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We consider the most general action for gravity which is quadratic in curvature. In this case first order and second order formalisms are not equivalent. This framework is a good candidate for a unitary and renormalizable theory of the…
We consider theories with an arbitrary coupling between matter and gravity and obtain the perturbation equation of matter on subhorizon scales. Also, we derive the effective gravitational constant $G_{eff}$ and two parameters $\Sigma$ and…
The concept of smooth deformations of a Riemannian manifolds, recently evidenced by the solution of the Poincar\'e conjecture, is applied to Einstein's gravitational theory and in particular to the standard FLRW cosmology. We present a…
A momentum-space approach to conformal field theory offers a new perspective on cosmological correlators and better reveals the underlying connections to scattering amplitudes. This thesis explores the interplay between integral…
This article investigates the signatures of various models of dark energy on weak gravitational lensing, including the complementarity of the linear and non-linear regimes. It investigates quintessence models and their extension to…
The universal character of the gravitational interaction provided by the equivalence principle motivates a geometrical description of gravity. The standard formulation of General Relativity \`a la Einstein attributes gravity to the…
We discuss some of the consequences of changing the matter to gravity coupling without affecting the gravitational dynamics. The Einstein tensor is usually assumed to be proportional to the stress tensor due to the divergence free property…
We consider a Weyl invariant extension of Dirac-Born-Infeld type gravity. An appropriate choice of the metric hides the scalar degree of freedom which is required by the local scale invariance of the action at the first sight, and then a…
We study the effect of modifications to General Relativity on large scale weak lensing observables. In particular, we consider three modified gravity scenarios: f(R) gravity, the DGP model, and TeVeS theory. Weak lensing is sensitive to the…
We propose a universal description of dark energy and modified gravity that includes all single-field models. By extending a formalism previously applied to inflation, we consider the metric universally coupled to matter fields and we write…
We analyze the foundations of Finsler gravity theories with metric compatible connections constructed on nonholonomic tangent bundles, or (pseudo) Riemannian manifolds. There are considered "minimal" modifications of Einstein gravity…
We study modified theories of gravity of the f(R) type in Palatini formalism. For a generic f(R) lagrangian, we show that the metric can be solved as the product of a scalar function times a rank-two tensor (or auxiliary metric). The scalar…
The best motivated alternatives to general relativity are scalar-tensor theories, in which the gravitational interaction is mediated by one or several scalar fields together with the usual graviton. The analysis of their various…
We review the classical and quantum mechanics of Stueckelberg, and introduce the compensation fields necessary for the gauge covariance of the Stueckelberg- Schr\"odinger equation. To achieve this, one must introduce a fifth, Lorentz…
In this article, we propose different background models of extended theories of gravity, which are minimally coupled to the SM fields, to explain the possibility of genesis of dark matter without affecting the SM particle sector. We modify…
Gravity theory is the basis of modern cosmological models. Thirring-Feynman's tensor field approach to gravitation is an alternative to General Relativity (GR). Though Field Gravity (FG) approach is still developing subject, it opens new…
Theories of scalars and gravity, with non-minimal interactions, $\sim (M_P^2 +F(\phi) )R +L(\phi)$, have graviton exchange induced contact terms. These terms arise in single particle reducible diagrams with vertices $\propto q^2$ that…
Solar system observations have traditionally allowed for very stringent tests of Einstein's theory of general relativity. We here revisit the possibility of using these observations to constrain gravitational parity violation as…
In a Lorentzian spacetime there exists a smooth regular line element field $(\bm{X},-\bm{X}) $ and a unit vector $ \bm{u} $ collinear with one of the pair of vectors in the line element field. An orthogonal decomposition of symmetric…
We explore the evolutionary behaviors of compact objects in a modified gravitational theory with the help of structure scalars. Particularly, we consider the spherical geometry coupled with heat and radiation emitting shearing viscous…