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The emergent scenario provides a possible way to avoid the big bang singularity by assuming that the universe originates from an Einstein static state. Therefore, an Einstein static universe stable under perturbations is crucial to a…
Modifications to gravity that add additional functions of the Ricci curvature to the Einstein-Hilbert action -- collectively known as $f(R)$ theories -- have been studied in great detail. When considered as complete theories of gravity they…
The hypothesis that gravitational self-binding energy may be the source for the vacuum energy term of cosmology is studied in a Newtonian Ansatz. For spherical spaces the attractive force of gravitation and the negative pressure of the…
We investigate the Einstein static universe (ESU) and the emergent universe scenario in the framework of Ho\v{r}ava-Lifshitz-like $F(R)$ gravity. We first perform a dynamical analysis in the phase space, and amongst others we show that a…
One resolution of the ancient cosmic singularity, i.e., the Big Bang Singularity (BBS), is to assume an inflationary stage preceded by a long enough static state in which the universe and its physical properties would oscillate around…
Scalar tensor theories of gravity can be formulated in the Einstein or in the Jordan frame, which are related by the conformal transformations. Although the two frames are describe the same physics, and are equivalent, the stability of the…
We investigate the stability of the Einstein static universe as a non-LRS Bianchi type IX solution of the Einstein equations in the presence of both non-tilted and tilted fluids. We find that the static universe is unstable to homogeneous…
We analyze the stability of the Einstein static universe in scalar-tensor theory of gravity, and find it can be stable against both scalar and tensor perturbations under certain conditions. By assuming the emergent scenario originating from…
We study the cosmological evolution of an induced gravity model with a self-interacting scalar field $\sigma$ and in the presence of matter and radiation. Such model leads to Einstein Gravity plus a cosmological constant as a stable…
We construct explicitly deformations of Einstein's theory of gravity that are consistent and phenomenologically viable since they respect, in particular, cosmological backgrounds. We show that these deformations have unique symmetries in…
We consider the model of modified gravity with dynamical torsion. This model was found to have promising stability properties about various backgrounds. The model admits a self-accelerating solution. We have shown previously that if the…
We derive here the metric for Einstein's static universe (ESU) directly from Einstein equation, i.e., by considering both $G_{ik}$ and $T_{ik}$. We find that in order that the fluid pressure and acceleration are {\em uniform} and finite…
We consider the classical linear stability of a static universe filled with a non-interacting mixture of isotropic radiation and a ghost scalar field. Unlike the conventional Einstein static model, this cosmology is stable against…
In recent years, a number of alternative theories of gravity have been proposed as possible resolutions of certain cosmological problems or as toy models for possible but heretofore unobserved effects. However, the implications of such…
Conditions for the existence and stability of de Sitter space in modified gravity are derived by considering inhomogeneous perturbations in a gauge-invariant formalism. The stability condition coincides with the corresponding condition for…
We investigate the stability and gravitational waves (GWs) in the four-dimensional general Einstein-vector theory in a cosmological background. The theory accommodates up to six propagating degrees of freedom, comprising two tensor, two…
We study self-consistent static solutions for an Einstein universe in a graph-based induced gravity. In the generalization of the deconstruction model based on the graph, the eigenvalues of the graph Laplacian and the adjacent matrix gives…
We discuss the possibility of obtaining the present acceleration of the universe via f(R) gravity theories which recently attracted much attention. It is known that f(R) theories generally have room for this. In this work we stress that the…
Along the general framework of the gauge invariant perturbation theory developed in the papers [K. Nakamura, Prog. Theor. Phys. {\bf 110} (2003), 723; {\it ibid}, {\bf 113} (2005), 481.], we formulate the second order gauge invariant…
The theory of gravity with a quadratic contribution of scalar curvature is investigated using a dynamical systems approach. The simplest Friedmann--Robertson--Walker metric is employed to formulate the dynamics in both the Jordan frame and…