Related papers: Correspondence between Jordan-Einstein frames and …
We examine the conformal equivalence between the $f(R)$ gravity and the interacting dark sector model. We review the well-known result that the conformal transformation physically corresponds to the mass dilation which marks the strength of…
Jordan and Einstein frame are studied under the light of Hamiltonian formalism. Dirac's constraint theory for Hamiltonian systems is applied to Brans-Dicke theory in the Jordan Frame. In both Jordan and Einstein frame, Brans-Dicke theory…
A general framework of the novel matter coupling in the Einstein gravity is introduced. We firstly prove that a class of theories whose Hamiltonian constraint is given by an arbitrary function $f(H_g)$, where $H_g$ is the Hamiltonian…
The Hamiltonian description of classical gauge theories is a well studied subject. The two best known approaches, namely the covariant and canonical Hamiltonian formalisms have received a lot of attention in the literature. However, in our…
We extend the idea of unimodular gravity to the modified $f(R,T)$ theories. A new class of cosmological solutions, that the unimodular constraint on the metric imposes on the $f(R,T)$ theories, are studied. This extension is done in both…
Our conventional system of physical units is based on local or microscopic {\it dimensional} quantities which are {\it defined}, for convenience or otherwise aesthetic reasons, to be spacetime-independent. A more general choice of units may…
$[n+1]$-dimensional ($n\geq 3$) smooth Einsteinian spaces of Euclidean and Lorentzian signature are considered. The base manifold $M$ is supposed to be smoothly foliated by a two-parameter family of codimension-two-surfaces which are…
Scalar-tensor theories of gravity are considered to be competitors to Einstein's theory of general relativity for the description of classical gravity, as they are used to build feasible models for cosmic inflation. These theories can be…
We derive the field equations and the equations of motion for massive test particles in modified theories of gravity with an arbitrary coupling between geometry and matter by using the Palatini formalism. We show that the independent…
In a Palatini $f(\mathcal{R})$-model, we define chonodynamical effects due to the choice of atomic clocks as standard reference clocks and we develop a formalism able to quantitatively separate them from the usual effective dark sources one…
We show the exact equality of the path integral of the general renormalizable fourth order gravitational action to the path integral of the Einstein action coupled to a massive spin-0 field and a massive spin-2 ghost-like field with…
We revisit the dynamical equivalence between different representations of vacuum modified gravity models in view of Legendre transformations. The equivalence is discussed for both bulk and boundary space, by including in our analysis the…
We intend to clarify the interplay between boundary terms and conformal transformations in scalar-tensor theories of gravity. We first consider the action for pure gravity in five dimensions and show that, on compactifing a la Kaluza-Klein…
With a scalar field non-minimally coupled to curvature, the underlying geometry and variational principle of gravity - metric or Palatini - becomes important and makes a difference, as the field dynamics and observational predictions…
We investigate cosmological perturbations of scalar-tensor theories in Palatini formalism. First we introduce an action where the Ricci scalar is conformally coupled to a function of a scalar field and its kinetic term and there is also a…
Current generalizations of the classical Einstein-Hilbert Lagrangian formulation of General Relativity are reviewed. Some alternative variational principles are known to reproduce Einstein's gravitational equations, and should therefore be…
One version of the principle of equivalence, as originally formulated by Einstein, states that ``gravity" can be mimicked locally by going to an ``accelerated frame of reference". As highlighted by Synge, the physical content of this…
We study the evolution of linear perturbations in metric f(R) models of gravity and identify a potentially observable characteristic scale-dependent pattern in the behavior of cosmological structures. While at the background level viable…
We analyze Born-Infeld inspired gravity in Palatini formulation in the framework of covariant canonical formalism. We determine covariant Hamiltonian and corresponding equations of motion.
We investigate static spherically symmetric solutions in the Palatini kinetically coupled scalar-tensor theory, which reduces to gravity minimally coupled to a scalar field in Einstein frame. Using the fact that the Jordan and Einstein…