Related papers: Characteristic Formulation for Metric $f(R)$ Gravi…
The geometric trinity of gravity offers a platform in which gravity can be formulated in three analogous approaches, namely curvature, torsion and nonmetricity. In this vein, general relativity can be expressed in three dynamically…
A general approach to viable modified $f(R)$ gravity is developed in both the Jordan and the Einstein frames. A class of exponential, realistic modified gravities is introduced and investigated with care. Special focus is made on step-class…
We show that the well-known problem of frame dependence and violation of local Lorentz invariance in the usual formulation of $f(T)$ gravity is a consequence of neglecting the role of spin connection. We re-formulate $f(T)$ gravity…
General properties of vacuum solutions of $f(R)$ gravity are obtained by the condition that the divergence of the Weyl tensor is zero and $f''\neq 0$. Specifically, a theorem states that the gradient of the curvature scalar, $\nabla R$, is…
It is widely believed that classical gravity breaks down and quantum gravity is needed to deal with a singularity. We show that there is a class of spacetime curvature singularities which can be resolved with metric and matter field…
The initial value problem of metric and Palatini f(R)gravity is studied by using the dynamical equivalence between these theories and Brans-Dicke gravity. The Cauchy problem is well-formulated for metric f(R)gravity in the presence of…
We derive the expression for the jerk parameter in $f(R)$ gravity. We use the Palatini variational principle and the field equations in the Einstein conformal gauge. For the particular case $f(R)=R-\frac{\alpha^2}{3R}$, the predicted value…
We investigate the linearized form of metric f(R)-gravity, assuming that f(R) is analytic about R = 0 so it may be expanded as f(R) = R + a_2 R^2/2 + ... . Gravitational radiation is modified, admitting an extra mode of oscillation, that of…
Faddeev formulation of general relativity (GR) is considered where the metric is composed of ten vector fields or a ten-dimensional tetrad. Upon partial use of the field equations, this theory results in the usual GR. Earlier we have…
This Thesis is devoted to the study of Metric-Affine Theories of Gravity and Applications to Cosmology. The thesis is organized as follows. In the first Chapter we define the various geometrical quantities that characterize a non-Riemannian…
The new model of modified $F(R)$ gravity theory with the function $F(R) = R+(a/\gamma) \arcsin(\gamma R)$ is suggested and investigated. Constant curvature solutions corresponding to the extremum of the effective potential are obtained. We…
The metric tensor field equations for the general quadratic curvature gravity in four spacetime dimensions are derived by making use of the algebra of the exterior forms defined on pseudo-Riemannian manifolds and the identities satisfied by…
We show that the relativistic gravity theory can offer a framework to formulate the non-relativistic effective field theory in a general coordinate invariant way. We focus on the parity violating case in 2+1 dimensions which is particularly…
In this paper we investigate spherically symmetric vacuum solutions of $f(R)$ gravity in a higher dimensional spacetime. With this objective we construct a system of non-linear differential equations, whose solutions depend on the explicit…
We review quantum gravity model building using the new formalism of `quantum Riemannian geometry' to construct this on finite discrete spaces and on fuzzy ones such as matrix algebras. The formalism starts with a `differential structure' as…
We study modified theories of gravity of the f(R) type in Palatini formalism. For a generic f(R) lagrangian, we show that the metric can be solved as the product of a scalar function times a rank-two tensor (or auxiliary metric). The scalar…
General Relativity (GR) exists in different formulations. They are equivalent in pure gravity but generically lead to distinct predictions once matter is included. After a brief overview of various versions of GR, we focus on metric-affine…
In the context of metric $f(R)$ gravity, the Geodesic Deviation Equation (GDE) was first studied in arXiv:1010.5279v3, giving a general expression and studying a particular case, the FLRW universe. In the paper arXiv:1312.2022v1 a similar…
The models of New General Relativity have recently got attention of research community, and there are some works studying their dynamical properties. The formal aspects of this investigation have been mostly restricted to the primary…
A variational principle is applied to 4D Euclidean space provided with a tensor refractive index, defining what can be seen as 4-dimensional optics (4DO). The geometry of such space is analysed, making no physical assumptions of any kind.…