Related papers: On Spacetimes with Given Kinematical Invariants: C…
In this brief review, we present the results of the fractional differential approach in cosmology in the context of the exact models of cosmological accelerated expansion obtained by several authors to date. Most of these studies are…
We review recent theoretical progress and observational constraints on multifractional spacetimes, geometries that change with the probed scale. On the theoretical side, the basic structure of the Standard Model and of the gravitational…
The averaging problem in cosmology is of considerable importance for the correct interpretation of cosmological data. A rigorous mathematical definition of averaging in a cosmological model is necessary. In general, a spacetime is…
Two algorithms are proposed to simulate space-time Gaussian random fields with a covariance function belonging to an extended Gneiting class, the definition of which depends on a completely monotone function associated with the spatial…
The gravitational field equations on cosmological scales are obtained by averaging the Einstein field equations of general relativity. By assuming spatial homogeneity and isotropy on the largest scales, the local inhomogeneities affect the…
We consider a dynamical systems formulation for models with an exponential scalar field and matter with a linear equation of state in a spatially flat and isotropic spacetime. In contrast to earlier work, which only considered linear…
A D-dimensional gravitational model with Gauss-Bonnet term is considered. When ansatz with diagonal cosmological type metrics is adopted, we find solutions with exponential dependence of scale factors (with respect to "synchronous-like"…
The gravitational dynamics and cosmological implications of three classes of recently introduced multi-scale spacetimes (with, respectively, ordinary, weighted and q-derivatives) are discussed. These spacetimes are non-Riemannian: the…
We construct a scalar field based cosmological model, possessing a cosmological singularity characterized by a finite value of the cosmological radius and an infinite scalar curvature. Using the methods of the qualitative theory of…
I give a geometric construction of certain first order natural dynamical observables in multifield cosmological models with arbitrary target space topology and discuss a system of related dynamical approximations and regimes for such…
We provide the full classification, in arbitrary even and odd dimensions, of global conformal invariants, i.e., scalar densities in the spacetime metric and its derivatives that are invariant, possibly up to a total derivative, under local…
We study the cosmology of a covariant scalar field respecting a Galilean symmetry in flat space-time. We show the existence of a tracker solution that finally approaches a de Sitter fixed point responsible for cosmic acceleration today. The…
We consider the problem of calculating the Gaussian curvature of a conical 2-dimensional space by using concepts and techniques of distribution theory. We apply the results obtained to calculate the Riemannian curvature of the 4-dimensional…
We construct a covariant version of the Tolman-Oppenheimer-Volkoff equations in the case of isotropic sources. The new equations make evident the mathematical problems in the determination of interior solutions of relativistic stellar…
We investigate the interplay and connections between symmetry properties of equations, the interpretation of coordinates, the construction of observables, and the existence of physical relativity principles in spacetime theories. Using the…
We present time-dependent analytic solutions to the Einstein equations coupled with a dilaton (scalar) field. The background geometry for the solutions is a product of an N-dimensional spherically symmetric space and a d-dimensional flat…
In this work we study models described by a single real scalar field in two-dimensional space-time, using the deformation procedure to propose and investigate new families of models and their kink solutions.
This survey is devoted to recent developments in the statistical analysis of spherical data, with a view to applications in Cosmology. We will start from a brief discussion of Cosmological questions and motivations, arguing that most…
We simplify the gravitational equations which apply in accelerating spacetimes and are consistent with the cosmological principle. Solutions to these equations should be tantamount to all order re-summations of the perturbative leading…
We have derived the invariants of cosmological models with Gurzadyan-Xue dark energy, along with the solutions for any time dependent light speed and gravitational constant. The correspondence of the invariants with the separatrices found…