Related papers: Unified formalism for Palatini gravity
A variational principle is suggested within Riemannnian geometry, in which an auxiliary metric and the Levi Civita connection are varied independently. The auxiliary metric plays the role of a Lagrange multiplier and introduces non-minimal…
We consider a novel class of $f(\R)$ gravity theories where the connection is related to the conformally scaled metric $\hat g_{\mu\nu}=C(\R)g_{\mu\nu}$ with a scaling that depends on the scalar curvature $\R$ only. We call them C-theories…
After reviewing the Lagrangian-Hamiltonian unified formalism (i.e, the Skinner-Rusk formalism) for higher-order (non-autonomous) dynamical systems, we state a unified geometrical version of the Variational Principles which allows us to…
We derive the dynamical equations for a non-local gravity model in the Palatini formalism and we discuss some of the properties of this model. We have shown that, in some specific cases, the vacuum solutions of general relativity are also…
Spacetime geometry is described by two -- {\em a priori} independent -- geometric structures: the symmetric connection $\Gamma$ and the metric tensor $g$. Metricity condition of $\Gamma$ (i.e. $\nabla g = 0$) is implied by the Palatini…
I review recent results obtained for extensions of general relativity formulated within the Palatini formalism, an approach in which metric and connection are treated as independent geometrical entities. The peculiar dynamics of these…
The well-formulation and the well-posedness of the Cauchy problem is discussed for {\it hybrid metric-Palatini gravity}, a recently proposed modified gravitational theory consisting of adding to the Einstein-Hilbert Lagrangian an $f(R)$…
Within the framework of the path-integral formalism we reinvestigate the different methods of removing the unphysical degrees of freedom from spontanously broken gauge theories. These are: construction of the unitary gauge by gauge fixing;…
A new systematic approach extending the notion of frames to the Palatini scalar-tensor theories of gravity in various dimensions n>2 is proposed. We impose frame transformation induced by the group action which includes almost-geodesic and…
Palatini (or metric-affine) theories of gravity are characterized by having {\it a priori} independent metric and affine structures. The theories built in this framework have their field equations obtained as independent variations of the…
This work contains an exposition of foundations of the variational calculus in fibered manifolds. The emphasis is laid on the geometric aspects of the theory. Especially functionals defined by real functions (Lagrange functions) or…
The generalized hybrid metric-Palatini gravity is a theory of gravitation that has an action composed of a Lagrangian $f(R,\cal R)$, where $f$ is a function of the metric Ricci scalar $R$ and a new Ricci scalar $\cal R$ formed from a…
We introduce the concept of gauged Lagrangian $1$-forms, extending the notion of Lagrangian $1$-forms to the setting of gauge theories. This general formalism is applied to a natural geometric Lagrangian $1$-form on the cotangent bundle of…
Linearized supergravity in arbitrary dimension is reformulated into a first order formalism which treats the graviton and its dual on the same footing at the level of the action. This generalizes previous work by other authors in two…
We work out the description of the gauge symmetry of unimodular gravity in the constrained Hamiltonian formalism. In particular, we demonstrate how the transversality conditions restricting the diffeomorphism parameters emerge from the…
We reconstruct the geometrical $f(T)$ actions in the framework of unimodular $f(T)$ gravity. The unimodular $f(T)$ gravity yields stunning properties related to the generalized Friedmann equations. Indeed, it has been found that depending…
Lepage equivalents of Lagrangians are a higher order, field-theoretical generalization of the notion of Poincare-Cartan form from mechanics and play a similar role: they give rise to a geometric formulation (and to a geometric…
A Lagrangian depending on geometric variables (metric, affine connection, gauge group generators) is given which maintains compatibility with General Relativity. It generates the dynamics for Electromagnetism and other Gauge Fields along…
We present the invariant structure of a Holomorphic Unified Field Theory in which gravity and gauge interactions arise from a single geometric framework. The theory is formulated using a product principal bundle, with one connection, and…
Our main aim in this paper is to promote the coframe variational method as a unified approach to derive field equations for any given gravitational action containing the algebraic functions of the scalars constructed from the Riemann…