Search

We address in this article the criticism in a recently submitted article by Clement and Noiucer (arXiv:2312.17662 [gr-qc]) on "Cotton Gravity" (CG), a gravity theory alternative to General Relativity. These authors claim that CG is "not predictive" for producing "too many" spherically symmetric vacuum solutions, while taking the Bianchi I vacuum as test case they argue that geometric constraint on the Cotton tensor lead to an undetermined problem, concluding in the end that CG "is not a physical theory". We provide arguments showing that this critique is incorrect and misrepresents the theory., Comment: Important corrections and extra arguments added. 5 pages, all typos corrected

The "Codazzi formulation", based on a Codazzi tensor, provides a more robust and straightforward theoretical framework for "Cotton Gravity" (CG) than its original formulation in terms of the Cotton tensor. Using this formulation we provide a self-consistent procedure to generate non-trivial exact solutions in CG that generalize well known General Relativity (GR) solutions. We re-derive a known CG solution that generalizes the Schwarzschild solution of GR, showing that it is the unique vacuum solution of static spherical symmetry in CG, extending this result to a CG generalization of the Reissner-Nordstrom solution of GR, all of which places a strong case supporting the fulfillment of Birkhoff's theorem. When applied to Friedman-Lema\^\i tre-Robertson-Walker (FLRW) models CG naturally identifies the $\Lambda$CDM model as the unique FLRW dust model with constant negative spatial curvature. We also obtain CG generalizations of the Lema\^\i tre-Tolman-Bondi (LTB) and Szekeres dust solutions of GR, allowing for time and space dependent changes from decelerated to accelerated evolution, without necessarily assuming a dark energy source. The CG generalization of static perfect fluid spheres allows in the weak field regime to model the flattening of rotation velocities in spherical galactic systems without assuming dark matter. We also generalize non-static spherically symmetric perfect fluid solutions with a shear-free 4 velocity. Our results suggest the need for further research using the Codazzi formulation to explore the potential for applications of CG to current open problems in gravitational systems., Comment: Important updates and corrections, new references added, discussion on criticism of the theory. Typos and minors errors corrected. 11 pages, one figure

We derive Friedman-Lemaitre-Robertson-Walker (FLRW) models as non-trivial solutions of "Cotton Gravity" (CG), a recently proposed gravity theory alternative to General Relativity (GR) based on the Cotton tensor. Using an equivalent formulation, we show that CG leads to FLRW models with a modified expression for spatial curvature in terms of the Ricci scalar of hypersurfaces orthonormal to the 4-velocity. Considering models compatible with a well posed initial value formulation leads to operationally the same FLRW models in GR, but endowed with a precise covariant characterization of the positive/negative cosmological constant as the case with constant negative/positive spatial curvature. Under CG, the $\Lambda$CDM model becomes the unique FLRW dust model with constant negative spatial curvature., Comment: 3 pages. Important corrections to previous versions

We present numerical solutions to Einstein's equations describing large spherical cosmic voids constituted by two components; dark matter and baryons, with a non-vanishing initial relative velocity, in an asymptotically homogeneous background compatible with the $\Lambda$CDM concordance model. We compute numerically the evolution of such configurations in the dark matter frame, with a hypothetical homogeneous distribution of baryons, but respecting the values dictated by the concordance model for the average baryon-to-dark matter density ratio. We reproduce the well known formation of overdensities at the edge of the void, and recover the Lemaitre-Tolman-Bondi solutions in the comoving limit of our simulations. We compute the average growth factor of matter fluctuations, and find that it departs significantly from the linear perturbative prescription even in the comoving case, where the non-linearity of inhomogeneities has an impact., Comment: 20 pages, 7 figures, 2 appendices

Gravitational entropy is an elusive concept. Various theoretical proposals have been presented, initially based on Penrose's Weyl Curvature Hypothesis, and variations of it. A more recent proposal by Clifton, Ellis, and Tavakol (CET) considered a novel approach by defining such entropy from a Gibbs equation constructed from an effective stress-energy tensor that emerges from the 'square root' algebraic decomposition of the Bel-Robinson tensor, the simplest divergence-less tensor related to the Weyl tensor. Since, so far all gravitational entropy proposals have been applied to highly restrictive and symmetric spacetimes, we probe in this paper the CET proposal for a class of much less idealized spactimes (the Szekeres class I models) capable of describing the joint evolution of arrays of arbitrary number of structures: overdensities and voids, all placed on selected spatial locations in an asymptotic $\Lambda$CDM backgound. By using suitable covariant variables and their fluctuations, we find the necessary and sufficient conditions for a positive CET entropy production to be a negative sign of the product of the density and Hubble expansion fluctuations. To examine the viability of this theoretical result we examine numerically the CET entropy production for two elongated over dense regions surrounding a central spheroidal void, all evolving jointly from initial linear perturbations at the last scattering era into present day Mpc-size CDM structures. We show that CET entropy production is positive for all times after last scattering at the precise spatial locations where structure growth occurs and where the exact density growing mode is dominant. The present paper provides the least idealized (and most physically robust) probe of a gravitational entropy proposal in the context of structure formation.

We consider inhomogeneous spherically symmetric models based on the Lema\^{i}tre-Tolman-Bondi (LTB) metric, assuming as its source an interactive mixture of ordinary baryonic matter, cold dark matter and dark energy with a coupling term proportional to the addition of energy densities of both dark fluids. We reduce Einstein's field equations to a first order 7-dimensional autonomous dynamical system of evolution equations and algebraic constraints. We study in detail the evolution of the energy density and spatial curvature profiles along the phase space by means of two subspace projections: a three-dimensional projection associated with the solutions of the Friedman-Lema\^\i tre-Robertson-Walker metric (invariant subspace) and a four-dimensional projection describing the evolution of the inhomogeneous fluctuations. We also classify and study the critical points of the system in comparison with previous work on similar sources, as well as solving numerically the equations for initial energy density and curvature profiles that lead to a spherical bounce whose collapsing time we estimate appropriately., Comment: 20 pages. Accepted for publication in Modern Physics Letters A

In this paper we explore the possibility to find exact solutions for Teleparallel Gravity (TG) of the type of spherically symmetric Lema\^\i tre-Tolman-Bondi (LTB) dust models. We apply to the LTB metric the formalism of Teleparallel Gravity in its extension to $f(T,B)$ models, which can be seen it as the analagous from the Schwarzschild solution in General Relativity. An exact LTB solution is obtained which is compatible with a specific $f(T,B)$ model whose observational constraints are cosmological viable in a standard spatially flat Robertson-Walker geometry., Comment: 17 pages, accepted for publication in IJGMMP

We examine in this paper the possibility of finding exact solutions for Teleparallel Gravity (TG) of the type of spherically symmetric Lema\^\i tre-Tolman-Bondi (LTB) dust models. We apply to the LTB metric, as obtained from the Schwarzschild solution in General Relativity, the formalism of Teleparallel Gravity in its extension to $f(T,B)$ models. An exact LTB solution is obtained that is compatible with a specific $f(T,B)$ model that seems to be appropriate to fit observations when applied to standard spatially flat Robertson-Walker geometry., Comment: 5 pages

Two recently published papers (J.D. Barrow and A. Paliathanasis, Eur. Phys. J. C. (2018, 2019)) claim to have found exact solutions of Einstein's field equations belonging to the class of non-trivial Szekeres models, whose source is a mixture of dust and a homogeneous time-dependent scalar field, where the energy-momentum tensors of both mixture components are independently conserved. We prove that the independent conservation of these two mixture components necessarily leads to solutions belonging to the set of spatially homogeneous subcases of the Szekeres family: Friedmann-Lema\^itre-Robertson-Walker for class I, and Kantowski-Sachs, Bianchi-Behr I or Bianchi-Behr $\mbox{VI}_{\tiny{\mbox{-1}}}$ for class II., Comment: 2 pages. Comment on "Szekeres universes with homogeneous scalar fields" and "Cyclic Szekeres universes" by Barrow and Paliathanasis, Eur. Phys. J. C. (2018, 2019); arXiv:1808.00173 and arXiv:1901.09173

We examine the evolution of peculiar velocities of cold dark matter (CDM) in localized arrays of inhomogeneous cosmic structures in a $\Lambda$CDM background that can be identified as a frame comoving with the Cosmic Microwave (CMB). These arrays are constructed by smoothly matching to this cosmological background regions of Szekeres-II models whose source is an imperfect fluid reinterpreted as non-comoving dust, keeping only first order terms in $v/c$. Considering a single Szekeres-II region matched along two comoving interfaces to a $\Lambda$CDM background, the magnitudes of peculiar velocities within this region are compatible with values reported in the literature, while the present day Hubble expansion scalar differs from that of the $\Lambda$CDM background value by a 10\% factor, a result that might provide useful information to the ongoing debate on the $H_0$ tension. While the models cannot describe the virialization process, we show through a representative example that structures of galactic cluster mass reach the onset of this process at redshifts around $z\sim 3$., Comment: 15 pages, 8 figures

We examine a novel class of toy models of cosmological inhomogeneities by smoothly matching along a suitable hypersurface an arbitrary number of sections of "quasi flat" inhomogeous and anisotropic Szekeres-II models to sections of any spatially flat cosmology that can be described by the Robertson-Waker metric (including de Sitter, anti de Sitter and Minkowski spacetimes). The resulting "pancake" models are quasi-flat analogues to the well known spherical "Swiss-cheese" models found in the literature. Since Szekeres-II models can be, in general, compatible with a wide range of sources (dissipative fluids, mixtures of non-comoving fluids, mixtures of fluids with scalar or magnetic fields or gravitational waves), the pancake configurations we present allow for a description of a wide collection of localized sources embedded in a Robertson-Waker geometry. We provide various simple examples of arbitrary numbers of Szekeres-II regions (whose sources are comoving dust and energy flux interpreted as a field of peculiar velocities) matched with Einstein de Sitter, $\Lambda$CDM and de Sitter backgrounds. We also prove that the Szekeres-II regions can be rigorously regarded as "exact" perturbations on a background defined by the matching discussed above. We believe that these models can be useful to test ideas on averaging and backreaction and on the effect of inhomogeneities on cosmic evolution and observations., Comment: 19 pages, 4 figures

We propose in this letter a relativistic coordinate independent interpretation for Milgrom's acceleration $a_{0}=1.2 \times 10^{-8} \hbox{cm/s}^{2}$ through a geometric constraint obtained from the product of the Kretschmann invariant scalar times the surface area of 2--spheres defined through suitable characteristic length scales for local and cosmic regimes, described by Schwarzschild and Friedman--Lema\^\i tre--Robertson--Walker (FLRW) geometries, respectively. By demanding consistency between these regimes we obtain an appealing expression for the empirical (so far unexplained) relation between the accelerations $a_0$ and $c H_0$. Imposing this covariant geometric criterion upon a FLRW model, yields a dynamical equation for the Hubble scalar whose solution matches, to a very high accuracy, the cosmic expansion rate of the $\Lambda$CDM concordance model fit for cosmic times close to the present epoch. We believe that this geometric interpretation of $a_0$ could provide relevant information for a deeper understanding of gravity, Comment: 9 pages, IOP format, 3 figures

We examine the implementation of Buchert's and Green & Wald's averaging formalisms in exact spherically symmetric and plane symmetric dust-filled cosmological models. We find that, given a cosmological space-time, Buchert's averaging scheme gives a faithful way of interpreting the large-scale expansion of space, and explicit terms that precisely quantify deviations from the behaviour expected from the Friedmann equations of homogeneous and isotropic cosmological models. The Green & Wald formalism, on the other hand, does not appear to yield any information about the large-scale properties of a given inhomogeneous space-time. Instead, this formalism is designed to calculate the back-reaction effects of short-wavelength fluctuations around a given "background" geometry. We find that the inferred expansion of space in this approach is entirely dependent on the choice of this background, which is not uniquely specified for any given inhomogeneous space-time, and that the "back-reaction" from small-scale structures vanishes in every case we study. This would appear to limit the applicability of Green & Wald's formalism to the study of large-scale expansion in the real Universe, which also has no pre-defined background. Further study is required to enhance the evaluation and comparison of these averaging formalisms, and determine whether the same difficulties exist, in less idealized space-time geometries., Comment: 34 pages, 7 figures

We examine the fully relativistic evolution of cosmic voids constituted by baryons and cold dark matter (CDM), represented by two non-comoving dust sources in a $\Lambda$CDM background. For this purpose, we consider numerical solutions of Einstein's field equations in a fluid-flow representation adapted to spherical symmetry and multiple components. We present a simple example that explores the frame-dependence of the local expansion and the Hubble flow for this mixture of two dusts, revealing that the relative velocity between the sources yields a significantly different evolution in comparison with that of the two sources in a common 4-velocity (which reduces to a Lemaitre-Tolman-Bondi model). In particular, significant modifications arise for the density contrast depth and void size, as well as in the amplitude of the surrounding over-densities. We show that an adequate model of a frame-dependent evolution that incorporates initial conditions from peculiar velocities and large-scale density contrast observations may contribute to understand the discrepancy between the local value of $H_0$ and that inferred from the CMB., Comment: Discussion of the evolution of baryon-CDM relative velocity added. Other minor but important corrections were incorporated. Version accepted for publication in EPJC

Current observations suggest that our Universe is not incompatible with a small positive spatial curvature that can be associated with rest frames having a "closed" standard topology. We examine a toy model generalisation of the $\Lambda$CDM model in the form of ever expanding Lema\^{i}tre-Tolman-Bondi (LTB) models with positive spatial curvature. It is well known that such models with $\Lambda=0$ exhibit a thin layer distribution at the turning values of the area distance that must be studied through the Israel-Lanczos formalism. We find that this distributional source exhibits an unphysical behaviour for large cosmic times and its presence can be detected observationally. However, these unphysical features can always be avoided by assuming $\Lambda >0$. While these LTB models are very simplified, we believe that these results provide a simple argument favouring the assumption of a nonzero positive cosmological constant in cosmological models., Comment: 18 Pages, 6 figures

We examine the gravitational collapse and black hole formation of multiple non--spherical configurations constructed from Szekeres dust models with positive spatial curvature that smoothly match to a Schwarzschild exterior. These configurations are made of an almost spherical central core region surrounded by a network of "pancake-like" overdensities and voids with spatial positions prescribed through standard initial conditions. We show that a full collapse into a focusing singularity, without shell crossings appearing before the formation of an apparent horizon, is not possible unless the full configuration becomes exactly or almost spherical. Seeking for black hole formation, we demand that shell crossings are covered by the apparent horizon. This requires very special fine-tuned initial conditions that impose very strong and unrealistic constraints on the total black hole mass and full collapse time. As a consequence, non-spherical non-rotating dust sources cannot furnish even minimally realistic toy models of black hole formation at astrophysical scales: demanding realistic collapse time scales yields huge unrealistic black hole masses, while simulations of typical astrophysical black hole masses collapse in unrealistically small times. We note, however, that the resulting time--mass constraint is compatible with early Universe models of primordial black hole formation, suitable in early dust-like environments. Finally, we argue that the shell crossings appearing when non-spherical dust structures collapse are an indicator that such structures do not form galactic mass black holes but virialise into stable stationary objects., Comment: Matches published version. 11 pages, 5 figures. Minor but important corrections were incorporated

We examine the evolution of an inhomogeneous mixture of non-relativistic pressureless cold dark matter (CDM), coupled to dark energy (DE) characterised by the equation of state parameter $w<-1/3$, with the interaction term proportional to the DE density. This coupled mixture is the source of a spherically symmetric Lema\^\ itre-Tolman-Bondi (LTB) metric admitting an asymptotic Friedman-Lema\^\ itre-Robertson-Walker (FLRW) background. Einstein's equations reduce to a 5-dimensional autonomous dynamical system involving quasi--local variables related to suitable averages of covariant scalars and their fluctuations. The phase space evolution around the critical points (past/future attractors and five saddles) is examined in detail. For all parameter values and both directions of energy flow (CDM to DE and DE to CDM) the phase space trajectories are compatible with a physically plausible early cosmic times behaviour near the past attractor. This result compares favourably with mixtures with the interaction driven by the CDM density in which conditions for a physically plausible past evolution are more restrictive. Numerical examples are provided describing the evolution of an initial profile that can be associated with idealised structure formation scenarios, Comment: 23 pages, IOP format, 8 figures

We derive a class of non-static inhomogeneous dust solutions in f(R) gravity described by the Lemaitre-Tolman-Bondi (LTB) metric. The field equations are fully integrated for all parameter subcases and compared with analogous subcases of LTB dust solutions of GR. Since the solutions do not admit regular symmetry centres, we have two possibilities: (i) a spherical dust cloud with angle deficit acting as the source of a vacuum Schwarzschild-like solution associated with a global monopole, or (ii) fully regular dust wormholes without angle deficit, whose rest frames are homeomorphic to the Schwarzschild-Kruskal manifold or to a 3d torus. The compatibility between the LTB metric and generic f(R) ansatzes furnishes an "inverse procedure" to generate LTB solutions whose sources are found from the f(R) geometry. While the resulting fluids may have an elusive physical interpretation, they can be used as exact non--perturbative toy models in theoretical and cosmological applications of f(R) theories., Comment: 17 pages. Version accepted for publication in Classical and Quantum Gravity. IOP LaTex format. Typos corrected, references added

Recently we have studied in great detail a model of Hybrid Natural Inflation (HNI) by constructing two simple effective field theories. These two versions of the model allow inflationary energy scales as small as the electroweak scale in one of them or as large as the Grand Unification scale in the other, therefore covering the whole range of possible energy scales. In any case the inflationary sector of the model is of the form $V(\phi)=V_0 \left(1+a \cos(\phi/f)\right)$ where $0\leq a<1$ and the end of inflation is triggered by an independent waterfall field. One interesting characteristic of this model is that the slow-roll parameter $\epsilon(\phi)$ is a non-monotonic function of $\phi$ presenting a {\it maximum} close to the inflection point of the potential. Because the scalar spectrum $\mathcal{P}_s(k)$ of density fluctuations when written in terms of the potential is inversely proportional to $\epsilon(\phi)$ we find that $\mathcal{P}_s(k)$ presents a {\it minimum} at $\phi_{min}$. The origin of the HNI potential can be traced to a symmetry breaking phenomenon occurring at some energy scale $f$ which gives rise to a (massless) Goldstone boson. Non-perturbative physics at some temperature $T

Quasi--local scalar variables approach is applied to a spherically symmetric inhomogeneous Lema\^\i tre--Tolman--Bondi metric containing a mixture of non-relativistic cold dark matter and coupled dark energy with constant equation of state. The quasi--local coupling term considered is proportional to the quasi--local cold dark matter energy density and a quasi--local Hubble factor-like scalar via a coupling constant $\alpha$. The autonomous numerical system obtained from the evolution equations is classified for different choices of the free parameters: the adiabatic constant of the dark energy $w$ and $\alpha$. The presence of a past attractor in a non-physical region of the energy densities phase-space of the system makes the coupling term non physical when the energy flows from the matter to the dark energy in order to avoid negative values of the dark energy density in the past. On the other hand, if the energy flux goes from dark energy to dark matter, the past attractor lays in a physical region. The system is also numerically solved for some interesting initial profiles leading to different configurations: an ever expanding mixture, a scenario where the dark energy is completely consumed by the non-relativistic matter by means of the coupling term, a scenario where the dark energy disappears in the inner layers while the outer layers expand as a mixture of both sources, and, finally, a structure formation toy model scenario, where the inner shells containing the mixture collapse while the outer shells expand., Comment: 27 pages, 12 figures

We study the differences and equivalences between the non-perturbative description of the evolution of cosmic structure furnished by the Szekeres dust models (a non-spherical exact solution of Einstein's equations) and the dynamics of Cosmological Perturbation Theory (CPT) for dust sources in a $\Lambda$CDM background. We show how the dynamics of Szekeres models can be described by evolution equations given in terms of "exact fluctuations" that identically reduce (at all orders) to evolution equations of CPT in the comoving isochronous gauge. We explicitly show how Szekeres linearised exact fluctuations are specific (deterministic) realisations of standard linear perturbations of CPT given as random fields but, as opposed to the latter perturbations, they can be evolved exactly into the full non-linear regime. We prove two important results: (i) the conservation of the curvature perturbation (at all scales) also holds for the appropriate approximation of the exact Szekeres fluctuations in a $\Lambda$CDM background, and (ii) the different collapse morphologies of Szekeres models yields, at nonlinear order, different functional forms for the growth factor that follows from the study of redshift space distortions. The metric based potentials used in linear CPT are computed in terms of the parameters of the linearised Szekeres models, thus allowing us to relate our results to linear CPT results in other gauges. We believe that these results provide a solid starting stage to examine the role of non-perturbative General Relativity in current cosmological research., Comment: V2: Minor comments and a couple of references added. Version accepted for publication in PRD

We take a pragmatic, model independent approach to single field slow-roll canonical inflation by imposing conditions, not on the potential, but on the slow-roll parameter $\epsilon(\phi)$ and its derivatives $\epsilon^{\prime }(\phi)$ and $\epsilon^{\prime\prime }(\phi)$, thereby extracting general conditions on the tensor-to-scalar ratio $r$ and the running $n_{sk}$ at $\phi_{H}$ where the perturbations are produced, some $50$ $-$ $60$ $e$-folds before the end of inflation. We find quite generally that for models where $\epsilon(\phi)$ develops a maximum, a relatively large $r$ is most likely accompanied by a positive running while a negligible tensor-to-scalar ratio implies negative running. The definitive answer, however, is given in terms of the slow-roll parameter $\xi_2(\phi)$. To accommodate a large tensor-to-scalar ratio that meets the limiting values allowed by the Planck data, we study a non-monotonic $\epsilon(\phi)$ decreasing during most part of inflation. Since at $\phi_{H}$ the slow-roll parameter $\epsilon(\phi)$ is increasing, we thus require that $\epsilon(\phi)$ develops a maximum for $\phi > \phi_{H}$ after which $\epsilon(\phi)$ decrease to small values where most $e$-folds are produced. The end of inflation might occur trough a hybrid mechanism and a small field excursion $\Delta\phi_e\equiv |\phi_H-\phi_e |$ is obtained with a sufficiently thin profile for $\epsilon(\phi)$ which, however, should not conflict with the second slow-roll parameter $\eta(\phi)$. As a consequence of this analysis we find bounds for $\Delta \phi_e$, $r_H$ and for the scalar spectral index $n_{sH}$. Finally we provide examples where these considerations are explicitly realised., Comment: V2: 9 pages, 4 figures. Version accepted for publication in JCAP

We examine the spatial extrema (local maxima, minima and saddle points) of the covariant scalars (density, Hubble expansion, spatial curvature and eigenvalues of the shear and electric Weyl tensors) of the quasi-spherical Szekeres dust models. Sufficient conditions are obtained for the existence of distributions of multiple extrema in spatial comoving locations that can be prescribed through initial conditions. These distributions evolve without shell crossing singularities at least for ever expanding models (with or without cosmological constant) in the full evolution range where the models are valid. By considering the local maxima and minima of the density, our results allow for setting up elaborated networks of "pancake" shaped evolving cold dark matter over-densities and density voids whose spatial distribution and amplitudes can be controlled from initial data compatible with standard early Universe initial conditions. We believe that these results have an enormous range of potential application by providing a fully relativistic non-perturbative coarse grained modelling of cosmic structure at all scales., Comment: Matches published version. 28 pages, 9 figures. Minor but important corrections were incorporated

We show that the full dynamical freedom of the well known Szekeres models allows for the description of elaborated 3--dimensional networks of cold dark matter structures (over--densities and/or density voids) undergoing "pancake" collapse. By reducing Einstein's field equations to a set of evolution equations, which themselves reduce in the linear limit to evolution equations for linear perturbations, we determine the dynamics of such structures, with the spatial comoving location of each structure uniquely specified by standard early Universe initial conditions. By means of a representative example we examine in detail the density contrast, the Hubble flow and peculiar velocities of structures that evolved, from linear initial data at the last scattering surface, to fully non--linear 10--20 Mpc. scale configurations today. To motivate further research, we provide a qualitative discussion on the connection of Szekeres models with linear perturbations and the pancake collapse of the Zeldovich approximation. This type of structure modelling provides a coarse grained -- but fully relativistic non--linear and non--perturbative -- description of evolving large scale cosmic structures before their virialisation, and as such it has an enormous potential for applications in cosmological research., Comment: V3: Discussion of the expansion eigenvalues and of the Zeldovich approximation added. Figures modified accordingly. References updated. Version accepted for publication in JCAP

We undertake a hydrodynamical study of a mixture of tightly coupled primordial radiation, neutrinos, baryons, electrons and positrons, together with a gas of already decoupled dark matter WIMPS and an already existing "frozen" magnetic field in the infinite conductivity regime. Considering this cosmic fluid as the source of a homogeneous but anisotropic Bianchi I model, we describe its interaction with the magnetic field by means of suitable equations of state that are appropriate for the particle species of the mixture between the end of the leptonic era and the beginning of the radiation-dominated epoch. Fulfilment of observational bounds on the magnetic field intensity yields a "near FLRW" (but strictly non-perturbative) evolution of the geometric, kinematic and thermodynamical variables. This evolution is roughly comparable to the weak field approximation in linear perturbations on a spatially flat FLRW background of sources in which the frozen magnetic fields are coherent over very large supra-horizon scales. Our approach and results may provide interesting guidelines in potential situations in which non-perturbative methods are required to study the interaction between magnetic fields and the cosmic fluid., Comment: Accepted in General Relativity and Gravitation. The final publication will be available at Springer via http://dx.doi.org/10.1007/s10714-015-2004-3

We undertake a non-perturbative study of the evolution of the "gravitational entropy" proposed by Clifton, Ellis and Tavakol (CET) on local expanding cosmic CDM voids of $\sim 50-100$ Mpc size described as spherical under-dense regions with negative spatial curvature, whose dynamics is determined by Lemaitre-Tolman-Bondi (LTB) dust models asymptotic to three different types of FLRW background: $\Lambda$CDM, Einstein de Sitter and "open" FLRW with $\Lambda=0$ and negative spatial curvature. By assuming generic nearly spatially flat and linear initial conditions at the last scattering time, we examine analytically and numerically the CET entropy evolution into a fully non-linear regime in our present cosmic time and beyond. Both analytic and numerical analysis reveal that the late time CET entropy growth is determined by the amplitude of initial fluctuations of spatial curvature at the last scattering time. This entropy growth decays to zero in the late asymptotic time range for all voids, but at a faster rate in voids with $\Lambda$CDM and open FLRW backgrounds. However, only for voids in a $\Lambda$CDM background this suppression is sufficiently rapid for the CET entropy itself to reach a terminal equilibrium (or "saturation") value. The CET gravitational temperature vanishes asymptotically if $\Lambda=0$ and becomes asymptotically proportional to $\Lambda$ for voids in a $\Lambda$CDM background. In the linear regime of the LTB evolution our results coincide, qualitatively and quantitatively, with previous results based on linear perturbation theory., Comment: 24 pages, 6 figures. Replaced to match the published version

We examine the relation between the dynamics of Lema\^{\i}tre-Tolman-Bondi (LTB) dust models (with and without $\Lambda$) and the dynamics of dust perturbations in two of the more familiar formalisms used in cosmology: the metric based Cosmological Perturbation Theory (CPT) and the Covariant Gauge Invariant (GIC) perturbations. For this purpose we recast the evolution of LTB models in terms of a covariant and gauge invariant formalism of local and non-local "exact fluctuations " on a Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) background defined by suitable averages of covariant scalars. We examine the properties of these fluctuations, which can be defined for a confined comoving domain or for an asymptotic domain extending to whole time slices. In particular, the non-local density fluctuation provides a covariant and precise definition for the notion of the "density contrast ". We show that in their linear regime these LTB exact fluctuations (local and non-local) are fully equivalent to the conventional cosmological perturbations in the synchronous-comoving gauge of CPT and to GIC perturbations. As an immediate consequence, we show the time-invariance of the spatial curvature perturbation in a simple form. The present work may provide important theoretical connections between the exact and perturbative (linear or no-linear) approach to the dynamics of dust sources in General Relativity., Comment: V2: References added and typos corrected. Version accepted for publication in PRD

We apply a recent proposal to define "gravitational entropy" to the expansion of cosmic voids within the framework of non-perturbative General Relativity. By considering CDM void configurations compatible with basic observational constraints, we show that this entropy grows from post-inflationary conditions towards a final asymptotic value in a late time fully non-linear regime described by the Lemaitre-Tolman-Bondi (LTB) dust models. A qualitatively analogous behavior occurs if we assume a positive cosmological constant consistent with a $\Lambda$-CDM background model. However, the $\Lambda$ term introduces a significant suppression of entropy growth with the terminal equilibrium value reached at a much faster rate., Comment: 5 Pages, 2 figures, AN style. Contribution to Proceedings of the Second Caribbean Symposium on Nuclear and Astroparticle Physics (STARS 2013), La Habana, Cuba, 5-9 May 2013

We analyse Hybrid Natural Inflation in view of the recent results for the tensor index reported by BICEP2. We find that it predicts a large running of the scalar spectrum which is potentially detectable by large scale structure and $21\, \mathrm{cm} $ observations. The running of the running is also relatively large becoming close to $10^{-2}$. Along the way, we find general consistency relations at which observables are subject if the slow-roll approximation is imposed. Failure to satisfy these equations by the values obtained for the observables in surveys would be a failure of the slow-roll approximation itself., Comment: V3: Published version

We consider generic Lemaitre-Tolman-Bondi (LTB) dust models to probe the gravitational entropy proposals of Clifton, Ellis and Tavakol (CET) and of Hosoya and Buchert (HB). We also consider a variant of the HB proposal based on a suitable quasi-local scalar weighted average. We show that the conditions for entropy growth for all proposals are directly related to a negative correlation of similar fluctuations of the energy density and Hubble scalar. While this correlation is evaluated locally for the CET proposal, it must be evaluated in a non--local domain dependent manner for the two HB proposals. By looking at the fulfillment of these conditions at the relevant asymptotic limits we are able to provide a well grounded qualitative description of the full time evolution and radial asymptotic scaling of the three entropies in generic models. The following rigorous analytic results are obtained for the three proposals: (i) entropy grows when the density growing mode is dominant, (ii) all ever-expanding hyperbolic models reach a stable terminal equilibrium characterized by an inhomogeneous entropy maximum in their late time evolution; (iii) regions with decaying modes and collapsing elliptic models exhibit unstable equilibria associated with an entropy minimum (iv) near singularities the CET entropy diverges while the HB entropies converge; (v) the CET entropy converges for all models in the radial asymptotic range, whereas the HB entropies only converge for models asymptotic to an FLRW background. The fact that different independent proposals yield fairly similar conditions for entropy production, time evolution and radial scaling in generic LTB models seems to suggest that their common notion of a "gravitational entropy" may be a theoretically robust concept applicable to more general spacetimes., Comment: Version accepted for publication in Classical and Quantum Gravity. 39 pages, 6 figures

We obtain covariant expressions that generalize the growing and decaying density modes of linear perturbation theory of dust sources by means of the exact density perturbation from the formalism of quasi--local scalars associated to weighed proper volume averages in LTB dust models. The relation between these density modes and theoretical properties of generic LTB models is thoroughly studied by looking at the evolution of the models through a dynamical system whose phase space is parametrized by variables directly related to the modes themselves. The conditions for absence of shell crossings, as well as sign conditions on the modes, become interrelated fluid flow preserved constraints that define phase space invariant subspaces. In the general case (both density modes being nonzero) the evolution of phase space trajectories exhibits the expected dominance of the decaying/growing in the early/late evolution times defined by past/future attractors characterized by asymptotic density inhomogeneity. In particular, the growing mode is also dominant for collapsing layers that terminate in a future attractor associated with a "Big Crunch" singularity, which is qualitatively different from the past attractor marking the "Big Bang". Suppression of the decaying mode modifies the early time evolution, with phase space trajectories emerging from an Einstein--de Sitter past attractor associated with homogeneous conditions. Suppression of the growing mode modifies the late time evolution as phase space trajectories terminate in future attractors associated with homogeneous states. General results are obtained relating the signs of the density modes and the type of asymptotic density profile (clump or void). A critical review is given of previous attempts in the literature to define these density modes for LTB models., Comment: Final version accepted for publication in Classical and Quantum Gravity. 34 pages, 6 figures and 4 tables, IOP LaTeX format

We examine the dynamics of a self--gravitating magnetized electron gas at finite temperature near the collapsing singularity of a Bianchi-I spacetime. Considering a general and appropriate and physically motivated initial conditions, we transform Einstein--Maxwell field equations into a complete and self--consistent dynamical system amenable for numerical work. The resulting numerical solutions reveal the gas collapsing into both, isotropic ("point-like") and anisotropic ("cigar-like") singularities, depending on the initial intensity of the magnetic field. We provide a thorough study of the near collapse behavior and interplay of all relevant state and kinematic variables: temperature, expansion scalar, shear scalar, magnetic field, magnetization and energy density. A significant qualitative difference in the behavior of the gas emerges in the temperature range $\hbox{T} sim10^{4}\hbox{K}$ and $\hbox{T}\sim 10^{7}\hbox{K}$., Comment: 9 pages, 7 figures. arXiv admin note: substantial text overlap with arXiv:1211.5980

We examine the exact perturbations that arise from the q-average formalism that was applied in the preceding article (part I) to Lemaitre-Tolman-Bondi (LTB) models. By introducing an initial value parametrization, we show that all LTB scalars that take a FLRW "look alike" form (frequently used in the literature dealing with LTB models) follow as q-averages of covariant scalars that are common to FLRW models. These q--scalars determine for every averaging domain a unique FLRW background state through Darmois matching conditions at the domain boundary, though the definition of this background does not require an actual matching with a FLRW region (Swiss cheese type models). Local perturbations describe the deviation from the FLRW background state through the local gradients of covariant scalars at the boundary of every comoving domain, while non-local perturbations do so in terms of the intuitive notion of a "contrast" of local scalars with respect to FLRW reference values that emerge from q-averages assigned to the whole domain or the whole time slice in the asymptotic limit. We derive fluid flow evolution equations that completely determine the dynamics of the models in terms of the q-scalars and both types of perturbations. A rigorous formalism of exact spherical non-linear perturbations is defined over the FLRW background state associated to the q-scalars, recovering the standard results of linear perturbation theory in the appropriate limit. We examine the notion of the amplitude and illustrate the differences between local vs non-local perturbations by qualitative diagrams and through an example of a cosmic density void that follows from the numeric solution of the evolution equations., Comment: 31 pages IOP format, 12 figures. Matches version accepted for publication in Classical and Quantum Gravity

We examine the near collapse dynamics of a self-gravitating magnetized electron gas at finite temperature, taken as the source of a Bianchi-I spacetime described by the Kasner metric. The set of Einstein-Maxwell field equations reduces to a complete and self-consistent system of non-linear autonomous ODE's. By considering a representative set of initial conditions, the numerical solutions of this system show the gas collapsing into both, isotropic ("point--like") and anisotropic ("cigar-like") singularities, depending on the intensity of the magnetic field. We also examined the behavior during the collapse stage of all relevant state and kinematic variables: the temperature, the expansion scalar, the magnetic field, the magnetization and energy density. We notice a significant qualitative difference in the behavior of the gas for a range of temperatures between the values $\hbox{T}\sim10^{3}\hbox{K}$ and $\hbox{T}\sim 10^{7}\hbox{K}$., Comment: 16 pages, 7 figures, submitted to JCAP

We introduce a weighed scalar average formalism ("q-average") for the study of the theoretical properties and the dynamics of spherically symmetric Lemaitre-Tolman-Bondi (LTB) dust models models. The "q-scalars" that emerge by applying the q-averages to the density, Hubble expansion and spatial curvature (which are common to FLRW models) are directly expressible in terms of curvature and kinematic invariants and identically satisfy FLRW evolution laws without the back-reaction terms that characterize Buchert's average. The local and non-local fluctuations and perturbations with respect to the q-average convey the effects of inhomogeneity through the ratio of curvature and kinematic invariants and the magnitude of radial gradients. All curvature and kinematic proper tensors that characterize the models are expressible as irreducible algebraic expansions on the metric and 4-velocity, whose coefficients are the q-scalars and their linear and quadratic local fluctuations. All invariant contractions of these tensors are quadratic fluctuations, whose q-averages are directly and exactly related to statistical correlation moments of the density and Hubble expansion scalar. We explore the application of this formalism to a definition of a gravitational entropy functional proposed by Hosoya et al (2004 Phys. Rev. Lett. 92 141302). We show that a positive entropy production follows from a negative correlation between fluctuations of the density and Hubble scalar, providing a brief outline on its fulfillment in various LTB models and regions. While the q-average formalism is specially suited for LTB and Szekeres models, it may provide a valuable theoretical insight on the properties of scalar averaging in inhomogeneous spacetimes in general., Comment: 27 pages in IOP format, 1 figure. Matches version accepted for publication in Classical and Quantum Gravity

We obtain an elegant and useful description of the dynamics of Szekeres dust models (in their full generality) by means of `quasi-local' scalar variables constructed by suitable integral distributions that can be interpreted as weighed proper volume averages of the local covariant scalars. In terms of these variables, the field equations and basic physical and geometric quantities are formally identical to their corresponding expressions in the spherically symmetric LTB dust models. Since we can map every Szekeres model to a unique LTB model, rigorous results valid for the latter models can be readily generalized to a non-spherical Szekeres geometry. The new variables lead naturally to an initial value formulation in which all scalars are expressed as scaling laws in terms of their values at an arbitrary initial space slice. These variables also yield a significant simplification of numerical work, since the fluid flow evolution equations become a system of autonomous ordinary differential equations subjected to algebraic constraints containing the information on the deviations from spherical symmetry. As an example of how this formalism can be applied, we show that spherical symmetry is stable against small dipole-like perturbations. This new approach to the dynamics of the Szekeres solutions has an enormous potential for dealing with a wide variety of theoretical issues and for constructing non-spherical models of cosmological inhomogeneities to fit observational data., Comment: 26 pages, 2 figures

We provide a thorough examination of the conditions for the existence of back-reaction and an "effective" acceleration (in the context of Buchert's averaging formalism) in regular generic spherically symmetric Lemaitre-Tolman-Bondi (LTB) dust models. By considering arbitrary spherical comoving domains, we verify rigorously the fulfillment of these conditions expressed in terms of suitable scalar variables that are evaluated at the boundary of every domain. Effective deceleration necessarily occurs in all domains in: (a) the asymptotic radial range of models converging to a FLRW background, (b) the asymptotic time range of non-vacuum hyperbolic models, (c) LTB self-similar solutions and (d) near a simultaneous big bang. Accelerating domains are proven to exist in the following scenarios: (i) central vacuum regions, (ii) central (non-vacuum) density voids, (iii) the intermediate radial range of models converging to a FLRW background, (iv) the asymptotic radial range of models converging to a Minkowski vacuum and (v) domains near and/or intersecting a non-simultaneous big bang. All these scenarios occur in hyperbolic models with negative averaged and local spatial curvature, though scenarios (iv) and (v) are also possible in low density regions of a class of elliptic models in which local spatial curvature is negative but its average is positive. Rough numerical estimates between -0.003 and -0.5 were found for the effective deceleration parameter. While the existence of accelerating domains cannot be ruled out in models converging to an Einstein de Sitter background and in domains undergoing gravitational collapse, the conditions for this are very restrictive. The results obtained may provide important theoretical clues on the effects of back-reaction and averaging in more general non-spherical models., Comment: Final version accepted for publication in Classical and Quantum Gravity. 47 pages in IOP LaTeX macros, 12 pdf figures

Inhomogeneous cosmological models are able to fit cosmological observations without dark energy under the assumption that we live close to the "center" of a very large-scale under-dense region. Most studies fitting observations by means of inhomogeneities also assume spherical symmetry, and thus being at (or very near) the center may imply being located at a very special and unlikely observation point. We argue that such spherical voids should be treated only as a gross first approximation to configurations that follow from a suitable smoothing out of the non-spherical part of the inhomogeneities on angular scales. In this Letter we present a toy construction that supports the above statement. The construction uses parts of the Szekeres model, which is inhomogeneous and anisotropic thus it also addresses the limitations of spherical inhomogeneities. By using the thin-shell approximation (which means that the Israel-Darmois continuity conditions are not fulfilled between the shells) we construct a model of evolving cosmic structures, containing several elongated supercluster-like structures with underdense regions between them, which altogether provides a reasonable coarse-grained description of cosmic structures. While this configuration is not spherically symmetric, its proper volume average yields a spherical void profile of 250 Mpc that roughly agrees with observations. Also, by considering a non-spherical inhomogeneity, the definition of a "center" location becomes more nuanced, and thus the constraints placed by fitting observations on our position with respect to this location become less restrictive., Comment: 6 pages, 5 figures, accepted for publication in Phys. Lett. B

We undertake a comprehensive and rigorous analytic study of the evolution of radial profiles of covariant scalars in regular Lemaitre-Tolman-Bondi dust models. We consider specifically the phenomenon of "profile inversions" in which an initial clump profile of density, spatial curvature or the expansion scalar, might evolve into a void profile (and vice versa). Previous work in the literature on models with density void profiles and/or allowing for density profile inversions is given full generalization, with some erroneous results corrected. We prove rigorously that if an evolution without shell crossings is assumed, then only the 'clump to void' inversion can occur in density profiles, and only in hyperbolic models or regions with negative spatial curvature. The profiles of spatial curvature follow similar patterns as those of the density, with 'clump to void' inversions only possible for hyperbolic models or regions. However, profiles of the expansion scalar are less restrictive, with profile inversions necessarily taking place in elliptic models. We also examine radial profiles in special LTB configurations: closed elliptic models, models with a simultaneous big bang singularity, as well as a locally collapsing elliptic region surrounded by an expanding hyperbolic background. The general analytic statements that we obtain allow for setting up the right initial conditions to construct fully regular LTB models with any specific qualitative requirements for the profiles of all scalars and their time evolution. The results presented can be very useful in guiding future numerical work on these models and in revising previous analytic work on all their applications., Comment: Final version to appear in Classical and Quantum Gravity. Readers eager to know the results and implications without having to go through the technical detail are recommended to go directly to the summary and discussion in the final section (section 11). Typos have been corrected and an important reference has been added

We consider spherically symmetric inhomogeneous dust models with a positive cosmological constant, $\Lambda$, given by the Lemaitre-Tolman-Bondi metric. These configurations provide a simple but useful generalization of the Lambda-CDM model describing cold dark matter (CDM) and a Lambda term, which seems to fit current cosmological observations. The dynamics of these models can be fully described by scalar evolution equations that can be given in the form of a proper dynamical system associated with a 4-dimensional phase space whose critical points and invariant subspaces are examined and classified. The phase space evolution of various configurations is studied in detail by means of two 2-dimensional subspaces: a projection into the invariant homogeneous subspace associated with Lambda-CDM solutions with FLRW metric, and a projection into a subspace generated by suitably defined fluctuations that convey the effects of inhomogeneity. We look at cases with perpetual expansion, bouncing and loitering behavior, as well as configurations with "mixed" kinematic patters, such as a collapsing region in an expanding background. In all cases, phase space trajectories emerge from and converge to stable past and future attractors in a qualitatively analogous way as in the case of the FLRW limit. However, we can identify in both projections of the phase space various qualitative features absent in the FLRW limit that can be useful in the construction of toy models of astrophysical and cosmological inhomogeneities., Comment: Final version published in Classical and Quantum Gravity: 26 pages in IOP LaTeX macro style, 9 pdf figures

We examine the radial asymptotic behavior of spherically symmetric Lemaitre-Tolman-Bondi dust models by looking at their covariant scalars along radial rays, which are spacelike geodesics parametrized by proper length $\ell$, orthogonal to the 4-velocity and to the orbits of SO(3). By introducing quasi-local scalars defined as integral functions along the rays, we obtain a complete and covariant representation of the models, leading to an initial value parametrization in which all scalars can be given by scaling laws depending on two metric scale factors and two basic initial value functions. Considering regular "open" LTB models whose space slices allow for a diverging $\ell$, we provide the conditions on the radial coordinate so that its asymptotic limit corresponds to the limit as $\ell\to\infty$. The "asymptotic state" is then defined as this limit, together with asymptotic series expansion around it, evaluated for all metric functions, covariant scalars (local and quasi-local) and their fluctuations. By looking at different sets of initial conditions, we examine and classify the asymptotic states of parabolic, hyperbolic and open elliptic models admitting a symmetry center. We show that in the radial direction the models can be asymptotic to any one of the following spacetimes: FLRW dust cosmologies with zero or negative spatial curvature, sections of Minkowski flat space (including Milne's space), sections of the Schwarzschild--Kruskal manifold or self--similar dust solutions., Comment: 44 pages (including a long appendix), 3 figures, IOP LaTeX style. Typos corrected and an important reference added. Accepted for publication in General Relativity and Gravitation

We introduce quasi-local integral scalar variables for the study of spherically symmetric Lemaitre-Tolman-Bondi (LTB) dust models. Besides providing a covariant, and theoretically appealing, interpretation for the parameters of these models, these variables allow us to study their dynamics (in their full generality) by means of fluid flow evolution equations that can be handled with simple numerical techniques and has a significant potential for astrophysical and cosmological applications. These evolution equations can also be understood in the framework of a gauge invariant and covariant formalism of spherical non-linear perturbations on a FLRW background. The covariant time splitting associated with the new variables leads, in a natural way, to rephrase the known analytic solutions within an initial value framework in which covariant scalars are given by simple scaling laws. By using this re-parametrization of the analytic solutions, we re-examine and provide an alternative outlook to various theoretical issues already treated in the literature: regularity conditions, an Omega parameter, as well as the fitting of a given LTB model to radial profiles of density or velocity at different cosmic times. Other theoretical issues and numeric applications will be examined in separate articles., Comment: 24 pages, RevTeX two column style, no figures. Typos corrected, references added

We introduce quasi--local (QL) scalar variables in spherically symmetric LTB models. If the QL scalars are defined as functionals, they become weighed averages that generalize the standard proper volume averages on space slices orthogonal to the 4-velocity. We examine the connection between QL functions and functionals and the "back-reaction" term $Q$ in the context of Buchert's scalar averaging formalism. With the help of the QL scalars we provide rigorous proof that back--reaction is positive for (i) all LTB models with negative and asymptotically negative spatial curvature, and (ii) models with positive curvature decaying to zero asymptotically in the radial direction. We show by means of qualitative, but robust, arguments that generic LTB models exist, either with clump or void profiles, for which an "effective" acceleration associated with Buchert's formalism can mimic the effects of dark energy., Comment: Submitted contribution for the proceedings of the "Invisible Universe Internationale Confernce", Palais de L'UNESCO, Paris, France, June 29-July 3, 2009. Jean-Michel ALIMI, editor. 10 pages, 2 figures. AIP macros: layoutstyle 8x11single

We interpret as shear viscosity the anisotropic pressure that emerges in inhomogeneous spherically symmetric spacetimes described by the Lemaitre-Tolman-Bondi (LTB) metric in a comoving frame. By assuming that local isotropic pressure and energy density satisfy a generic ideal gas equation of state, we reduce the field equations to a set of evolution equations based on auxiliary quasi-local variables. We examine the transport equation of shear viscosity from Extended Irreversible Thermodynamics and use a numerical solution of the evolution equations to obtain the relaxation times for the full and "truncated" versions. Considering a gas of cold dark matter WIMPS after its decoupling from the cosmic fluid, we show that the relaxation times for the general equation are qualitatively analogous to collision times, while the truncated version is inadequate to describe transient phenomena of transition to equilibrium., Comment: Invited contribution in "Casimir effect and Cosmology", special volume on the occasion of 70th birthday of Prof. I. Brevik, collection of articles, Odintsov, S. D., E.Elizalde and O.G. Gorbunova, -Scientific Editors, TSPU Publishing Company, TSPU, Tomsk, single book, 2008. IOP LaTeX style, 15 pages, 3 pdf figures

We examine the dynamics of a self--gravitating magnetized neutron gas as a source of a Bianchi I spacetime described by the Kasner metric. The set of Einstein-Maxwell field equations can be expressed as a dynamical system in a 4-dimensional phase space. Numerical solutions of this system reveal the emergence of a point--like singularity as the final evolution state for a large class of physically motivated initial conditions. Besides the theoretical interest of studying this source in a fully general relativistic context, the resulting idealized model could be helpful in understanding the collapse of local volume elements of a neutron gas in the critical conditions that would prevail in the center of a compact object., Comment: 17 pages, 6 figures, JHEP style, published version

We examine a large class of inhomogeneous spherically symmetric spacetimes that generalize the Lemaitre-Tolman-Bondi dust solutions to nonzero pressure ("LTB spacetimes"). Local covariant LTB objects can be expressed as perturbations of covariant quasi-local (QL) scalars that satisfy evolution equations of equivalent Friedman-Lemaitre-Robertson-Walker (FLRW) scalars. Thus, the dynamics of these spacetimes can be rigorously described as non-linear, gauge invariant and covariant perturbations on a formal FLRW background given by the QL scalars. Since LTB spacetimes are compatible with a wide variety of "equations of state" and theoretical assumptions, they provide an ideal framework for numerical models of cosmological sources under idealized but fully non-linear conditions. As an illustrative example, we briefly examine the formation of a black hole in an expanding Chaplygin gas universe., Comment: 8 pages, 2 pdf figures. Provides a concise summary of some of the results of arXiv:0801.3324v4 [gr-qc]. Submitted to the AIP Conference Proceedings of the III International Meeting on Gravitation and Cosmology, Morelia, Mexico, May 26-30, 2008