Relativistic interpretation and cosmological signature of Milgroms acceleration

We propose in this letter a relativistic coordinate independent interpretation for Milgroms 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

Non-Spherical Szekeres models in the language of Cosmological Perturbations

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 Einsteins 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.

Coarse-grained description of cosmic structure from Szekeres models

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 Einsteins 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.

Gravitational collapse of a magnetized fermion gas with finite temperature

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 $hbox{T}sim 10^{7}hbox{K}$.

Gravity induced evolution of a magnetized fermion gas with finite temperature

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 ODEs. 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 $hbox{T}sim 10^{7}hbox{K}$.

Local dynamics and gravitational collapse of a self-gravitating magnetized Fermi gas

We use the Bianchi-I spacetime to study the local dynamics of a magnetized self-gravitating Fermi gas. The set of Einstein-Maxwell field equations for this gas becomes a dynamical system in a 4-dimensional phase space. We consider a qualitative study and examine numeric solutions for the degenerate zero temperature case. All dynamic quantities exhibit similar qualitative behavior in the 3-dimensional sections of the phase space, with all trajectories reaching a stable attractor whenever the initial expansion scalar H_{0} is negative. If H_{0} is positive, and depending on initial conditions, the trajectories end up in a curvature singularity that could be isotropic(singular point) or anisotropic (singular line). In particular, for a sufficiently large initial value of the magnetic field it is always possible to obtain an anisotropic type of singularity in which the line points in the same direction of the field.