Related papers: Quadratic Metric-Affine Gravity: Solving for the A…
We consider the most general Quadratic Metric-Affine Gravity setup in the presence of generic matter sources with non-vanishing hypermomentum. The gravitational action consists of all $17$ quadratic invariants (both parity even and odd) in…
This article presents a systematic way to solve for the Affine Connection in Metric-Affine Geometry. We start by adding to the Einstein-Hilbert action, a general action that is linear in the connection and its partial derivatives and…
We investigate the cosmological aspects of the most general parity preserving Metric-Affine Gravity theory quadratic in torsion and non-metricity in the presence of a cosmological hyperfluid. The equations of motion are obtained by varying…
A new geometric interpretation for General Relativity (GR) is proposed. We show that in the presence of an arbitrary affine connection, the gravitational field is described as nonmetricity of the affine connection. An affine connection can…
General Relativity (GR) exists in different formulations, which are equivalent in pure gravity. Once matter is included, however, observable predictions generically depend on the version of GR. In order to quantify the resulting ambiguity,…
We derive the generalized Gauss-Codazzi-Mainardi (GCM) equation for a general affine connection with torsion and non-metricity. Moreover, we show that the metric compatibility and torsionless condition of a connection on a manifold are…
In this article, we consider a special case of Metric-Affine f(R)-gravity for f(R) = R, i.e. the Metric-Affine General Relativity (MAGR). As a companion to the first article in the series, we perform the (3+1) decomposition to the…
We state and prove a simple Theorem that allows one to generate invariant quantities in Metric-Affine Geometry, under a given transformation of the affine connection. We start by a general functional of the metric and the connection and…
We extend the results of antecedent literature on quadratic Metric-Affine Gravity by studying a new quadratic gravity action in vacuum which, besides the usual (non-Riemannian) Einstein-Hilbert contribution, involves all the parity even…
We explore a new route toward a non-perturbative quantization of gravity based on a purely affine formulation, where the affine connection is the fundamental field and the metric, when it exists, emerges as a derived quantity. Starting from…
We extend the usual vacuum Metric-Affine $f(R)$ Gravity by supplementing it with all parity even quadratic invariants in torsion and non-metricity. As we show explicitly this supplementation drastically changes the status of the Theory…
Based on the distinction between the covariant and contravariant metric tensor components in the framework of the affine geometry approach and also on the choice of the contravariant components, it was shown that a wide variety of third,…
The intriguing choice to treat alternative theories of gravity by means of the Palatini approach, namely elevating the affine connection to the role of independent variable, contains the seed of some interesting (usually under-explored)…
We study a parity violating Metric-Affine gravitational theory given by the Einstein-Hilbert action plus the so-called Holst term in vacuum. We find out that for a certain value of the Barbero-Immirzi parameter the total action possesses a…
In Einstein's gravitational theory, the spacetime is Riemannian, that is, it has vanishing torsion and vanishing nonmetricity (covariant derivative of the metric). In the gauging of the general affine group ${A}(4,R)$ and of its subgroup…
We classify the metric-affine theories of gravitation, in which the metric and the connections are treated as independent variables, by use of several constraints on the connections. Assuming the Einstein-Hilbert action, we find that the…
Starting from an affinely connected space, we consider a model of gravity whose fundamental field is the connection. We build up the action using as sole premise the invariance under diffeomorphisms, and study the consequences of a…
This Thesis is devoted to the study of Metric-Affine Theories of Gravity and Applications to Cosmology. The thesis is organized as follows. In the first Chapter we define the various geometrical quantities that characterize a non-Riemannian…
The metric-affine variational principle is applied to generate teleparallel and symmetric teleparallel theories of gravity. From the latter is discovered an exceptional class which is consistent with a vanishing affine connection. Based on…
We construct new explicit vacuum solutions of quadratic metric-affine gravity. The approach of metric-affine gravity in using an independent affine connection produces a theory with 10+64 unknowns, which implies admitting torsion and…