arXiv subjects

Rodrigo Maier

Publications and source records attributed to Rodrigo Maier.

30 records · Page 2Linked to original sources

arXiv2018

Curvature Late-Time Acceleration in an Eternal Universe

We construct a FLRW universe considering an anisotropic scaling between space and time at extremely high and low energies only. In this context, Friedmann equations contain an additional term arising from spatial curvature which implements nonsingular bounces in the early Universe. The matter content of the model is a nonrelativistic pressureless perfect fluid and radiation. By breaking covariance diffeomorphism also at extreme large scales, an additional term furnishes late-time acceleration due to spatial curvature so that a cosmological constant is not needed. In order to probe the final fate of the universe we also introduce a lower order curvature term which dominates in deep IR. Given the observational parameters we obtain a concrete model in eternal recurrence in which the end of late-time acceleration takes place at a redshift $z \simeq -0.14$ and the universe recollapses at $z\simeq - 0.32$.

gr-qc↗

arXiv2017

Hořava-Lifshitz Bouncing Bianchi IX Universes: A Dynamical System Analysis

We examine the Hamiltonian dynamics of bouncing Bianchi IX cosmologies in Hořava-Lifshitz gravity. The $6$-dim phase space presents two critical points, one asymptotic de Sitter attractor at infinity and a $2$-dim invariant plane. We identified four distinct parameter domains $A$, $B$, $C$ and $D$ for which the pair of critical points engenders distinct features in the dynamics. In the domain $A$ the dynamics consists basically of periodic bouncing orbits, or oscillatory orbits with a finite number of bounces. The center with multiplicity two engenders in its neighborhood the topology of stable and unstable cylinders $R \times S^3$ of orbits. We show that the stable and unstable cylinders coalesce realizing a smooth homoclinic connection to the center manifold, a rare event of regular/non-chaotic dynamics in bouncing Bianchi IX cosmologies. The presence of a saddle of multiplicity two in the domain $B$ engenders a high instability in the dynamics so that the cylinders emerging from the center manifold towards the bounce have four distinct attractors: the center manifold itself, the de Sitter attractor at infinity and two further momentum-dominated attractors with infinite anisotropy. In the domain $C$ we examine the features of invariant manifolds of orbits about a saddle of multiplicity two. The presence of the saddle of multiplicity two engenders bifurcations of the invariant manifold as the energy $E_0$ of the system increases relative to the energy $E_{cr}$ providing structures that were not yet observed in the literature. The domain $D$ is not examined as most of its features are present already in the previous domains.

gr-qc↗

arXiv2016

On the Stability of Cubic Galileon Accretion

We examine the stability of steady-state galileon accretion for the case of a Schwarzshild black hole. Considering the galileon action up to the cubic term in a static and spherically symmetric background we obtain the general solution for the equation of motion which is divided in two branches. By perturbing this solution we define an effective metric which determines the propagation of fluctuations. In this general picture we establish the position of the sonic horizon together with the matching condition of the two branches on it. Restricting to the case of a Schwarzschild background, we show, via the analysis of the energy of the perturbations and its time derivative, that the accreting field is linearly stable.

gr-qc↗

arXiv2015

General Bianchi IX dynamics in bouncing braneworld cosmology: homoclinic chaos and the BKL conjecture

We examine the dynamics of a Bianchi IX model on a 4-dim brane embedded in a 5-dim conformally flat empty bulk with a timelike extra dimension. Einstein's equations on the brane reduces to a 6-dim Hamiltonian dynamical system with additional terms that implement nonsingular bounces in the model. The phase space of the model has two critical points (a saddle-center-center and a center-center-center) in a finite region of phase space, and two asymptotic de Sitter critical points, one acting as an attractor to late-time dynamics. The saddle-center-center engenders in the phase space the topology of stable and unstable 4-dim cylinders $R \times S^3$, where $R$ is a saddle direction and $S^3$ is the center manifold of unstable periodic orbits (the nonlinear extension of the center-center sector). By a proper canonical transformation we separate the degrees of freedom of the dynamics into one degree connected with the expansion/contraction of the scales of the model, and two rotational degrees of freedom connected to the $S^3$. The typical dynamical flow is then an oscillatory mode about a neighborhood of the cylinders. For the stable and unstable cylinders the oscillatory motion about the separatrix towards the bounce leads to the homoclinic transversal intersection of the cylinders, as shown numerically in two distinct experiments. We show that the homoclinic intersection manifold has the topology of $R \times S^2$ consisting of homoclinic orbits biasymptotic to the center manifold $S^3$. This behavior defines a {\it chaotic saddle} associated with $S^3$, indicating that the intersection points of the cylinders have the nature of a Cantor set with a compact support $S^2$, characterizing chaos in the model. We discuss the oscillatory approach to the bounce together with its chaotic behavior, and analogous features present in the BKL conjecture in general relativity.

gr-qc↗

arXiv2014

Static Vacuum Solutions in Non-Riemannian Gravity

In the framework of non-riemannian geometry, we derive exact static vacuum solutions of the field equations obtained from the full equivalent version of the Einstein-Hilbert action when torsion degrees of freedom are taken into account. By imposing spherical symmetry and a suitable choice for the contorsion degrees of freedom, the static geometry provides deviations on the predictions of the observational tests predicted by General Relativity -- namely on the advance of planetary perihelia and the bending of light rays -- which we infer. The analytical extension is built in two particular domains of the parameter space. In the first domain we obtain a solution exhibiting an event horizon analogous to that of the Schwarzschild geometry. For the second domain, we show that the metric furnishes an exterior event horizon, and two interior horizons which enclose the singularity. For both branches we examine the effects of torsion corrections on the Hawking radiation. In this scenario the model extends Bekenstein's black hole geometrical thermodynamics, with an extra work term connected to a torsion parameter.

gr-qc↗

arXiv2013

Bounded Scalar Perturbations in Bouncing Brane World Cosmologies

We examine the dynamics of scalar perturbations in closed Friedmann-Lemaître-Robertson- Walker (FLRW) universes in the framework of Brane World theory with a timelike extra dimension. In this scenario, the unperturbed Friedmann equations contain additional terms arising from the bulk-brane interaction that implement non-singular bounces in the models with a cosmological constant and non-interacting perfect fluids. The structure of the phase-space of the models allows for two basic configurations, namely, one bounce solutions or eternal universes. Assuming that the matter content of the model is given by dust and radiation, we derive the dynamical field equations for scalar hydrodynamical perturbations considering either a conformally flat (de Sitter) bulk or a perturbed bulk. We perform a numerical analysis which can shed some light on the study of cosmological scalar perturbations in bouncing brane world models. From a mathematical point of view we show that although the bounce enhances the amplitudes of scalar perturbations for one bounce models in the case of a de Sitter bulk, the amplitudes of the perturbations remain sufficiently small and bounded relative to the background values up to a certain scale. For one bounce models in the case of a perturbed bulk the amplitudes of all perturbations (apart from the Weyl fluid energy density) remain sufficiently small and bounded relative to the background values for any scale of the perturbations. We also discuss and compare the stability and bounded behaviour of the perturbations in the late accelerated phase of one bounce solutions. For eternal universes we argue that some of these features are maintained only for early times (typically of the order of the first bounce). In this sense we show that eternal solutions are highly unstable configurations considering the background model of this paper.

gr-qc↗

arXiv2013

Nonlinear Resonance in Hořava-Lifshitz Bouncing Cosmologies

In this paper I examine the phase space dynamics in the framework of Non-Projectable Hořava-Lifshitz bouncing cosmologies. By considering a closed Friedmann-Lemaître-Robertson-Walker (FLRW) geometry, the first integral contains a correction term that leads to nonsingular metastable bounces in the early evolution of the universe. The matter content of the model is a massive conformally coupled scalar field, dust and radiation. A nonvanishing cosmological constant connected to a de Sitter attractor in the phase space is also assumed. In narrow windows of the parameter space, labeled by an integer $n\geq 2$, nonlinear resonance phenomena may destroy the KAM tori that trap the scalar field, leading to an exit to the de Sitter attractor. As a consequence nonlinear resonance imposes constraints on the parameters and in the initial configurations of the models so that an accelerated expansion may be realized.

gr-qc↗

arXiv2013

Bouncing Model in Brane World Theory

We examine the nonlinear dynamics of a closed Friedmann-Robertson-Walker universe in the framework of Brane World formalism with a timelike extra dimension. In this scenario, the Friedmann equations contain additional terms arising from the bulk-brane interaction which provide a concrete model for nonsingular bounces in the early phase of the Universe. We construct a nonsingular cosmological scenario sourced with dust, radiation and a cosmological constant. The structure of the phase space shows a nonsingular orbit with two accelerated phases, separated by a smooth transition corresponding to a decelerated expansion. Given observational parameters we connect such phases to a primordial accelerated phase, a soft transition to Friedmann (where the classical regime is valid), and a graceful exit to a de Sitter accelerated phase.

gr-qc↗

arXiv2012

Bouncing Braneworld Cosmologies and Initial Conditions to Inflation

We examine the full nonlinear dynamics of closed FRW universes in the framework of D-branes formalism. Friedmann equations contain additional terms arising from the bulk-brane interaction that provide a concrete model for nonsingular bounces in the early phase of the universe. We construct nonsingular cosmological scenarios sourced with perfect fluids and a massive inflaton field which are past eternal, oscillory and may emerge into an inflationary phase due to nonlinear resonance mechanisms. Oscillatory behaviour becomes metastable when the system is driven into a resonance window of the parameter space of the models, with consequent break-up of KAM tori that trap the inflaton, leading the universe to the inflationary regime. A construction of the resonance chart of the models is made. Resonance windows are labeled by an integer $n \geq 2$, where $n$ is related to the ratio of the frequencies in the scale factor/scalar field degrees of freedom. They are typically small compared to volume of the whole parameter space, and we examine the constraints imposed by nonlinear resonance in the physical domain of initial configurations so that inflation may be realized. We discuss the complex dynamics arising in this pre-inflationary stage, the structural stability of the resonance pattern and some of its possible imprints in the physics of inflation. We also approach the issue of initial configurations that are connected to a chaotic exit to inflation. Pure scalar field bouncing cosmologies are constructed. Contrary to models with perfect fluid components, the structure of the bouncing dynamics is highly sensitive to the initial amplitude and to the mass of the inflaton; dynamical potential barriers allowing for bounces appear as a new feature of the dynamics.

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arXiv2012

Brane world in Non-Riemannian Geometry

We carefully investigate the modified Einstein's field equation in a four dimensional (3-brane) arbitrary manifold embedded in a five dimensional Non-Riemannian bulk spacetime with a noncompact extra dimension. In this context the Israel-Darmois matching conditions are extended assuming that the torsion in the bulk is continuous. The discontinuity in the torsion first derivatives are related to the matter distribution through the field equation. In addition, we develop a model that describes a flat FLRW model embedded in a 5-dimensional de Sitter or Anti de Sitter, where a 5-dimensional cosmological constant emerges from the torsion.

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arXiv2012

Gravitational Collapse and Black Hole Thermodynamics In Braneworld Scenario

We examine the dynamics of the gravitational collapse in a 4-dim Lorentzian brane embedded in a 5-dim bulk with an extra timelike dimension. By considering the collapse of pure dust on the brane we derive a bouncing FLRW interior solution and match it with a corrected Schwarzschild exterior geometry. In the physical domain considered for the parameters of the solution, the analytical extension is built, exhibiting an exterior event horizon and a Cauchy horizon, analogous to the Reissner-Nordström solution. For such an exterior geometry we examine the effects of the bulk-brane corrections in the Hawking radiation. In this scenario the model extends Bekenstein's black hole geometrical thermodynamics for quasi-extremal configurations, with an extra work term in the laws associated with variations of the brane tension. We also propose a simple statistical mechanics model for the entropy of the bouncing collapsed matter by quantizing its fluctuations and constructing the associated partition function. This entropy differs from the geometrical entropy by an additive constant proportional to the area of the extremal black hole and satisfies an analogous first law of thermodynamics. A possible connection between both entropies is discussed.

gr-qc↗

arXiv2012

Bouncing models with a cosmological constant

Bouncing models have been proposed by many authors as a completion, or even as an alternative to inflation for the description of the very early and dense Universe. However, most bouncing models contain a contracting phase from a very large and rarefied state, where dark energy might have had an important role as it has today in accelerating our large Universe. In that case, its presence can modify the initial conditions and evolution of cosmological perturbations, changing the known results already obtained in the literature concerning their amplitude and spectrum. In this paper, we assume the simplest and most appealing candidate for dark energy, the cosmological constant, and evaluate its influence on the evolution of cosmological perturbations during the contracting phase of a bouncing model, which also contains a scalar field with a potential allowing background solutions with pressure and energy density satisfying p = w*rho, w being a constant. An initial adiabatic vacuum state can be set at the end of domination by the cosmological constant, and an almost scale invariant spectrum of perturbations is obtained for w~0, which is the usual result for bouncing models. However, the presence of the cosmological constant induces oscillations and a running towards a tiny red-tilted spectrum for long wavelength perturbations.

astro-ph.CO↗