Related papers: Friedmann's Equations in All Dimensions and Chebys…
So far, the standard attitude to solve the Friedmann equations in the simultaneous presence of radiation $R$, matter $M$ and cosmological constant ${\Lambda}$ is to find solutions $R_R (t)$, $R_M (t)$ and $R_{\Lambda} (t)$ separately for…
In five dimensional cosmological models, the convention is to include the fifth dimension in a way similar to the other space dimensions. In this work we attempt to introduce the fifth dimension in a way that a time dimension would be…
An explicit and complete set of constants of the motion are constructed algorithmically for Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) models consisting of an arbitrary number of non-interacting species. The inheritance of constants of…
We test the Yilmaz theory of gravitation by working out the corresponding Friedmann-type equations generated by assuming the Friedmann-Robertson-Walker cosmological metrics. In the case that space is flat the theory is consistent only with…
Strong field (exact) solutions of the gravitational field equations of General Relativity in the presence of a Cosmological Constant are investigated. In particular, a full exact solution is derived within the inhomogeneous Szekeres-Szafron…
We provide a detailed description for power--law scaling Friedmann-Robertson-Walker cosmological scenarios dominated by two interacting perfect fluid components during the expansion. As a consequence of the mutual interaction between the…
We formulate Friedmann's equations as second-order linear differential equations. This is done using techniques related to the Schwarzian derivative that selects the $\beta$-times $t_\beta:=\int^t a^{-2\beta}$, where $a$ is the scale…
In this paper we performed investigation of the spatially-flat cosmological models whose spatial section is product of three- ("our Universe") and extra-dimensional parts. The matter source chosen to be the perfect fluid which exists in the…
We systematically study the evolution of the Friedmann-Robertson-Walker (FRW) universe coupled with a cosmological constant $\Lambda$ and a perfect fluid that has the equation of state $p=w\rho$, where $p$ and $\rho$ denote, respectively,…
Solutions to flat space Friedmann-Robertson-Walker cosmologies in Brans-Dicke theory with a cosmological constant are investigated. The matter is modelled as a $\gamma$-law perfect fluid. The field equations are reduced from fourth order to…
Geometry of the universe has always intrigued mathematicians and cosmologists. Recent results from the Wilkinson Microwave Anisotropy Project (WMAP) indicate that the visible universe is incredibly flat. This apparent flatness could be due…
Here we prove a global existence theorem for sufficiently small however fully nonlinear perturbations of a family of background solutions of the $`n+1$' vacuum Einstein equations in the presence of a positive cosmological constant…
We show that any solution of the 4D Einstein equations of general relativity in vacuum with a cosmological constant may be embedded in a solution of the 5D Ricci-flat equations with an effective 4D cosmological "constant" that is a specific…
There are many ways of embedding a 4D spacetime in a given higher-dimensional manifold while, satisfying the field equations. In this work we extend and generalize a recent paper by Mashhoon and Wesson ({\it Gen. Rel. Gravit.} {\bf 39},…
We present a numerical framework to study the cosmological background evolution in $f(R)$ gravity by employing a \textit{spectral Chebyshev collocation approach}. Unlike standard integration methods such as Runge--Kutta that often encounter…
We investigate exact and analytic solutions in $f\left( T\right) $ gravity within the context of a Friedmann--Lema\^{\i}tre--Robertson--Walker background space with nonzero spatial curvature. For the power law theory $f\left( T\right)…
Multidimensional cosmological models in the presence of a bare cosmological constant and a perfect fluid are investigated under dimensional reduction to 4-dimensional effective models. Stable compactification of the internal spaces is…
We extend the fully non-linear and exact cosmological perturbation equations in a Friedmann background universe to include the background curvature. The perturbation equations are presented in a gauge ready form, so any temporal gauge…
We extend various recent results regarding the derivation of effective cosmological Friedmann equations from the dynamics of group field theory (GFT). Restricting ourselves to a single GFT field mode (or fixed values of Peter-Weyl…
We review analytical solutions of the Einstein equations which are expressed in terms of elementary functions and describe Friedmann-Lema\^itre-Robertson-Walker universes sourced by multiple (real or effective) perfect fluids with constant…