arXiv subjects

Roberto A. Sussman

Publications and source records attributed to Roberto A. Sussman.

At least 37 records · Page 2Linked to original sources

arXiv2017

Dynamics of a spherically symmetric inhomogeneous coupled dark energy model with coupling term proportional to non relatvistic matter

Quasi--local scalar variables approach is applied to a spherically symmetric inhomogeneous Lema\^ıtre--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 $α$. 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 $α$. 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.

gr-qc↗

arXiv2017

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 Einstein's equations) and the dynamics of Cosmological Perturbation Theory (CPT) for dust sources in a $Λ$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 $Λ$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.

gr-qc↗

arXiv2016

Canonical single field slow-roll inflation with a non-monotonic tensor-to-scalar ratio

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 $ε(ϕ)$ and its derivatives $ε^{\prime }(ϕ)$ and $ε^{\prime\prime }(ϕ)$, thereby extracting general conditions on the tensor-to-scalar ratio $r$ and the running $n_{sk}$ at $ϕ_{H}$ where the perturbations are produced, some $50$ $-$ $60$ $e$-folds before the end of inflation. We find quite generally that for models where $ε(ϕ)$ 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 $ξ_2(ϕ)$. To accommodate a large tensor-to-scalar ratio that meets the limiting values allowed by the Planck data, we study a non-monotonic $ε(ϕ)$ decreasing during most part of inflation. Since at $ϕ_{H}$ the slow-roll parameter $ε(ϕ)$ is increasing, we thus require that $ε(ϕ)$ develops a maximum for $ϕ> ϕ_{H}$ after which $ε(ϕ)$ 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 $Δϕ_e\equiv |ϕ_H-ϕ_e |$ is obtained with a sufficiently thin profile for $ε(ϕ)$ which, however, should not conflict with the second slow-roll parameter $η(ϕ)$. As a consequence of this analysis we find bounds for $Δϕ_e$, $r_H$ and for the scalar spectral index $n_{sH}$. Finally we provide examples where these considerations are explicitly realised.

astro-ph.CO↗

arXiv2016

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 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.

gr-qc↗

arXiv2015

A non-perturbative study of the evolution of cosmic magnetised sources

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.

gr-qc↗

arXiv2015

Multiple non-spherical structures from the extrema of Szekeres scalars

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.

gr-qc↗

arXiv2015

Gravitational entropy of local cosmic voids

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: $Λ$CDM, Einstein de Sitter and "open" FLRW with $Λ=0$ 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 $Λ$CDM and open FLRW backgrounds. However, only for voids in a $Λ$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 $Λ=0$ and becomes asymptotically proportional to $Λ$ for voids in a $Λ$CDM background. In the linear regime of the LTB evolution our results coincide, qualitatively and quantitatively, with previous results based on linear perturbation theory.

gr-qc↗

arXiv2015

On spherical dust fluctuations: the exact vs. the perturbative approach

We examine the relation between the dynamics of Lema\^ıtre-Tolman-Bondi (LTB) dust models (with and without $Λ$) 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\^ıtre-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.

gr-qc↗

arXiv2014

Gravitational entropy of cosmic expansion

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 $Λ$-CDM background model. However, the $Λ$ term introduces a significant suppression of entropy growth with the terminal equilibrium value reached at a much faster rate.

gr-qc↗

arXiv2013

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

gr-qc↗

arXiv2013

Weighed scalar averaging in LTB dust models, part I: statistical fluctuations and gravitational entropy

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.

gr-qc↗

arXiv2013

Weighed scalar averaging in LTB dust models, part II: a formalism of exact perturbations

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.

gr-qc↗

arXiv2012

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

hep-th↗

arXiv2012

A novel approach to the dynamics of Szekeres dust models

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.

gr-qc↗

arXiv2011

Cosmic spherical void via coarse-graining and averaging non-spherical structures

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.

astro-ph.CO↗

arXiv2011

A dynamical systems study of the inhomogeneous Lambda-CDM model

We consider spherically symmetric inhomogeneous dust models with a positive cosmological constant, $Λ$, 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.

gr-qc↗

arXiv2010

Evolution of radial profiles in regular Lemaitre-Tolman-Bondi dust models

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.

gr-qc↗

arXiv2010

Dynamics of a self-gravitating neutron source

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.

gr-qc↗