These models describing the background cosmological evolution were completed by the addition of cosmological perturbation theory to populate them with cosmic structures. It allowed the combination of ideas from Friedmann and Lemaître about expanding universes (Friedmann 1922 Lemaître 1931) along with the geometry of homogeneous and isotropic spacetimes of Robertson ( 1935) and Walker ( 1937) in order to produce the so-called Friedmann–Lemaître–Robertson–Walker models (FLRW).

Shortly after that, GR gave birth to the current standard model of cosmology predicting exact solutions with expanding or contracting universes. Astonishingly, the same simple but powerful equations remain to date the most accurate description of gravitational physics at all scales. Taking into account further requirements, such as coordinate invariance, conservation laws, and limits that must be consistent with Newtonian gravity, he proposed his gravitational field equations (Einstein 1915). Guided by some key principles, Einstein came to the important realization of a very close relationship between the curvature of spacetime and gravity. It can also serve as a quick reference to recent results and constraints on testing gravity at cosmological scales.įor over a century, Einstein’s general relativity (GR) has continued to be an impressive theory of gravity that fits observations from our solar system to the entire cosmological model of the universe. The review aims at providing an overall picture of the subject and an entry point to students and researchers interested in joining the field. Next, we summarize some results on MG parameter forecasts with and without astrophysical systematics that will dominate the uncertainties. We supplement these cosmological constraints with a summary of implications from the recent binary neutron star merger event. We then provide summaries of recent cosmological constraints on MG parameters and selected MG models. We overview cosmological probes of gravity, formalisms and parameterizations for testing deviations from GR at cosmological scales, selected modified gravity (MG) theories, gravitational screening mechanisms, and computer codes developed for these tests. However, with the advent of precision cosmology, it has also become a well-motivated endeavor by itself to test gravitational physics at cosmic scales. The subject has witnessed rapid growth during the last two decades with the aim of addressing the question of cosmic acceleration and the dark energy associated with it. We review recent developments and results in testing general relativity (GR) at cosmological scales.

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