Related papers: Einstein flow with matter sources: stability and c…
Owing to the quadratic nature of the theory, Einstein-Gauss-Bonnet gravity generically permits two distinct vacuum solutions. One solution (the "Einstein" vacuum) has a well defined limit as the Gauss-Bonnet coupling goes to zero, whereas…
We study the dynamics of homogeneous isotropic FRW cosmologies with positive spatial curvature in $f(R)$-gravity, paying special attention to the existence of Einstein static models and only study forms of $f(R)=R^n$ for which these static…
The idea that the vacuum energy density $\rho_{\Lambda}$ could be time dependent is a most reasonable one in the expanding Universe; in fact, much more reasonable than just a rigid cosmological constant for the entire cosmic history. Being…
In this note, we show that a nontrivial, compact, degenerate or nondegenerate, gradient Einstein-type manifold of constant scalar curvature is isometric to the standard sphere with a well defined potential function. Moreover, under some…
We study the linearization stability of the Einstein constraint equations on an asymptotically hyperbolic manifold. In particular we prove that these equations are linearization stable in the neighborhood of vacuum solutions for a…
Based upon the intrinsic symmetries approach to inhomogeneous cosmologies, we propose an exact solution to Einstein's field equations where the spatial sections are flat and the source is a non-perfect fluid such that the dissipative terms…
We compute non-perturbative flow equations for the couplings of quantum gravity in fourth order of a derivative expansion. The gauge invariant functional flow equation for arbitrary metrics allows us to extract $\beta$-functions for all…
The special conformal transformation (composed by inversion - translation - inversion) is used to generate a time dependent conformally flat spacetime. In order to be an exact solution of Einstein's equations, we need as a source a stress…
The usual derivation of Einstein's field equations from the Einstein--Hilbert action is performed by silently assuming the metric tensor's symmetric character. If this symmetry is not assumed, the result is a new theory, such as Einstein's…
In the field equations of Einstein-Cartan theory with cosmological constant a static spherically symmetric perfect fluid with spin density satisfying the Weyssenhoff restriction is considered. This serves as a rough model of space filled…
We derive the Boltzmann equation in the context of a gravity theory with non-minimal coupling between matter and curvature. We show that as the energy-momentum tensor is not conserved in these theories, it follows a condition on the…
Various classification schemes exist for homogeneous and isotropic (CP) world models, which include pressureless matter (so-called dust) and Einstein's cosmological constant Lambda. We here classify the solutions of more general world…
We show that the spatially homogeneous Boltzmann equation evolves as the gradient flow of the entropy with respect to a suitable geometry on the space of probability measures which takes the collision process into account. This gradient…
The idea that the cosmological term, Lambda, should be a time dependent quantity in cosmology is a most natural one. It is difficult to conceive an expanding universe with a strictly constant vacuum energy density, namely one that has…
The existence of a simple spherically symmetric and static solution of the Einstein equations in the presence of a cosmological constant vanishing outside a definite value of the radial distance is investigated. A particular succession of…
The origin of negative pressure fluid (the dark energy) is investigated in the quantum model of the homogeneous, isotropic and closed universe filled with a uniform scalar field and a perfect fluid which defines a reference frame. The…
We present the classical solutions to the Einstein field equations derived using the WKB-like and Hamilton procedures. The investigation is carried out in the commutative and noncommutative scenario for the Bianchi type I cosmological model…
We show that derivation of Friedmann's equations from the Einstein-Hilbert action, paying attention to the requirements of isotropy and homogeneity during the variation, leads to a different interpretation of pressure than what is typically…
A linear relationship between the Hubble expansion parameter and the time derivative of the scalar field is assumed in order to derive exact analytic cosmological solutions to Einstein's gravity with two fluids: a barotropic perfect fluid…
An additional variation of the Einstein-Hilbert action with respect to the Planck mass provides a constraint on the average Ricci scalar that prevents vacuum energy from gravitating. Consideration of the evolution of the inhomogeneous…