arXiv subjects

Leandro G. Gomes

Publications and source records attributed to Leandro G. Gomes.

11 recordsLinked to original sources

arXiv2026

A class of decelerating inhomogeneous cosmological models giving rise to accelerating FLRW universes at large scales

In this manuscript, we develop a class of inhomogeneous relativistic cosmological models with the following properties: (i) They contain cosmological observers to whom the spatial geometry and the expansion are homogeneous and isotropic; (ii) Matter behaves closely to dust, as it is formed by an ensemble of massive particles whose number density $4$-vector is conserved and reacts viscously to the local tidal forces; (iii) They generalize the dust FLRW model; (iv) They give rise to effective models on large scales that reproduce the FLRW behaviour with dust and a running dark-energy term, which appears as a backreaction effect from the local gravitational potential; (v) By suitably setting the distribution of energy in the current universe, the effective large-scale equation-of-state parameter can reproduce, in principle, any polynomial on the scale factor whose term of order zero is negative; (vi) The luminous distance observations imply an apparent large-scale acceleration, as the deceleration parameter is negative, while in reality the universe is decelerating.

gr-qc↗

arXiv2024

Einstein's equations constrained by homogeneous and isotropic expansion: Initial value problems and applications

In this manuscript, we put forth a general scheme for defining initial value problems from Einstein's equations of General Relativity constrained by homogeneous and isotropic expansion. The cosmological models arising as solutions are naturally interpreted as spatially homogeneous and isotropic on ``large scales". In order to show the well-posedness and applicability of such a scheme, we specialize in a class of spacetimes filled with the general homogeneous perfect fluid and inhomogeneous viscoelastic matter. We prove the existence, uniqueness, and relative stability of solutions, and an additional inequality for the energy density. As a consequence of our theorems, a new mechanism of energy transfer appears involving the different components of matter. A class of exact solutions is also obtained to exemplify the general results.

gr-qc↗

arXiv2024

Spacetimes with homogeneous and isotropic expansion

In this short note, we define and characterize all the spacetimes admitting observers to whom the cosmic expansion is homogeneous and isotropic and interpret their Einstein's equations.

gr-qc↗

arXiv2024

Breaking the Cosmological Principle into pieces: a prelude to the intrinsically homogeneous and isotropic spacetimes

In this manuscript, we show that three fundamental building blocks are supporting the Cosmological Principle. The first of them states that there is a special frame in the universe where the spatial geometry is intrinsically homogeneous and isotropic. The second demands the existence of a fiducial observer to whom the Hubble parameter is isotropic. The last piece states that matter and radiation behave as a perfect fluid. We show that these three hypotheses give us the Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes, the central pillar of the standard model of Cosmology. We keep with the first of them and start to investigate the so-called intrinsically homogeneous and isotropic spacetimes. They emerge after the decoupling of the CMB with the geometric frame of reference. Furthermore, a ``$Λ$CDM-like" effective theory arises naturally in those backgrounds, together with some new density parameters relating to the local inhomogeneities, the internal energy density, and the local and global magnitudes of the Hubble anisotropy. All those properties make this class of inhomogeneous models, which roughly speaking, keeps "1/3" of the Cosmological Principle, worth investigating in applications to Cosmology, for it can accommodate the same ingredients of the standard model, as a geometric frame and a free-falling isotropic cosmic background radiation, and reduce to the latter when some observable parameters vanish.

gr-qc↗

arXiv2022

On the intrinsically flat cosmological models in a lattice

In this manuscript we investigate the intrinsically flat (space-flat) spacetimes as viable cosmological models. We show that they have a natural geometric structure which is suitable to describe inhomogeneous matter distributions forming a periodic pattern throughout the space. We prove theorems for their local representation and for existence and uniqueness of the Einstein's equations with these periodic boundary conditions. We also find an interesting class of exact solutions, which illustrates the applicability of such spacetimes in cosmology, with an early time behavior close to homogeneity and isotropy and a late time aspect with peaks and voids in the matter distribution.

gr-qc↗

arXiv2021

The nonlinear patterns of the cosmic anisotropy in the late time universe

In this manuscript, we investigate the patterns satisfied by the cosmological anisotropy under the hypothesis of the observers being co-moving with a perfect fluid whose induced space sections are homogeneous with vanishing scalar curvature. We describe the positive increment $ΔR$ that the Hubble parameter in the anisotropic model will have as it is compared to its isotropic counterpart. In general, it has an exponential awakening at a specific redshift $z_A$. We also show that the deceleration and the jerk along the principal directions of the anisotropy are constrained by simple algebraic equations that do not depend on the type of matter present. These characteristic patterns form a valuable framework to distinguish the cosmological anisotropy from any other kind, thus adding a useful tool to probe its upper limits in the supernovae surveys, which are orders of magnitude away from those observed in the CMB.

gr-qc↗

arXiv2017

Bianchi-I cosmology from causal thermodynamics

We investigate diagonal Bianchi-I spacetimes in the presence of viscous fluids by using the shear and the anisotropic pressure components as the basic variables, where the viscosity is driven by the (second-order) causal thermodynamics. A few exact solutions are presented, among which we mention the anisotropic versions of de Sitter/anti-de Sitter geometries as well as an asymptotically isotropic spacetime presenting an effective constant cosmic acceleration without any cosmological constant. The qualitative analysis of the solutions for barotropic fluids with linear equations of state suggests that the behaviour is quite general.

gr-qc↗

arXiv2015

On the local form of static plane symmetric space-times in the presence of matter

For any configuration of a static plane-symmetric distribution of matter along space-time, there are coordinates where the metric can be put explicitly as a functional of the energy density and pressures. It satisfies Einstein equations as far as we require the conservation of the energy-momentum tensor, which is the single ODE for self-gravitating hydrostatic equilibrium. As a direct application, a general solution is given when the pressures are linearly related to the energy density, recovering, as special cases, most of known solutions of static plane-symmetric Einstein equations.

gr-qc↗

arXiv2013

General Solutions to Static Plane Symmetric Einstein's Equations

A general formula for the metric as an explicit function of the generic energy-momentum tensor is given which satisfies static plane symmetric Einstein's equations with cosmological constant.In order to illustrate it, the solutions for the vacuum with cosmological constant, the perfect fluid with a linear equation of state and the electrically charged plane are derived and compared with known results. The general solution with a linear relation among the energy-momentum tensor components is also obtained.

gr-qc↗

arXiv2009

Some maximal isotropic distributions and their relation to field theory

We study the behaviour of differential forms in a manifold having at least one of their maximal isotropic local distributions endowed with the special algebraic property of being decomposable. We show that they can be represented as the sum of a form with constant coefficients and one that vanishes whenever contracted with vector fields in the former distribution, provided some simple integrability conditions are ensured. We also classify possible 'canonical coordinates' for a certain class of forms with potential applications in classical field theory.

math.DG↗

arXiv2008

Multisymplectic and polysymplectic structures on fiber bundles

We introduce the concepts of a multisymplectic structure and a polysymplectic structure on a general fiber bundle over a general base manifold, define the concept of the symbol of a multisymplectic form, which is a polysymplectic form representing its leading order contribution, and prove Darboux theorems for the existence of canonical local coordinates.

math.DG↗