Related papers: "Gauge" freedom and relationship between the Einst…
We show that the action of Einstein's gravity with a scalar field coupled in a generic way to spacetime curvature is invariant under a particular set of conformal transformations. These transformations relate dual theories for which the…
In this paper, we examine stacky structures in Einstein's theory of gravity. In brief, we first give a construction of the moduli stack of solutions to (vacuum) Einstein field equations on $n$-dimensional spacetimes, with vanishing…
A discussion is given of the conformal Einstein field equations coupled with matter whose energy-momentum tensor is trace-free. These resulting equations are expressed in terms of a generic Weyl connection. The article shows how in the…
We consider the relation between exact solutions of cosmological models having minimally and non-minimally coupled scalar fields. This is done for a particular class of solvable models which, in the Einstein frame, have potentials depending…
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…
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,…
Solutions of the field equations of theories of gravity which admit distinct conformal frame representations can look very different in these frames. We show that Brans class IV solutions describe wormholes in the Jordan frame (in a certain…
Here we follow the mainstream of thinking about physical equivalence of different representations of a theory, regarded as the consequence of invariance of the laws of physics -- represented by an action principle and the derived motion…
Beginning with the self-dual two-forms approach to the Einstein equations, we show how, by choosing basis spinors which are proportional to solutions of the Dirac equation, we may rewrite the vacuum Einstein equations in terms of a set of…
We present a formalism to study screening mechanisms in modified theories of gravity via perturbative methods in different cosmological scenarios. We consider Einstein frame posed theories that are recast as Jordan frame theories, where a…
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…
Using conformal invariance of gravitational waves, we show that for a luminal modified gravity theory, the gravitational-wave propagation and luminosity distance are the same as in general relativity. The relation between the…
We investigate stability of the Einstein static universe against the scalar, vector and tensor perturbations in the context of induced matter brane gravity. It is shown that in the framework of this model, the Einstein static universe has a…
We compare Einstein-Boltzmann solvers that include modifications to General Relativity and find that, for a wide range of models and parameters, they agree to a high level of precision. We look at three general purpose codes that primarily…
In this paper we consider conformal symmetry in the context of manifolds with general affine connection. We extend the conformal transformation law of the metric to a general metric compatible affine connection, and find that it is a…
I discuss how one can apply the covariant formalism developed by Vilkovisky and DeWitt to obtain frame invariant fifth force calculations for scalar-tensor theories. Fifth forces are severely constrained by astrophysical measurements. It…
Here we discuss a topic that comes up more often than expected: A same theory or theoretical model arises in two different presentations which are assumed to be actually different theories so that these are independently developed.…
A formulation of Einstein equations is presented that could yield advantages in the study of collisions of binary compact objects during regimes between linear-nonlinear transitions. The key idea behind this formulation is a separation of…
General relativity (GR) as described in terms of curvature by the Einstein-Hilbert action is dynamically equivalent to theories of gravity formulated in terms of spacetime torsion or non-metricity. This forms what is called the geometrical…
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…