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The main objective of this article is to derive a new set of gravitational field equations and to establish a new unified theory for dark energy and dark matter. The new gravitational field equations with scalar potential $\varphi$ are…
If we want to explain the recently discovered accelerated stage of the universe, one of the option we have is to modify the Einstein tensor. The simplest such modification, in agreement with all observations, is the positive cosmological…
It is well known that, making the Abelian projection of Einstein's theory one can obtain the restricted gravity which is simpler than Einstein's theory but describes the core dynamics of Einstein's gravity. In this paper we present the…
The propagation of gravitational waves (GWs) at cosmological distances offers a new way to test the gravitational interaction at the largest scales. Many modified theories of gravity, usually introduced to explain the observed acceleration…
We demonstrate that any scaling source in the radiation era produces a background of gravitational waves with an exact scale-invariant power spectrum. Cosmic defects, created after a phase transition in the early Universe, are such a…
We investigate the idea that current cosmic acceleration could be the consequence of gravitational leakage into extra dimensions on cosmological scales rather than the result of a non-zero cosmological constant, and consider the ability of…
We present a new mechanism for addressing the cosmological constant problem based on global constraints arising from a lapse function in a higher-dimensional gravitational theory. Inspired by Horava-Lifshitz gravity, we consider a 5d…
We construct a generalized massive gravity by combining quadratic curvature gravity with the Chern-Simons term in four dimensions. This may be a candidate for the parity-odd tricritical gravity theory. Considering the AdS$_4$ vacuum…
We have recently proposed a new action principle for combining Einstein equations and the Dirac equation for a point mass. We used a length scale $L_{CS}$, dubbed the Compton-Schwarzschild length, to which the Compton wavelength and…
We investigate the problem of metric fluctuations in the presence of the vacuum fluctuations of matter fields and critically assess the usual assertion that vacuum energy implies a Planckian cosmological constant. A new stochastic classical…
Gravitational waves (GWs) emitted by binary sources are interesting signals for testing gravity on cosmological scales since they allow measurements of the luminosity distance. When followed by electromagnetic counterparts, in particular,…
The interaction of a gravitational wave (GW) with an elastic body is usually described in terms of a GW "force" driving the oscillations of the body's normal modes. However, this description is only possible for GW frequencies for which the…
We discuss the detectability of gravitational waves with a time dependent mass contribution, by means of the stochastic gravitational wave observations. Such a mass term typically arises in the cosmological solutions of massive gravity…
The dynamics of a gravitational wave propagating through a cosmic gauge field are dramatically different than in vacuum. We show that a gravitational wave acquires an effective mass, is birefringent, and its normal modes are a linear…
We consider the Einstein-Hilbert action without cosmological constant in 5-dimensions and implement the Kaluza-Klein (KK) reduction by compactifying the fifth direction on a circle of small but finite radius. For non-zero compactification…
The 5D Cosmological General Relativity theory developed by Carmeli reproduces all of the results that have been successfully tested for Einstein's 4D theory. However the Carmeli theory because of its fifth dimension, the velocity of the…
Gravitational Wave (GW) data bring an exceptional avenue to test the underlying models of coalescing compact objects. In the regime of strong gravity and high curvature, they allow the exploration of minute deviations from the best-fit…
In the weak field approximation the gravitational wave is approximated as a linear wave, which ignores the nonlinear effect. In this paper, we present an exact general solution of the cylindrical gravitational wave. The exact solution of…
The existence of gravitational radiation is a natural prediction of any relativistic description of the gravitational interaction. In this chapter, we focus on gravitational waves, as predicted by Einstein's general theory of relativity.…
A Poincar\'{e} gauge theory of (2+1)-dimensional gravity is developed. Fundamental gravitational field variables are dreibein fields and Lorentz gauge potentials, and the theory is underlain with the Riemann-Cartan space-time. The most…