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Modifications to gravity that add additional functions of the Ricci curvature to the Einstein-Hilbert action -- collectively known as $f(R)$ theories -- have been studied in great detail. When considered as complete theories of gravity they…
Minisuperpace Quantum Cosmology is an approach by which it is possible to infer initial conditions for dynamical systems which can suitably represent observable and non-observable universes. Here we discuss theories of gravity which, from…
In this lecture I address the issue of possible large distance modification of gravity and its observational consequences. Although, for the illustrative purposes we focus on a particular simple generally-covariant example, our conclusions…
The configuration space of general relativity is superspace - the space of all Riemannian 3-metrics modulo diffeomorphisms. However, it has been argued that the configuration space for gravity should be conformal superspace - the space of…
The cosmology of general fourth order corrections to Einstein gravity is considered, both for a homogeneous and isotropic background and for general tensor perturbations. It is explicitly shown how the standard cosmological history can be…
Modifications to gravity can provide attractive alternatives to the dark components of the standard model of cosmology. These modifications to general relativity (GR) must be hidden at small scales where theory is well tested, and so one…
Modified gravity theories are a popular alternative to dark energy as a possible explanation for the observed accelerating cosmic expansion, and their cosmological tests are currently an active research field. Studies in recent years have…
We present a formalism to compute Lagrangian displacement fields for a wide range of cosmologies in the context of perturbation theory up to third order. We emphasize the case of theories with scale dependent gravitational strengths, such…
Over the past decade, f(R) theories have been extensively studied as one of the simplest modifications to General Relativity. In this article we review various applications of f(R) theories to cosmology and gravity - such as inflation, dark…
We consider modified gravity models driven by a scalar field whose effects are screened in high density regions due to the presence of non-linearities in its interaction potential and/or its coupling to matter. Our approach covers…
In 'modified' gravity the observed acceleration of the universe is explained by changing the gravitational force law or the number of degrees of freedom in the gravitational sector. Both possibilities can be tested by measurements of…
A detailed analysis of dynamics of cosmological models based on $R^{n}$ gravity is presented. We show that the cosmological equations can be written as a first order autonomous system and analyzed using the standard techniques of dynamical…
We present a class of modified-gravity theories which we call ultra-local models. We add a scalar field, with negligible kinetic terms, to the Einstein-Hilbert action. We also introduce a conformal coupling to matter. This gives rise to a…
This paper examines a cosmological model of scale-dependent gravity. The gravitational action is taken to be the Einstein-Hilbert term supplemented with a cosmological constant, where the couplings, $G_k$ and $\Lambda_k$, run with the…
Despite many nice properties and numerous achievements, general relativity is not a complete theory. One of actual approaches towards more complete theory of gravity is its nonlocal modification. We present here a brief review of nonlocal…
Topological gravity is the reduction of general relativity to flat space-times. A lattice model describing topological gravity is developed starting from a Hamiltonian lattice version of $B\w F$ theory. The extra symmetries not present in…
As a classical approach, the dynamics of the Universe, influenced by its dark components, are unveiled through prior modifications of Einstein's equations. Cosmography, on the other hand, is a highly efficient tool for reconstructing any…
The Hamiltonian approach to General Relativity is developed similarly to the Wheeler-DeWitt Hamiltonian cosmology, where the cosmological scale factor is treated as a time-like dynamic variable and its canonical momentum is considered as an…
We develop a new approach to building cosmological models, in which small pieces of perturbed Minkowski space are joined together at reflection-symmetric boundaries in order to form a global, dynamical space-time. Each piece of this…
In this work we study the cosmology of the general f(T) gravity theory. We express the modified Einstein equations using covariant quantities, and derive the gauge-invariant perturbation equations in covariant form. We consider a specific…