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The Maxwell extension of the conformal algebra is presented. With the help of gauging the Maxwell-conformal group, a conformally invariant theory of gravity is constructed. In contrast to the conventional conformally invariant actions, our…
f(Lovelock) gravities are simple generalizations of the usual f(R) and Lovelock theories in which the gravitational action depends on some arbitrary function of the corresponding dimensionally-extended Euler densities. In this paper we…
In this work we explore the dynamics of the generalized hybrid metric-Palatini theory of gravity in the weak-field, slow-motion regime. We start by introducing the equivalent scalar-tensor representation of the theory, which contains two…
We put forward the idea that in addition to diffeomorphism invariance of general relativity (GR) the gravitational interaction is invariant under arbitrary scale-deformations of the metric field. In addition, we assume that the scaling…
General static solutions of effectively 2-dimensional Einstein-Dilaton-Maxwell-Scalar theories are obtained. Our model action includes a class of 2-d dilaton gravity theories coupled with a $U(1)$ gauge field and a massless scalar field.…
We naturally extend the theory of gravity with a conformally coupled scalar field by only requiring conformal invariance of the scalar field equation of motion and not of the action. The classically extended theory incorporates a…
We discuss two aspects of f(R) theories of gravity in metric formalism. We first study the reasons to introduce a scalar-tensor representation for these theories and the behavior of this representation in the limit to General Relativity,…
The correspondence of single-field cosmological models based on Einstein gravity to modern observational data is considered. A method is proposed to determine possible types of dynamics based on extreme values of the scalar field. It is…
Recent progress in the quantization of nonrenormalizable scalar fields has found that a suitable non-classical modification of the ground state wave function leads to a result that eliminates term-by-term divergences that arise in a…
The dynamics of any spherical cosmology with a scalar field (`scalaron') coupling to gravity is described by the nonlinear second-order differential equations for two metric functions and the scalaron depending on the `time' parameter. The…
We construct a gauge theory based on general nonlinear Lie algebras. The generic form of `dilaton' gravity is derived from nonlinear Poincar{\' e} algebra, which exhibits a gauge-theoretical origin of the non-geometric scalar field in…
We study some aspects of classical & quantum cosmology in the context of two-dimensionsal dilaton gravity theories with matter being described by a perfect fluid. We derive the classical equations obeyed by the metric function & the dilaton…
The main aim of this thesis is to reveal some interesting aspects of the purely affine theory of gravity and its cosmological implication. A particular attention will be devoted to its consequences when applied to cosmological inflation.…
We present a novel equivalence between scale-dependent gravity and scalar-tensor theories that have only a single scalar field with a canonical kinetic term in the Einstein frame and a conformal coupling to the metric tensor. In particular,…
When constructing general relativity (GR), Einstein required 4D general covariance. In contrast, we derive GR (in the compact, without boundary case) as a theory of evolving 3-dimensional conformal Riemannian geometries obtained by imposing…
We establish a well-posedness theory for the f(R) theory of modified gravity, which is a generalization of Einstein's theory of gravitation. The scalar curvature R of the spacetime, which arises in the integrand of the Einstein-Hilbert…
We consider a novel class of $f(\R)$ gravity theories where the connection is related to the conformally scaled metric $\hat g_{\mu\nu}=C(\R)g_{\mu\nu}$ with a scaling that depends on the scalar curvature $\R$ only. We call them C-theories…
We give an overview on the status and on the perspectives of Finsler gravity, beginning with a discussion of various motivations for considering a Finslerian modification of General Relativity. The subjects covered include Finslerian…
Modified gravity theories often contain a scalar field of gravitational strength which interacts with matter. We examine constraints on the range and the coupling strength of a scalar gravitational degree of freedom using a subset of…
We consider a scale invariant model which includes a $R^{2}$ term in action and show that a stable "emerging universe" scenario is possible. The model belongs to the general class of theories, where an integration measure independent of the…