Related papers: Revisiting the energy-momentum squared gravity
A unification of dark matter and dark energy based on a dynamical space time theory is suggested. By introducing a dynamical space time vector field $\chi_\mu$ as a Lagrange multiplier, a conservation of an energy momentum tensor…
Considerations on the complementary time-dependent coordinate transformations emboding Lorentz transformation (LT) show that the relativistic energy-momentum relationship, implicitly the relativistic mass and energy, do not depend on the…
We derive a generic identity which holds for the metric (i.e. variational) energy-momentum tensor under any field transformation in any generally covariant classical Lagrangian field theory. The identity determines the conditions under…
We present an extension of $f(T)$ gravity, allowing for a general coupling of the torsion scalar $T$ with the trace of the matter energy-momentum tensor $\mathcal{T}$. The resulting $f(T,\mathcal{T})$ theory is a new modified gravity, since…
We study the dynamical description of gravity, the appropriate definition of the scalar field energy-momentum tensor, and the interrelation between them in scalar-tensor theories of gravity. We show that the quantity which one would naively…
It is shown that the accelerated expansion of the universe in the framework of the relativistic theory of gravitation can be achieved by the introduction of the quintessential term in the energy-momentum tensor. The value of the minimum…
A generally covariant version of Erik Verlinde's emergent gravity model is proposed. The Lagrangian constructed here allows an improved interpretation of the underlying mechanism. It suggests that de-Sitter space is filled with a…
We present a novel theory of gravity, namely, an extension of symmetric teleparallel gravity. This is done by introducing a new class of theories where the nonmetricity $Q$ is coupled nonminimally to the matter Lagrangian. This nonminimal…
We reformulate the standard Lagrangian formalism to a reparameterisation invariant Lagrangian formalism by means of Finsler and Kawaguchi geometry. In our formalism, various types of symmetries that appears in theories of physics are…
In this work, we investigate the cosmological dynamics of the $f(R, \mathcal{L}_m)$ gravity framework with a particular focus on the contributions of the scalar field. Considering a functional form that includes linear and exponential…
We introduce the scalar and tensor modes of the gravitational perturbation in the presence of a scalar field which describes inflation. We investigate the back-reaction of the perturbations to the background by studying the effective…
In this paper, we discuss a gravitational theory based on the generalized gauge field. Our Lagrangian is invariant not only under local Lorentz transformation and the ordinary gauge transformation but also under a new gauge transformation.…
The theory of Gravitomagnetism and spinor quantum mechanics describing the interaction between the Dirac spinor field, the electromagnetic field, and a weak gravitational field is extended by including the Lagrangian density of the free…
In case of the Einstein's gravitation theory and its first order Palatini reformulation, the stress-energy-momentum of gravity has been proved to reduce to the Komar superpotential. We generalize this result to the affine-metric theory of…
We investigate whether the requirement of total energy-momentum conservation can act as a constraint on the family of admissible Lagrangian densities for an interaction field. The aim is not to give a mere field-theoretic derivation of…
We develop a cosmological model based on action-dependent Lagrangian theories. The main feature here is the nonconservation of the energy momentum tensor due to the nontrivial geometrical construction of the theory. We provide the basic set…
Quantum theory of the gravitation in the causal approach is studied up to the second order of perturbation theory. We prove gauge invariance and renormalizability in the second order of perturbation theory for the pure gravity system…
M\o ller's Tetrad Theory of Gravitation is examined with regard to the energy-momentum complex. The energy-momentum complex as well as the superpotential associated with M\o ller's theory are derived. M\o ller's field equations are solved…
In this paper, we explore a reconstruction scheme in the background of the $f(T,\mathcal{T})$ gravity theory for different cosmological scenarios, where $T$ is the scalar torsion and $\mathcal{T}$ is the trace of the energy-momentum tensor.…
Cosmological solutions for covariant canonical gauge theories of gravity are presented. The underlying covariant canonical transformation framework invokes a dynamical space-time Hamiltonian consisting of the Einstein-Hilbert term plus a…