Related papers: Variational principle and boundary terms in gravit…
After reformulating $F($Riemann$)$ gravity theory as a second derivative theory by introducing two auxiliary fields to the bulk action, we derive the surface term as well as the corner term supplemented to the bulk action for a generic…
General relativity is highly successful in explaining a wide range of gravitational phenomena including the gravitational waves emitted by binary systems and the shadows cast by supermassive black holes. From a modern perspective the theory…
Modified gravity theories have received increased attention lately due to combined motivation coming from high-energy physics, cosmology and astrophysics. Among numerous alternatives to Einstein's theory of gravity, theories which include…
This paper compares three different methods about computing joint terms in on-shell action of gravity, which are identifying the joint term by the variational principle in Dirichlet boundary condition, treating the joint term as the limit…
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…
f(R) gravity theories in the Palatini formalism has been recently used as an alternative way to explain the observed late-time cosmic acceleration with no need of invoking either dark energy or extra spatial dimension. However, its…
The non-equivalence between the metric and Palatini formalisms of $f(R)$ gravity is an intriguing feature of these theories. However, in the recently proposed hybrid metric-Palatini gravity, consisting of the superposition of the metric…
Although several models of $f(R)$ theories of gravity within the Palatini approach have been studied already, the interest was concentrated on those that have an effect on the late-time evolution of the universe, by the inclusion for…
We discuss some fundamental issues underlying gravitational physics and point out some of the main shortcomings of Einstein's General Relativity. In particular, after taking into account the role of the two main objects of relativistic…
The Palatini formalism is developed for gravitational theories in flat geometries. We focus on two particularly interesting scenarios. First, we fix the connection to be metric compatible, but we follow a completely covariant approach by…
The entropy of black holes in modified theories of gravity is examined in the Palatini formalism using the Noether Charge approach. It is shown that, if the gravitational coupling constant is properly identified, the entropy of a black hole…
The equations of motion describing all physical systems, except gravity, remain invariant if a constant is added to the Lagrangian. In the conventional approach, gravitational theories break this symmetry exhibited by all other physical…
With a scalar field non-minimally coupled to curvature, the underlying geometry and variational principle of gravity - metric or Palatini - becomes important and makes a difference, as the field dynamics and observational predictions…
We generalize the $f(R)$ type gravity models by assuming that the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar $R$ and of the matter Lagrangian $L_m$. We obtain the gravitational field equations in the…
The main objective of this thesis is to discuss scalar-tensor theories in the Palatini approach. Both scalar-tensor theories and Palatini formalism are means of alternating classical theory of gravity, general relativity, in order to…
A brief discussion is made about the relevance of surface terms in the Lagrangian and Hamiltonian formulations of theories of gravity. These surface terms play an important role in the variation of the action integral and in the definition…
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 $f(R)$ gravity and Born-Infeld-Einstein (BIE) gravity in formulations where the metric and connection are treated independently and integrate out the metric to find the corresponding models solely in terms of the connection, the…
Extended Theories of Gravity can be considered a new paradigm to cure shortcomings of General Relativity at infrared and ultraviolet scales. They are an approach that, by preserving the undoubtedly positive results of Einstein's Theory, is…
Starting from the action function, we have derived a theoretical background that leads to the quantization of gravity and the deduction of a correlation between the gravitational and the inertial masses, which depends on the kinetic…