Related papers: Macroscopic Einstein Equations for a Cosmological …
It seems likely that the generalized Einstein equations are not complete and only partly account for the effect on the Universe dynamics of that part of the energy of the space environment the change of which is purely geometric. There are…
The evolution equation of linear cosmic density perturbations in the realm of Einstein-Cartan theory of gravity is obtained.The de Sitter metric fluctuation is computed in terms of the spin-torsion background density.
We introduce a proposal to modify Einstein's equations by embedding them in a larger symmetric hyperbolic system. The additional dynamical variables of the modified system are essentially first integrals of the original constraints. The…
A broad class of generalized Einstein's gravity can be cast into Einstein's gravity with a minimally coupled scalar field using suitable conformal rescaling of the metric. Using this conformal equivalence between the theories, we derive the…
We present an exact analytical solution of the Einstein equations with cosmological constant in a spatially flat Robertson-Walker metric. This is interpreted as an isotropic Lemaitre-type version of the cosmological Friedmann model.…
A general covariant extension of Einstein\'{}s field equations is considered with a view to Numerical Relativity applications. The basic variables are taken to be the metric tensor and an additional four-vector $Z_\mu$. Einstein's solutions…
$f(R)$-Gravity, a simple generalization of Einstein's General theory of Relativity has been considered in the context of Cosmology as one of the approaches to explain phenomena such as early-time inflation and late-time accelerated…
One of the greatest problems of standard cosmology is the Big Bang singularity. Previously it has been shown that non-local ghostfree higher-derivative modifications of Einstein gravity in the ultra-violet regime can admit non-singular…
We present a cosmological model arising from a gravitational theory with an infinite tower of higher-order curvature invariants that can reproduce the entire evolution of the Universe: from inflation to late-time acceleration, without…
Self-consistent account of the most simple non-gauge vector fields leads to a broad spectrum of regular scenarios of temporal evolution of the Universe completely within the frames of the Einstein's General relativity. The longitudinal…
We perform large-scale cosmological simulations that solve Einstein's equations directly via numerical relativity. Starting with initial conditions sampled from the cosmic microwave background, we track the emergence of a cosmic web without…
We have studied the evolution of the Universe in the generalized Einstein action of the form $R+\beta R^2$, where $R$ is the scalar curvature and $\beta=\rm const.$. We have found exact cosmological solutions that predict the present cosmic…
The exact solution of a two-scale Buchert average of the Einstein equations is derived for an inhomogeneous universe which represents a close approximation to the observed universe. The two scales represent voids, and the bubble walls…
On the basis of qualitative theory of differential equations it is shown that dynamic system based on the system of Einstein - Klein - Gordon equations with regard to Friedman Universe has a stable center corresponding to zero values of…
A formalism for analyzing the complete set of field equations describing Macroscopic Gravity is presented. Using this formalism, a cosmological solution to the Macroscopic Gravity equations is determined. It is found that if a particular…
The theory of cosmological perturbations is extended to spacetimes displaying isotropic expansion but anisotropic curvature. The perturbed Einstein equation and Boltzmann equations for massless and massive particles are derived in a general…
The dynamics of the expanding universe is analyzed in terms of the quantum geometrodynamical model. It is shown that the equations of quantum theory in the form of the eigenvalues equation similar to the stationary Schr\"{o}dinger equation…
A new technique is presented for modifying the Einstein evolution equations off the constraint hypersurface. With this approach the evolution equations for the constraints can be specified freely. The equations of motion for the…
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…
We investigate a simple variation of the Generalized Harmonic method for evolving the Einstein equations. A flat space wave equation for metric perturbations is separated from the Ricci tensor, with the rest of the Ricci tensor becoming a…