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Einstein's general theory of relativity is the standard theory of gravity, especially where the needs of astronomy, astrophysics, cosmology and fundamental physics are concerned. As such, this theory is used for many practical purposes…
In Einstein's general relativity (GR), gravity is described by a massless spin-2 metric field, and the extension of GR to include a mass term for the graviton has profound implication for gravitation and cosmology. Besides the gravity…
The observation of gravitational waves with a global network of interferometric detectors such as advanced LIGO, advanced Virgo, and KAGRA will make it possible to probe into the nature of space-time structure. Besides Einstein's general…
Shortly after its discovery, General Relativity (GR) was applied to predict the behavior of our Universe on the largest scales, and later became the foundation of modern cosmology. Its validity has been verified on a range of scales and…
Modifications of general relativity provide an alternative explanation to dark energy for the observed acceleration of the universe. We review recent developments in modified gravity theories, focusing on higher dimensional approaches and…
The status of experimental tests of general relativity and of theoretical frameworks for analysing them are reviewed. Einstein's equivalence principle (EEP) is well supported by experiments such as the E\"otv\"os experiment, tests of…
Gravitational Wave (GW) observations of coalescing compact binaries will be unique probes of strong-field, dynamical aspects of relativistic gravity. We present a short review of various schemes proposed in the literature to test General…
The study of post-Einsteinian metric extensions of general relativity (GR), which preserve the metric interpretation of gravity while considering metrics which may differ from that predicted by GR, is pushed one step further. We give a…
The standard paradigm of cosmology assumes General Relativity (GR) is a valid theory for gravity at scales in which it has not been properly tested. Developing novel tests of GR and its alternatives is crucial if we want to give strength to…
Modifications to the classic time-delay effect and Doppler shift in General Relativity (GR) are studied in the context of the Lorentz-violating Standard-Model Extension (SME). We derive the leading Lorentz-violating corrections to the…
Gravitational wave (GW) observations provide a unique opportunity to test Einstein's General Relativity (GR) in the strong-field regime. While GR predicts only two tensor polarization modes, generic metric theories allow up to six…
This resource letter provides an introduction to some of the main current topics in experimental tests of general relativity as well as to some of the historical literature. It is intended to serve as a guide to the field for upper-division…
The current effort to test General Relativity employs multiple disparate formalisms for different observables, obscuring the relations between laboratory, astrophysical and cosmological constraints. To remedy this situation, we develop a…
We review recent progress in the construction of modified gravity models as alternatives to dark energy as well as the development of cosmological tests of gravity. Einstein's theory of General Relativity (GR) has been tested accurately…
The status of experimental tests of general relativity and of theoretical frameworks for analysing them are reviewed. Einstein's equivalence principle (EEP) is well supported by experiments such as the E\"otv\"os experiment, tests of…
Recently, a new kind of $f(z)$ theory is proposed to provide a different perspective for the development of reliable alternative models of gravity in which the $f(R)$ Lagrangian terms are reformulated as polynomial parameterizations $f(z)$.…
This review explores modified theories of gravity, particularly $f(R)$ gravity, as extensions to General Relativity (GR) that offer alternatives to dark energy for explaining cosmic acceleration. These models generalize the Einstein-Hilbert…
The predictions of General relativity (GR) are in good agreement with observations in the solar system. Nevertheless, unexpected anomalies appeared during the last decades, along with the increasing precision of measurements. Those…
Gravitational waves (GWs) emitted by binary sources are interesting signals for testing gravity on cosmological scales since they allow measurements of the luminosity distance. When followed by electromagnetic counterparts, in particular,…
The recent discovery of "dark energy" has challenged Einstein's general theory of relativity as a complete model for our macroscopic universe. From a theoretical view, the challenge is even stronger: general relativity clearly does not…