in the epoch when the Dark Matter (DM) already decoupled and is expanding adiabatically, while the usual matter should be regarded approximately massless and can be abundantly created from vacuum due to the decay of vacuum energy. By using the handy model of Reduced Relativistic Gas (RRG) for describing the Warm Dark Matter (WDM), we consider the dynamics of both cosmic background and linear perturbations and evaluate the impact of the vacuum decay on the matter power spectrum and to the first CMB peak. Additionally, using the combined SNIa+BAO data, we find the best-fit values for the free parameters of the model. Additionally, it is known than the inclusion of spatial curvature can modify the evolution of matter perturbations and affect the Large Scale Structure (LSS) formation. We quantify the effects of the non-zero space curvature in terms of LSS formation for a cosmological model with a RCC and a WDM component. The evolution of density perturbations and the modified shape of its power spectrum are also reconstructed and analyzed in this context. Finally, it is analytically constructed the scalar field actions minimally and nonminimally coupled to gravity, which are equivalent to RRG (describing the WDM component) in the sense they produce the same cosmological solutions for the conformal factor of the metric. In particular, we construct the scalar theory which corresponds to the model of an ultra-relativistic ideal gas of spinless particles possessing conformal symmetry. The possibility of supplementing our scalar field model for WDM with dynamical dark energy in the form of a RCC is also considered.
Dark matter, modified gravity and galaxy rotation curves analyses: novel methods
(Universidade Federal do Espírito Santo, 2023-12-18) Arboleda, Alejandro Hernandez; Amendola, Luca; Rodrigues, Davi Cabral; https://orcid.org/0000000316835443; http://lattes.cnpq.br/5465449494182034; https://orcid.org/0000000321738779; http://lattes.cnpq.br/2611380047360980; Ricaldi, Wiliam Santiago Hipolito; https://orcid.org/000000021748553X; http://lattes.cnpq.br/0293080746483402; Delmestre, Karin Menendez; Marra, Valerio; https://orcid.org/0000000277731579; http://lattes.cnpq.br/6846011112691877; Rivera, Celia Del Carmen Escamilla
The current ΛCDM cosmological model considers dark matter to be the most abundant type of matter on the universe, encompassing approximately 26.8% of it. As its name suggests, dark matter cannot be directly observed by means of electromagnetic radiation, it only interacts through gravitational fields. Historically, the discover of dark matter was made based on the study of the internal dynamics of clusters of galaxies and galaxy rotation curves. The latter provide the most precise local determination of dark matter. Currently, they continue to be one the main ways to study dark matter not only in the context of the ΛCDM but also modified theories of gravity. Here, we focus on the study of galaxy rotation curves in the context of modified gravity theories in two different but related ways: the first is an alternative approach to test whether modified gravity theories can provide or not a good fit for galaxies without previously needing individual fits. And the second one is a more focused study on a specific modified gravity theory called Vainshtein Screening. Our goal is to both develop a fast way to test viability of modified theories of gravity with rotation curves, and then focus on a specific modified gravity theory which is so far poorly explained with rotation curve data.
Enhancing constraints and precision studies for a deeper understanding of the universe using CMB and 21cm maps
(Universidade Federal do Espírito Santo, 2023-08-09) Mokeddem, Rahima; Ricaldi, Wiliam Santiago Hipolito; https://orcid.org/000000021748553X; http://lattes.cnpq.br/0293080746483402; https://orcid.org/0000000283795106; http://lattes.cnpq.br/3993334728622346; Souza, Carlos Alexandre Wuensche de; https://orcid.org/0000-0003-1373-4719; http://lattes.cnpq.br/1448223845901360; Rodrigues, Davi Cabral; https://orcid.org/0000000316835443; http://lattes.cnpq.br/5465449494182034; Leo, Armando Bartolome Bernui; https://orcid.org/0000-0003-3034-0762; http://lattes.cnpq.br/6926651124954505; Marra, Valerio; https://orcid.org/0000000277731579; http://lattes.cnpq.br/6846011112691877
This thesis focuses on enhancing constraints and precision studies to deepen our understanding of the universe. By improving measurements and testing methods, we aim to achieve higher-resolution simulations and more precise results. The thesis specifically addresses the lensing amplitude parameter, investigating its accuracy and quantifying any discrepancies. Additionally, we explore the generation of 21cm mocks in different cosmologies, using the remapping technique to obtain reliable results. The findings of this thesis have the potential to revolutionize our understanding of large-scale structures, the cosmic microwave background, and the early and late stages of the universe by precisely estimating the lensing amplitude AL and by introducing for the first time 21cm mocks in three different cosmologies, that were obtained in a very timely mannered way starting from one dark matter halo catalogue.
Modified gravity and large scale structure cosmology: a linear and non-linear treatment
(Universidade Federal do Espírito Santo, 2022-06-10) Oliveira, Guilherme Brando de; Falciano, Felipe Tovar; https://orcid.org/0000000322631252; http://lattes.cnpq.br/7214193952056222; https://orcid.org/0000000308051905; Fabris, Julio Cesar; https://orcid.org/000000018880107X; http://lattes.cnpq.br/5193649615872035; Bragança, Vinicius Miranda; Quartin, Miguel Boavista; https://orcid.org/0000000158536164; http://lattes.cnpq.br/3080181268936724; Abramo, Luis Raul Weber; Wands, David Graham
This thesis consists of a comprehensive study of beyond-ΛCDM cosmologies, in particular I investigate possible consequences of scalar-tensor theories of gravity on the Large Scale Structure of the Universe. Within the Standard Model of Cosmology, General Relativity is assumed to be the theory that describes gravity in all scales and this is supported by the highly accurate Astrophysical and Solar System tests. Notwithstanding, at cosmological scales, we still lack gravity tests with the same constraining power. Therefore, in addition to the motivation from the well-known conceptual problems of the Cosmological Constant, it is reasonable to investigate if General Relativity is the correct gravity theory at the largest scales of the Universe. In order to increase the accuracy of our cosmological tests of gravity, I develop numerical tools based on the linear and nonlinear regimes of cosmological perturbation theories, as well as a non-perturbative approach using quasi N-body simulations. I also present different ways of testing the large freedom introduced by modified theories of gravity in the parameter space. Indeed, modified gravity models cannot avoid introducing extra parameters besides the usual six cosmological parameters of the ΛCDM model. The main results of the thesis have been published in four papers cited along the text and I have tried to condensate them mainly in Chapters 3, 4 and 6. In chapter 3 I discuss the impact of modified gravity on cosmological observables such as the modifications Horndeski theories introduce in the growth and light propagation equations of motion. In particular, I perform a detailed analysis of the No Slip Gravity at the linear regime of structure formation. Then, I discuss how early modified gravity theories change the matter power spectrum at large and small scales. In Chapter 4, I start by analyzing the matter power spectrum at linear scales, namely how it is defined within ΛCDM and how massive neutrinos introduce a scale dependent on the growth function. Then, I introduce the formulation of the N-Body gauge, a specific coordinate system that facilitates the interpretation of Newtonian simulations within a relativistic framework, by consistently introducing the effects coming from photons, neutrinos and dark energy. As stage-IV LSS surveys will probe the Universe at increasingly large scales; it is imperative to include these species in our analysis inasmuch at large scales their imprint can be above the 1% threshold. I also present new cosmological tests of gravity by combining this framework with relativistic N-Body simulations. At the end I show how to correctly combine modified gravity effects and Newtonian simulations. In Chapter 5, I outline all the nonlinear mathematical tools have I have studied and developed during this project and on Chapter 6 I present the results of how we can construct computationally fast new numerical tools using all the new developments I have done in modified gravity, from linear to nonlinear scales. Chapter 7 ends the thesis with some conclusions and three future avenues I plan to pursue in the next few years.
On the degenerate dynamics of branched hamiltonians
(Universidade Federal do Espírito Santo, 2024-09-21) Ferreira Junior, Alexsandre Leite; Zanelli, Jorge; https://orcid.org/0000-0001-7512-4284; Pinto-Neto, Nelson; https://orcid.org/0000-0001-6713-5290; Fabris, Júlio; Piattella, Oliver Fabio; Bittencourt, Eduardo; Gannouji, Radouane; Helayël-Neto, José
Branched Hamiltonians and the corresponding singularity are present in several inter esting physical systems: Lovelock extension of General Relativity in higher dimensions, classical time crystals, k-essence fields, Horndeski theories, compressible fluids, and nonlinear electrodynamics. The emergent ill defined sympletic structure and tricky dynamical evolution poses challenges to a consistent interpretation. In this thesis, multi-valued Hamiltonians are investigated in the framework of degenerate dynamical system, whose sympletic form does not have a constant rank, allowing novel features and interpretations not present in previous investigations. In particular, it is shown how the multi-valuedness is associated with a dynamical mechanism of dimensional reduction, as some degrees of freedom turn into gauge symmetries when the system degenerates. In the case of classical time crystal, there is no “moving” ground state nor brick wall solution, as described previously. Moreover, the degenerate dynamics of a k–essence model enables it to be responsible for both primordial inflation and the present observed acceleration of the cosmological background geometry, while also admitting a non-singular de Sitter beginning of the Universe (it arises from de Sitter and ends in de Sitter). Furthermore, the model is free of pathologies such as propagating superluminal perturbations, negative energies, and perturbation instabilities. Henceforth, in thesis is demonstrated that the degenerate dynamics offer a consistent interpretation, under which the degeneracy and consequent branching is not a problem but a dynamical feature.
Probing cosmology with an eye on Rubin : from strong lensing to the large scale structure of the universe
(Universidade Federal do Espírito Santo, 2024-04-11) Oliveira, Renan Alves de; Ho, Shirley ; https://orcid.org/0000-0002-1068-160X; Makler, Martín; https://orcid.org/0000-0003-2206-2651; http://lattes.cnpq.br/6567844719949395; https://orcid.org/0000-0002-0200-3833; http://lattes.cnpq.br/1895596998416086; Abramo, Luis Raul Weber ; https://orcid.org/0000-0001-8295-7022; http://lattes.cnpq.br/4558796258762790; Bom, Clécio Roque de ; https://orcid.org/0000-0003-4383-2969; http://lattes.cnpq.br/5635352837026339; Velten, Hermano Endlich Schneider ; https://orcid.org/0000-0002-5155-7998; http://lattes.cnpq.br/0282590467459210; Marra, Valerio ; http://orcid.org/0000-0002-7773-1579; http://lattes.cnpq.br/6846011112691877
In 2024, the Vera C. Rubin Observatory will begin observing the Universe for the next ten years. Two key cosmological observables that Rubin will probe are gravitational lensing and the large-scale structure of the Universe. In this thesis, we derive analytical solutions for strongly lensed images that can be useful for generating fast simulations and as a starting point in parameter searches for lens inversion. Then, we obtain an expression in closed form for the magnification cross-section, which can be used to predict the abundance of highly magnified sources. Next, we focus on real data and assemble an extensive compilation of Strong Lensing candidate systems from the literature containing over 30,000 unique objects. We cross-match this sample with the current major photometric and spectroscopic catalogs. As preparation for Rubin, we generate image cutouts for these systems in most current wide-field surveys with subarcsecond seeing, namely DES, HSC, KiDS, CFHTLens, RCSLens, and CS82. This sample dubbed the “Last Stand Before Rubin” (LaStBeRu), has a myriad of applications, from using archival data to selections for follow-up projects and training of machine learning algorithms. As an application, we have performed a test of General Relativity (GR) with these data, combining information from strong lensing and velocity dispersions, which allow one to set constraints on the Post-Newtonian parameter γPPN. From the LaStBeRu database, we were able to provide the first independent test of γPPN from previous results and for the first time only for systems identifiable in ground-based images. We can obtain the most stringent constraint on γPPN by combining these data with the current samples. Moreover, we have obtained new spectroscopic data for systems selected from LaStBeRu, which were used to obtain the first end-to-end determination of γPPN. It is also the first determination derived purely from ground-based data and the first to use self-consistent priors. Our results are consistent with GR at the ∼ 1-σ level and with the previous results from the literature. Finally, in the context of the large structure, we present two neural emulators capable of making fast predictions for the density, displacement, and velocity fields of dark matter particles without necessarily having to run expensive N-body simulations. We compared these emulators with another fast method for the same task, showing that neural emulators provide the best results
Pushing the boundaries of modern cosmology: physics beyond the Copernican principle
(Universidade Federal do Espírito Santo, 2022-08-16) Torres, David Francisco Camarena; Marra, Valerio; https://orcid.org/0000000277731579; http://lattes.cnpq.br/6846011112691877; https://orcid.org/0000000171650439; http://lattes.cnpq.br/2093261235489631; Piattella, Oliver Fabio; https://orcid.org/0000000345580574; http://lattes.cnpq.br/5707156831919279; Amendola, Luca; https://orcid.org/0000-0002-0835-233X; http://lattes.cnpq.br/7512327723238183; Sapone, Domenico; https://orcid.org/; http://lattes.cnpq.br/; Clarkson, Chris
The standard paradigm of modern cosmology relies on a set of fundamental assumptions that simplify and make possible the modeling of the Universe. Among these critical hypotheses, there is the presumption that we do not occupy a special place in the Uni- verse, the so-called Copernican principle. The assumption of this principle constrains the degrees of freedom allowed by the theory, and, in particular, within the framework of the General Theory of Relativity, leads to a spatially homogeneous and isotropic space-time. Here, we present a program to observationally test the Copernican princi- ple and study the cosmological applications of inhomogeneous cosmologies. Under the assumption of a spherically inhomogeneous extension of the standard model and using the latest cosmological data, we test the Copernican principle by placing constraints on radial deviations of the spatially homogeneous and isotropic space-time. We also forecast the precision with which future surveys, such as DES, Euclid and LSST, will be able to test the Copernican principle and test their ability to detect any possible violations. Furthermore, we investigate if a local void could explain away the 5σ discrepancy between the early and late times determinations of the Hubble constant. Our goal is to take the first steps to extend the boundary of the standard paradigm of modern cosmology, and, in particular, to develop a suitable framework for the development of physics beyond the Copernican principle.
Quantum effects in cosmology
(Universidade Federal do Espírito Santo, 2020-08-28) Frion, Emmanuel; Pinto Neto, Nelson; https://orcid.org/0000-0001-6713-5290; http://lattes.cnpq.br/6196081550581346; https://orcid.org/0000000312800315; Fabris, Julio Cesar; https://orcid.org/000000018880107X; http://lattes.cnpq.br/5193649615872035; Rodrigues, Davi Cabral; https://orcid.org/0000000316835443; http://lattes.cnpq.br/5465449494182034; Bergliaffa, Santiago Esteban Perez; Alcaniz, Jailson Souza de; Peter, Patrick; Wands, David Graham
Even though predictions from inflationary models fit observations with great accuracy, inflation is not a theory, and it is therefore important to look at alternative mechanisms whose phenomenology can be constrained by cosmological data. It is possible to explain the origin of large-scale structures through bouncing models, taking into account the evolution of quantum perturbations in both a contracting phase and an expansion phase. This thesis is motivated by the effects of quantum perturbations on cosmological models. We first focus on a semi-classical description of quantum perturbations in the form of stochastic noise in a collapsing universe. The growth of perturbations is a fundamental issue in bouncing cosmologies that any acceptable model must treat accurately. To this end, we quantified how quantum perturbations may overcome the classical energy density in the simple case of a massless field with exponential potential. This is generally not the case within this configuration, although there is an important growth of quantum diffusion in the case of a matter-dominated model, which could possibly drive the system away from the classical evolution. This stochastic collapse is the first step towards a complete stochastic bouncing model. Numerous non-singular bouncing models resolve the initial singularity issue thanks to quantum effects. They constitute a broad class of relevant cosmological models, since they solve many problems of standard inflation. A subclass is obtained by considering the canonical quantisation of general relativity using the de Broglie-Bohm interpretation of quantum mechanics. In the second part of the thesis, we show that the generation of magnetic fields in such models compatible with observations on cosmological scales can be obtained with a simple coupling between gravity and electromagnetism. Interestingly, bouncing magnetogenesis have intrinsically less issues than inflationary magnetogenesis. The model presented here shows that acceptable magnetic fields can be obtained, depending on the energy scale of the coupling and the time when the bounce occurs. To close the thesis, we finish with a bouncing model obtained from the affine quantisation of the Brans-Dicke theory. Contrary to canonical quantisation, the affine procedure needs less assumptions and kinetic energy terms possess a quantum potential regularising the dynamics, resulting in a smooth bounce. Another advantage of this method lies in the choice of mathematical models one can use to tackle the same physical problem. We employ this asset to deal with the quantum equivalence of Jordan and Einstein frames, an issue of modified gravity models. The results point toward an unitary equivalence of the frames. We conclude with a summary of achievements.
Starobinsky Inflation And The Order Reduction Technique
(Universidade Federal do Espírito Santo, 2022-10-03) Medeiros, Waleska Priscylla Florencio de; Piattella, Oliver Fabio; https://orcid.org/0000000345580574; http://lattes.cnpq.br/5707156831919279; Fabris, Julio Cesar; https://orcid.org/000000018880107X; http://lattes.cnpq.br/5193649615872035; Chapiro, Ilia; http://lattes.cnpq.br/2644217574349073; Muller, Daniel; Moniz, Paulo Vargas; Apablaza, Ramon Alejandro Herrera
The order reduction technique (ORT) is an iterative method of solution of higher order di erential equations. It consists of treating the higher order terms perturbatively so that the lower order in the order reduction must be chosen according to which regime of solution the method is going to reproduce. In some cases, the presence of solutions that do not have physical behavior is observed, mainly associated with particularly higher order di erential equations. Nonetheless, as it is known in the literature, the order reduction method presents a smaller number of solutions, and with that, one of the intentions of the technique is to make it easier to select the solutions that present good physical behavior. However, it must be emphasized that one disadvantage of the method is that there could be some physical solutions that the order reduction will not detect. The ORT is applied to the following cases: 1. The study of the dynamics of the motion of a charged particle. 2. The harmonic oscillator. 3. The in ationary paradigm of Starobinsky. We show that, in the case of the examples cited above, the ORT as an iterative perturbative method does not show convergence in the oscillating regime of a weak coupling limit. This regime is excluded by the order reduction. In addition, the method shows good convergence in the strong coupling regime, non-oscillating which slowly approaches equilibrium. The main results discussed are based on the work [1].
Statistical tools in cosmology: model selection and covariance matrix comparison
(Universidade Federal do Espírito Santo, 2021-10-04) Ferreira, Tassia Andrade; Marra, Valerio; https://orcid.org/0000000277731579; http://lattes.cnpq.br/6846011112691877; https://orcid.org/0000000340163763; Sobreira, Flavia; Vitenti, Mariana Penna Lima; Makler, Martin; https://orcid.org/0000000322062651; http://lattes.cnpq.br/6567844719949395; Dodelson, Scott
Albeit ΛCDM’s fame as the concordance model, there are many interesting myster ies worth exploring, such as the nature of dark energy. Here, we test the viability of several classes of scenarios of the dark sector with linear and non-linear inter acting terms. To do so, we use a Bayesian model selection with data from type Ia supernovae, cosmic chronometers, cosmic microwave background and two sets of baryon acoustic oscillations measurements: 2-dimensional angular measurements (BAO2), and 3-dimensional angle-averaged measurements (BAO3). On the other hand, we consider covariance matrices, which are important tools for parameter estimation. We explore ways of compressing them by analysing their eigenvalues and signal-to-noise ratio, by employing a tomographic compression and, lastly, with the Massively Optimized Parameter Estimation and Data compression (MOPED). We find that MOPED is a powerful tool in the comparison of covariance matrices and, towards that end, we build a python code that uses a fast Monte Carlo simulation to obtain comprehensible values for differences between two covariance matrices. This method thus eliminates the need for a full cosmological analysis as we relate its output to the corresponding parameter constraints.
Testing clustering dark energy models with the skewness of matter distribution
(Universidade Federal do Espírito Santo, 2022-10-10) Fazolo, Raquel Emy; Velten, Hermano Endlich Schneider; https://orcid.org/0000000251557998; http://lattes.cnpq.br/0282590467459210; https://orcid.org/0000000340365170; Piattella, Oliver Fabio; https://orcid.org/0000000345580574; http://lattes.cnpq.br/5707156831919279; Amendola, Luca; Marinoni, Christian; Rampf, Cornelius
This work aims to test clustering dark energy with the cosmological skewness, the third statistical moment of the matter density distribution. Usually, dark energy is treated as a cosmological constant or a fluid with negative pressure that has the properties to accelerate the cosmic background expansion. We start our analysis by explaining the standard treatment about dark energy, then cosmological perturbations are introduced. In general relativity it is not trivial to work with higher order perturbations so we make a transition to the Neo Newtonian cosmology, using the fluid dynamics equations that are equivalent to the general relativity ones to a good approximation. We then studied the cosmological skewness in two approaches: the single-fluid and two-fluid analysis. In the first approach, we model the universe as an effective single fluid where the dark energy background contributions and perturbations are included via the total equation of state parameter. This is indeed a very simplified attempt, but this analysis was useful to provide preliminary hints about how dark energy affects the skewness of matter distribution. We then apply a more general approach, modeling the universe as two non-interacting components, pressureless matter and dark energy which is a more realistic scenario. The single fluid analysis shows a great increase in skewness when including the clustering dark energy terms. This can be explained by including the terms directly in the matter equation, not just as an additional source for the gravitational field. The two fluid model results show values around the standard cosmological ones. Tests are performed to probe the skewness dependence with the cosmological parameters. Until this work, only an expression for the skewness as a function of the matter density parameter Ωm0 was available in the literature. We go beyond introducing several fits for the cosmological skewness value as a function of the dark energy equation of state wde and the dark energy speed of sound c2 de. This result has been presented in the literature for the first time. In order to check the consistency of our results, we finish with an observational analysis using CFHTLS-Wide data. Whereas the current available data is not enough to promote the skewness to the status of a precise cosmological test, further analysis and observations are indeed needed to make skewness a better tool to study dark energy models in the future.
The redshift drift as a new cosmological probe
(Universidade Federal do Espírito Santo, 2024-09-19) Dutra, Pedro Henrique Bessa Rodrigues; Durrer, Ruth; https://orcid.org/0000-0001-9833-2086; Marra, Valerio; https://orcid.org/0000-0002-7773-1579; Marttens, Rodrigo vom; Piattella, Oliver Fabio; Koksbang, Sofie Marie; Martins, Carlos
With the advent of precision cosmology and the next generation of telescopes and sur veys, observations will allow the standard cosmological model to be tested in old and new regimes with unprecedented accuracy, and the data will demand accurate the oretical models of cosmological phenomena in order to be properly interpreted and processed. Theorists are reassessing old and new probes that allow the current cosmo logical paradigm to be tested to its limits. One promising new probe, the measurement which is one of the main objectives of the ELT ANDES spectrograph, is the cosmic redshift drift. One of the theoretical predictions of cosmological models based on Robertson-Walker metrics is the cosmic redshift drift, which measures the real-time rate of change of the spectra of far away sources, and is a generic consequence of cosmological models where the expansion rate is non-constant. Its observation provides a model independent way to measure the time variation of the Universe’s expansion and as such, an independent test of the late-time acceleration phase of the Universe and the existence of a cosmo logical constant. In this thesis we study the redshift drift in realistic cosmological models containing inhomogeneities in the !CDM paradigm. We derive for the first time a gauge-invariant expression for the redshift drift and its power spectrum, and implement the redshift drift f luctuation power spectrum numerically through Einstein-Boltzmann codes and using n-body simulations, providing a solid theoretical foundation for future measurements and observations of the redshift drift in !CDM cosmology and beyond.

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