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Over the past decades, General Relativity and the concordance $\Lambda$CDM model have been successfully tested using several different astrophysical and cosmological probes based on large datasets ({\it precision cosmology}). Despite their…
We study the growth of structures in modified gravity models where the Poisson equation and the relationship between the two Newtonian potentials are modified by explicit functions of space and time. This parameterisation applies to the…
The acceleration of the universe can be explained either through dark energy or through the modification of gravity on large scales. In this paper we investigate modified gravity models and compare their observable predictions with dark…
Motivated by the existence of hierarchies of structure in the Universe, we present four new families of exact initial data for inhomogeneous cosmological models at their maximum of expansion. These data generalise existing black hole…
We consider cosmological models based on the spectral action formulation of (modified) gravity. We analyze the coupled effects, in this model, of the presence of nontrivial cosmic topology and of fractality in the large scale structure of…
Extended theories of gravity have been extensively investigated during the last thirty years, aiming at fixing infrared and ultraviolet shortcomings of General Relativity and of the associated $\Lambda$CDM cosmological model. Recently,…
We suggest a new scenario in which the Universe starts its evolution with a fractal topological structure. This structure is described by a gas of wormholes. It is shown that the polarization of such a gas in external fields possesses a…
In spite of the growing observational evidence for dark matter and dark energy in the universe, their physical nature is largely unknown. In fact, several authors have proposed modifications of Newton's law of gravity at cosmological scales…
I briefly discuss the challenges presented by attempting to modify general relativity to obtain an explanation for the observed accelerated expansion of the universe. Foremost among these are the questions of theoretical consistency - the…
We review attempts to estimate the influence of global cosmological expansion on local systems. Here `local' is taken to mean that the sizes of the considered systems are much smaller than cosmologically relevant scales. For example, such…
The next generation of cosmological surveys will operate over unprecedented scales, and will therefore provide exciting new opportunities for testing general relativity. The standard method for modelling the structures that these surveys…
We investigate the cosmological dependence and the constraining power of large-scale galaxy correlations, including all redshift-distortions, wide-angle, lensing and gravitational potential effects on linear scales. We analyze the…
We discuss the galaxy clustering based on thermodynamics and statistical mechanics in the expanding universe in a modified theory of gravity. The modified general relativity (MGR) is developed using the regular line element field to…
We present the second-order general relativistic description of the observed galaxy number density in a cosmological framework. The observed galaxy number density is affected by the volume and the source effects, both of which arise due to…
The magnification effects of clustered matter produce variations in the image sizes and number density of galaxies across the sky. This paper advocates the use of these effects in wide field surveys to map large-scale structure and the…
We address the impact of consistent modifications of gravity on the largest observable scales, focusing on relativistic effects in galaxy number counts and the cross-correlation between the matter large scale structure (LSS) distribution…
The large scale structure bispectrum in the squeezed limit couples large with small scales. Since relativity is important at large scales and non-linear loop corrections are important at small scales, the proper calculation of the observed…
Modifications to Newtonian dynamics at low accelerations have long been proposed as an alternative to dark matter to explain galaxy rotation curves. More recently, similar corrections have been invoked to interpret anomalies in…
Cosmology is built on a relativistic understanding of gravity, where the geometry of the Universe is dynamically determined by matter and energy. In the cosmological concordance model, gravity is described by General Relativity, and it is…
Waveforms of gravitational waves provide information about a variety of parameters for the binary system merging. However, standard calculations have been performed assuming a FLRW universe with no perturbations. In reality this assumption…