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We derive for applications to isolated systems - on the scale of the Solar System - the first relativistic terms in the $1/c$ expansion of the space time metric $g_{\mu\nu}$ for metric $f(R)$ gravity theories, where $f$ is assumed to be…
Binary pulsars are excellent laboratories to test the building blocks of Einstein's theory of General Relativity. One of these is Lorentz symmetry which states that physical phenomena appear the same for all inertially moving observers. We…
Using the latest most accurate values of post-Newtonian parameters $\gamma$ and $\beta$ obtained by MESSENGER we impose restrictions on the recently proposed hybrid f(R)-gravity model in its scalar-tensor representation. We show that 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…
Although general relativity (GR) has been precisely tested at the solar system scale, precise tests at a galactic or cosmological scale are still relatively insufficient. Here, in order to test GR at the galactic scale, we use the newly…
Tests of gravity are important to the development of our understanding of gravitation and spacetime. Binary pulsars provide a superb playground for testing gravity theories. In this chapter we pedagogically review the basics behind pulsar…
We compute the complete post-Newtonian limit of the Palatini form of f(R) gravities using a scalar-tensor representation. By comparing the predictions of these theories with laboratory and solar system experiments, we find a set of…
The ever-increasing number of detections of gravitational waves (GWs) from compact binaries by the Advanced LIGO and Advanced Virgo detectors allows us to perform ever-more sensitive tests of general relativity (GR) in the dynamical and…
Gravitational waves allow us to test general relativity in the highly dynamical regime. While current observations have been consistent with waves emitted by quasi-circular binaries, eccentric binaries may also produce detectable signals in…
By using observations of the Hulse-Taylor pulsar we constrain the gravitational wave (GW) speed to the level of $10^{-2}$. We apply this result to scalar-tensor theories that generalize Galileon 4 and 5 models, which display anomalous…
Before the 1970s, precision tests for gravity theories were constrained to the weak gravitational fields of the Solar system. Hence, only the weak-field slow-motion aspects of relativistic celestial mechanics could be investigated. Testing…
We are developing 3 dimensional simulation codes for coalescing binary neutron stars. A code using the maximal slicing condition is obtained. To evaluate the gravitational radiation, we implemented a gauge-invariant wave extraction and…
The advent of gravitational wave astronomy provides new proving grounds for testing theories of gravity. Recent work has reinvigorated the study of bimetric theories of gravity and massive gravity theories. One of the most interesting…
General relativity predicts the existence of only two tensorial gravitational wave polarizations, while a generic metric theories of gravity can possess up to four additional polarizations, including two vector and two scalar ones. These…
General relativity predicts that energy and momentum conservation laws hold and that preferred frames do not exist. The parametrised post-Newtonian formalism (PPN) phenomenologically quantifies possible deviations from general relativity.…
We compute the accuracy at which a LISA-like space-based gravitational wave detector will be able to observe deviations from General Relativity in the low frequency approximation. To do so, we introduce six correction parameters that…
We present Keplerian-type parametrization for the solution of third post-Newtonian (3PN) accurate equations of motion for two non-spinning compact objects moving in an eccentric orbit. The orbital elements of the parametrization are…
This review is focused on tests of Einstein's theory of General Relativity with gravitational waves that are detectable by ground-based interferometers and pulsar timing experiments. Einstein's theory has been greatly constrained in the…
Despite the tremendous success of general relativity so far, modified theories of gravity have received increased attention lately, motivated from both theoretical and observational aspects. Gravitational wave observations opened new…
Precision tests of general relativity can be conducted by observing binary pulsars. Theories with massive fields exist to explain a variety of phenomena from dark energy to the strong CP problem. Existing pulsar binaries, such as the white…