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If visible matter alone is present in the Universe, general relativity (GR) and its Newtonian weak field limit (WFL) cannot explain several pieces of evidence, from the largest to the smallest scales. The most investigated solution is the…
After a brief introduction to the sixteenth and seventeenth century views of the Universe and the nineteenth century paradox of Olbers, we start the history of the cosmic expansion with Hubble's epochal discovery of the recession velocities…
In the present work, we review some general aspects of modified gravity theories, investigating mathematical and physical properties and, more specifically, the feature of viable and realistic models able to reproduce the dark energy epoch…
I consider the isolation of general relativity research from the rest of theoretical physics during the 1930s-1950s, and the subsequent reinvigoration of the field. I suggest that the main reason for the isolation was that relativists of…
In this review we present a thoroughly comprehensive survey of recent work on modified theories of gravity and their cosmological consequences. Amongst other things, we cover General Relativity, Scalar-Tensor, Einstein-Aether, and Bimetric…
The discovery of the accelerated expansion of the universe highlighted General Relativity's inability to naturally account for dark energy without invoking a finely tuned cosmological constant. In response, a wide range of alternative…
The cosmological Friedmann equation sourced by the trace anomaly of a conformal field theory that is dual to the five-dimensional Schwarzschild-AdS geometry can be derived from the first law of thermodynamics if the apparent horizon of the…
A large international effort is under way to assess the presence of a shadow in the radio emission from the compact source at the centre of our Galaxy, Sagittarius A$^*$ (Sgr A$^*$). If detected, this shadow would provide the first direct…
The existence of black holes is one of the key predictions of general relativity (GR) and therefore a basic consistency test for modified theories of gravity. In the case of spherical symmetry in GR the existence of an apparent horizon and…
We prove that a class of solutions to Einstein's equations---originally discovered by G. C. McVittie in 1933---includes regular black holes embedded in Friedman-Robertson-Walker cosmologies. If the cosmology is dominated at late times by a…
Soon after he proposed three classic observational tests for the general theory of relativity, Einstein realised that a consistent description of the universe as a whole provided another important challenge for the theory. In this essay, we…
One of the most favourable extensions of General Relativity is the $f(R)$ gravity. $f(R)$ gravity in Palatini formalism can be a realistic alternative to the dark energy problem. In this work we study a recently introduced dark energy…
Subject of this article is the relationship between modern cosmology and fundamental physics, in particular general relativity as a theory of gravity on one side, together with its unique application in cosmology, and the formation of…
Recent advances, including gravitational wave detections and imaging of black hole shadows, have strongly validated general relativity. Nevertheless, ongoing cosmological observations suggest potential limitations of general relativity,…
As we now know, there are indeed at least two major difficulties with General Relativity (GR). The first one is related with its incompatibility with quantum mechanics, in the absence of a widely accepted consistent theory that combines the…
Einstein established the theory of general relativity and the corresponding field equation in 1915 and its vacuum solutions were obtained by Schwarzschild and Kerr for, respectively, static and rotating black holes, in 1916 and 1963,…
The basic cosmological predictions of a `polarizable-vacuum' theory of gravity due to Dicke, predating the scalar-tensor theory, are investigated and tested for their compliance with current observations. A Friedmann-like equation is…
Black holes were predicted by Einstein General Relativity (GR). Because of unusual properties of these objects their existence is almost unbelievable. There are gravitation theories which do not predict the black hole appearance. By now,…
We propose a new model of cosmology based on an anisotropic background and a specific $f(R)$ theory of gravity. It is shown that field equations of $f(R)$ gravity in a Bianchi type I background give rise to a modified Friedmann equation.…
In general relativity (GR), spacetime geometry is no longer just a background arena but a physical and dynamical entity with its own degrees of freedom. We present an overview of approaches to quantum gravity in which this central feature…