Related papers: Einstein equations with cosmological constant in S…
A mathematically interesting hyperbolic solution to the Einstein field equations is studied on an eight-dimensional pseudo-Riemannian manifold $\mathbb{X}_{4,4}$ that is a spacetime of four space dimensions and four time dimensions. [The…
A systematic study of deformations of four-dimensional Einsteinian space-times embedded in a pseudo-Euclidean space $E^N$ of higher dimension is presented. Infinitesimal deformations, seen as vector fields in $E^N$, can be divided in two…
In this manuscript, we put forth a general scheme for defining initial value problems from Einstein's equations of General Relativity constrained by homogeneous and isotropic expansion. The cosmological models arising as solutions are…
It is shown that gravity can be incorporated into the Standard Model (SM) in a way solving the hierarchy problem. For this, the SM effective action in flat spacetime is adapted to curved spacetime via not only the general covariance but…
The principle part of Einstein equations in the harmonic gauge consists of a constrained system of 10 curved space wave equations for the components of the space-time metric. A well-posed initial boundary value problem based upon a new…
We propose a unified single-field description of the galactic Dark Matter and various uniform scalar fields for the inflation and cosmological constant. The two types of effects could originate from a fluid of both spatially and temporally…
In this paper, we investigate Bianchi type$-V$ cosmological models with bulk viscous fluid and time varying cosmological $\Lambda$ and Newtonian $G$ parameters. The Einstein's field equations have been transformed into a coupling…
We consider the Einstein equation with first order (semiclassical) quantum corrections. Although the quantum corrections contain up to fourth order derivatives of the metric, the solutions which are physically relevant satisfy a reduced…
The cosmological constant $\Lambda$ is a measure of the energy density of the vacuum. Therefore properties of the energy of the system in the metastable vacuum state reflect properties of $\Lambda = \Lambda(t)$. We analyze properties of the…
This research is an extension of the author's article \cite{zar}, in which conformally invariant generalization of string theory was suggested to higher-dimensional objects. Special cases of the proposed theory are Einstein's theory of…
Solutions with degenerate metric ($det(g_{\mu\nu})=0$ or $g_{\mu\nu}=0$) in the first order formalism (FOF) are physically acceptable: they may describe topology changes (Horowitz) and reduction of "metrical dimension" (Tseytlin) of…
We model the large scale late time universe as a Lambda-CDM cosmology driven by cosmological constant and perfect dust fluid. Our aim is to find new solutions in the matter and Lambda epoch consistent with inflationary initial conditions,…
Spaces equipped with two complementary (distinct) congruences of self-dual null strings and at least one congruence of anti-self-dual null strings are considered. It is shown that if such spaces are Einsteinian then the vacuum Einstein…
This paper discusses the problem of inflation in the context of Friedmann-Robertson-Walker Cosmology. We show how, after a simple change of variables, to quantize the problem in a way which parallels the classical discussion. The result is…
The vacuum cosmological model on the manifold $R \times M_1 \times \ldots \times M_n$ describing the evolution of $n$ Einstein spaces of non-zero curvatures is considered. For $n = 2$ the Einstein equations are reduced to the Abel (ordinary…
We propose and investigate the modified Born$-$Infeld-type gravity model with the function $F(R) = [1-(1-\beta R/\sigma)^\sigma]/\beta$. At different values of the dimensionless parameter $\sigma$ the action is converted into some models…
In this paper we introduce a new public Einstein-Boltzmann solver, \texttt{MGCLASS II}, built as a modification to the publicly available \texttt{CLASS} code, that allows to obtain cosmological observables for Modified Gravity theories. It…
The cosmological constant term, $\Lambda$, in Einstein's equations has been for three decades a building block of the concordance or standard $\Lambda$CDM model of cosmology. Although the latter is not free of fundamental problems, it…
We consider the Einstein-dust equations with positive cosmological constant $\lambda$ on manifolds with time slices diffeomorphic to an orientable, compact 3-manifold $S$. It is shown that the set of standard Cauchy data for the…
We derive the effects of a non-zero cosmological constant $\Lambda$ on gravitational wave propagation in the linearized approximation of general relativity. In this approximation we consider the situation where the metric can be written as…