Related papers: The Generic Expansion in Analytic Modified Gravity
In this paper we examine gravitational radiation in higher order non-local gravity described by the non-local gravitational Lagrangian density $\mathcal{L}_{g}=R+\sum_{h=1}^{n}a_{h}R\Box^{-h}R$. This non-local theory of gravitation always…
The effects implied for the structure of compact objects by the modification of General Relativity produced by the generalization of the Lagrangian density to the form f(R)=R+\alpha R^2, where R is the Ricci curvature scalar, have been…
The Einstein theory of general relativity provides a peculiar example of classical field theory ruled by non-linear partial differential equations. A number of supplementary conditions (more frequently called gauge conditions) have also…
Alternative theories of gravity have been recently studied in connection with their cosmological applications, both in the Palatini and in the metric formalism. The aim of this paper is to propose a theoretical framework (in the Palatini…
The non-linear evolution of one-dimensional perturbations in a three-dimensional expanding Universe is considered. A general Lagrangian scheme is derived, and compared to two previously introduced approximate models. These models are…
This work presents the foundations of Singular Semi-Riemannian Geometry and Singular General Relativity, based on the author's research. An extension of differential geometry and of Einstein's equation to singularities is reported.…
A method for finding the renormalization group (RG) improved effective Lagrangian for a massive interacting field theory in curved spacetime is presented. As a particular example, the $\lambda \varphi^4$-theory is considered and the RG…
The purpose of this article is to draw attention to some fundamental issues in General Relativity. It is argued that these deep issues cannot be resolved within the standard approach to general relativity that considers {\em every} solution…
We study the degrees of freedom in New General Relativity -- flat and metric compatible family of theories -- around the Minkowski background in a gauge invariant manner. First, we confirm the decoupling case, in which the theory reduces to…
Exact solutions of an $ f(R) $-theory (of gravity) in a static central (gravitational) field have been studied in the literature quite well, but, to find and study exact solutions in the case of a non-static central field are not easy at…
Gravitational instability in classical Jeans theory, General Relativity, and modified gravity is considered. The background density increase leads to a faster growth of perturbations in comparison with the standard theory. The transition to…
General Relativity is usually formulated as a theory with gauge invariance under the diffeomorphism group, but there is a 'dilaton' formulation where it is in addition invariant under Weyl transformations, and a 'unimodular' formulation…
We study perturbations around some cosmological backgrounds in the dRGT theory of massive gravity. We develop a general formalism to calculate the perturbations around any background. We derive the Lagrangian for fluctuations in the small…
We introduce additional restriction into "general ether theory" - a generalization of Lorentz ether theory to gravity - which fixes the signs of the cosmological constants in this theory. This leads to an oscillating universe, thus, solves…
We consider perturbative modifications of the Friedmann equations in terms of energy density corresponding to modified theories of gravity proposed as an alternative route to comply with the observed accelerated expansion of the universe.…
Gravity is perturbatively renormalizable for the physical states which can be conveniently defined via foliation-based quantization. In recent sequels, one-loop analysis was explicitly carried out for Einstein-scalar and Einstein-Maxwell…
We address the gravitation and inertia in the framework of 'general gauge principle', which accounts for 'gravitation gauge group' generated by hidden local internal symmetry implemented on the flat space. We connect this group to nonlinear…
When Einstein's equations for an asymptotically flat, vacuum spacetime are reexpressed in terms of an appropriate conformal metric that is regular at (future) null infinity, they develop apparently singular terms in the associated conformal…
Einstein's General Relativity (GR) is a dynamical theory of the spacetime metric. We describe an approach in which GR becomes an SU(2) gauge theory. We start at the linearised level and show how a gauge theoretic Lagrangian for…
We present herewith certain thoughts on the important subject of nowadays physics, pertaining to the so-called ``singularities'', that emanated from looking at the theme in terms of ADG (: abstract differential geometry). Thus, according to…