Roberto A. Sussman

Back-reaction and effective acceleration in generic LTB dust models

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 the 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. Communicated by L Andersson

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 weighted 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 Lema?tre?Tolman?Bondi (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.

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

Abstract 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.

Radial asymptotics of Lemaître–Tolman–Bondi dust models

We examine the radial asymptotic behavior of spherically symmetric Lemaître–Tolman–Bondi dust models by looking at their covariant scalars along radial rays, which are spacelike geodesics parametrized by proper length ℓ, 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 ℓ, we provide the conditions on the radial coordinate so that its asymptotic limit corresponds to the limit as ℓ → ∞. 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.

On the thermodynamical interpretation of perfect fluid solutions of the Einstein equations with no symmetry

The Gibbs–Duhem equation dU+pdV=TdS imposes restrictions on the perfect fluid solutions of Einstein equations that have a one-dimensional symmetry group or no symmetry at all. In this paper, we investigate the restrictions imposed on the Stephani Universe and on the two classes of models found by Szafron. Upon the Stephani Universe and the β≠0 class of Szafron symmetries are forced. We find the most general subcases of the β=0 model of Szafron that are consistent with the Gibbs–Duhem equation and have no symmetry.

Dark energy or apparent acceleration due to a relativistic cosmological model more complex than the Friedmann-Lemaitre-Robertson-Walker model?

We use the Szekeres inhomogeneous relativistic models in order to fit supernova combined data sets. We show that with a choice of the spatial curvature function that is guided by current observations, the models fit the supernova data almost as well as the Lambda-CDM model without requiring a dark energy component. The Szekeres models were originally derived as an exact solution to Einsteins equations with a general metric that has no symmetries, and they are regarded as good candidates to model the true lumpy universe that we observe. The null geodesics in these models are not radial. The best fit model found is also consistent with the requirement of spatial flatness at cosmic microwave background scales. The first results presented here seem to encourage further investigations of apparent acceleration using various inhomogeneous models, and other constraints from cosmic microwave background and large structure need to be explored next.

Quasi‐local variables and scalar averaging in LTB dust models

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.

Inhomogeneous models of interacting dark matter and dark energy

We derive and analyze a class of spherically symmetric cosmological models whose source is an interactive mixture of inhomogeneous cold dark matter (DM) and a generic homogeneous dark energy (DE) fluid. If the DE fluid corresponds to a quintessence scalar field, the interaction term can be associated with a well motivated non-minimal coupling to the DM component. By constructing a suitable volume average of the DM component we obtain a Friedman evolution equation relating this average density with an average Hubble scalar, with the DE component playing the role of a repulsive and time-dependent Λ term. Once we select an “equation of state” linking the energy density (μ) and pressure (p) of the DE fluid, as well as a free function governing the radial dependence, the models become fully determinate and can be applied to known specific DE sources, such as quintessence scalar fields or tachyonic fluids. Considering the simple equation of state p = (γ − 1) μ with 0 ≤ γ < 2/3, we show that the free parameters and boundary conditions can be selected for an adequate description of a local DM overdensity evolving in a suitable cosmic background that accurately fits current observational data. While a DE dominated scenario emerges in the asymptotic future, with total Ω and q tending respectively to 1 and −1/2 for all cosmic observers, the effects of inhomogeneity and anisotropy yield different local behavior and evolution rates for these parameters in the local overdense region. We suggest that the models presented can be directly applied to explore the effects of various DE formalisms on local DM cosmological inhomogeneities.

Quasi—local variables and inhomogeneous cosmological sources with spherical symmetry.

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.

Hydrodynamics of galactic dark matter

We consider simple hydrodynamical models of galactic dark matter in which the galactic halo is a self-gravitating and self-interacting gas that dominates the dynamics of the galaxy. Modelling this halo as a spherically symmetric and static perfect fluid satisfying the field equations of general relativity, visible baryonic matter can be treated as ‘test particles’ in the geometry of this field. We show that the assumption of an empirical ‘universal rotation curve’ that fits aw id ev ariety of galaxies is compatible, under suitable approximations, with state variables characteristic of a non-relativistic Maxwell–Boltzmann gas that becomes an isothermal sphere in the Newtonian limit. Consistency criteria lead to a minimal bound for particle masses in the range 30 eV <m< 60 eV and to a constraint between the central temperature and the particle mass. The allowed mass range includes popular supersymmetric particle candidates, such as the neutralino, axino and gravitino, as well as lighter particles (m ≈ keV) proposed by numerical n-body simulations associated with self-interactive CDM and WDM structure formation theories.