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Gravity theories with non-minimally coupled scalar fields are used as characteristic examples in order to demonstrate the challenges, pitfalls and future perspectives of considering alternatives to general relativity. These lecture notes…
In this work, we develop a q-deformed scalar-tensor theory of gravitation by combining Verlinde's entropic gravity paradigm with statistical deformation effects. The resulting model modifies the Brans-Dicke framework through a deformation…
Power-law corrections (having the exponent strictly between 2 and 3) to the Einstein-Hilbert action yield an extended theory of gravity which is consistent with Solar-System tests and properly reproduces the main phases of the Universe…
In this paper, we focus on the possibility to test General Relativity in the Solar System with radioscience measurements. To this aim, we present a new software that simulates Range and Doppler signals directly from the space-time metric.…
It is more important than ever to push experimental tests of gravitational theory to the limits of existing technology in both range and sensitivity. This brief review focuses on spin-based tests of General Relativity and their implications…
The {\it exact} formulation for the effect of the Brans-Dicke scalar field on the gravitational corrections to the Sagnac delay in the Jordan and Einstein frames is presented for the first time. The results completely agree with the known…
An argument is presented that if a theory of quantum gravity is physically discrete at the Planck scale and the theory recovers General Relativity as an approximation, then, at the current stage of our knowledge, causal sets must arise…
We consider a general scalar-tensor theory of gravity and review briefly different forms it can be presented (different conformal frames and scalar field parametrizations). We investigate the conditions under which its field equations and…
We review the fundamentals and highlight the differences between some commonly used definitions for the PPN gamma parameter ($\gamma$) and the gravitational slip ($\eta$). Here we stress the usefulness of a gamma-like parameter used by…
We introduce a designer approach for extended Brans-Dicke gravity that allows us to obtain the evolution of the scalar field by fixing the Hubble parameter to that of a $w$CDM model. We obtain analytical approximations for $\phi$ as a…
The laws of gravitation have been tested for a long time with steadily improving precision, leading at some moment of time to paradigmatic evolutions. Pursuing this continual effort is of great importance for science. In this communication,…
Recently, there has been an interest in inflation and modified gravity with a Weyl term added to the general-relativistic action (N. Derulle, M. Sasaki, Y. Sendouda and A. Youssef, JCAP, 3, 040 (2011)). In this paper we study empirical…
We consider an approach to Brans-Dicke theory of gravity in which the scalar field has a geometrical nature. By postulating the Palatini variation, we find out that the role played by the scalar field consists in turning the space-time…
Experiments on the violation of equivalence principle (EP) and solar system give a number of constraints in which any modified gravity model must satisfy them. We study these constraints on a kind of $f(R)$ gravity as $f(R) = R(1\pm…
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…
A satisfactory theory of quantum gravity may necessitate a drastic modification of our perception of space-time, by giving it a foamy structure at distances comparable to the Planck length. It is argued in this essay that the experimental…
The general theory of relativity is currently established as the most precise theory of gravity supported by observations, and its application is diverse ranging from astronomy to cosmology, while its application to astrophysics has been…
We consider a solution of the effective four-dimensional brane-world equations, obtained from the General Relativistic Schwarzschild metric via the principle of Minimal Geometric Deformation, and investigate the corresponding signatures…
The present acceleration of the Universe strongly indicated by recent observational data can be modeled in the scope of a scalar-tensor theory of gravity. We show that it is possible to determine the structure of this theory (the scalar…
General relativity probably is not the definitive theory of gravity, due a number or issues, both from the theoretical and from the observational point of view. Alternative theories of gravity were conceived to extend general relativity and…