Related papers: Variational approach to gravitational theories wit…
A recently proposed variational approach for general relativity where, in addition to the metric tensor, two independent affine connections enter the action as dynamical variables, is revised. Field equations always reduce to the Einstein…
A generalization of General Relativity is studied. The standard Einstein-Hilbert action is considered in the Palatini formalism, where the connection and the metric are independent variables, and the connection is not symmetric. As a result…
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…
A variational principle was recently suggested by Goenner, where an independent metric generates the spacetime connection. It is pointed out here that the resulting theory is equivalent to the usual Palatini theory. However, a bimetric…
It is well known that the Einstein-Hilbert action in two dimensions is topological and yields an identically vanishing Einstein tensor. Consequently one is faced with difficulties when formulating a non-trivial gravity model. We present a…
The starting point of this work is the original Einstein action, sometimes called the Gamma squared action. Continuing from our previous results, we study various modified theories of gravity following the Palatini approach. The metric and…
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)…
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…
In this paper, the hybrid metric-Palatini gravity is an approach to modified gravity in which is added to the usual Einstein-Hilbert action a supplementary term containing a Palatini-type correction of the form $f({\cal R},T)$. Here, ${\cal…
Metric-affine theories of gravity provide an interesting alternative to General Relativity: in such an approach, the metric and the affine (not necessarily symmetric) connection are independent quantities. Furthermore, the action should…
By applying Schwinger's variational principle to the Einstein$-$Cartan action for the gravitational field, we derive quantum commutation relations between the metric and torsion tensors.
Independent variation of the metric and connection in the Einstein-Hilbert action, called the Palatini variation, is generally taken to be equivalent to the usual formulation of general relativity in which only the metric is varied.…
The way one chooses to couple gravity to matter is an essential characteristic of any gravitational theory. In theories where the gravitational field is allowed to have more degrees of freedom than those of General Relativity (e.g.…
A covariant reformulation of General Relativity is briefly considered from three points of view: geometrodynamics, Lagrange-Euler field theory, and gauge field theory. From a geometrodynamics perspective, a definition of the reference frame…
It is known that in f(R) theories of gravity with an independent connection which can be both non-metric and non symmetric, this connection can always be algebraically eliminated in favour of the metric and the matter fields, so long as it…
We consider the cosmology of the Ricci-tensor-squared gravity in the Palatini variational approach. The gravitational action of standard general relativity is modified by adding a function f(R^abR_ab) to the Einstein-Hilbert action, and the…
I propose an alternative $f(R)$ theory of gravity constructed by applying the function $f$ directly to the Ricci tensor instead of the Ricci scalar. The main goal of this study is to derive the resulting modified Einstein equations for the…
In the Palatini action of general relativity the connection and the metric are treated as independent dynamical variables. Instead of assuming a relation between these quantities, the desired relation between them is derived through the…
A modified gravitational action is considered which involves the quantity $F_{\mu\nu}=\partial_{\mu}\Gamma_{\nu}-\partial_{\nu}\Gamma_{\mu}$, where $\Gamma_{\mu}=\Gamma^{\alpha}_{\mu\alpha}$. Since $\Gamma_{\mu}$ transforms like a U(1)…
Recently a class of alternative theories of gravity which goes under the name f(R) gravity, has received considerable attention, mainly due to its interesting applications in cosmology. However, the phenomenology of such theories is not…