Gravity drives the evolution of the Universe and is at the heart of its complexity. Einstein's field equations can be used to work out the detailed dynamics of space and time and to calculate the emergence of large-scale structure in the distribution of ...

The metric of a perturbed Robertson–Walker space–time is characterized by three functions: a scale-factor giving the expansion history and two potentials that generalize the single potential of Newtonian gravity. The Newtonian potential induces peculiar ...

General relativity (GR) is a phenomenologically successful theory that rests on firm foundations, but has not been tested on cosmological scales. The deep mystery of dark energy (and possibly even the requirement of cold dark matter (CDM)) has increased ...

We consider how upcoming, prospective large-scale structure surveys, measuring galaxy weak lensing and position in tandem with the cosmic microwave background temperature anisotropies, constrain cosmic scale modifications to general relativity. In such ...

Gravitation governs the expansion and fate of the universe, and the growth of large-scale structure within it, but has not been tested in detail on these cosmic scales. The observed acceleration of the expansion may provide signs of gravitational laws ...

The challenge to understand the physical origin of the cosmic acceleration is framed as a problem of gravitation. Specifically, does the relationship between stress–energy and space–time curvature differ on large scales from the predictions of general ...

The impressive success of the standard cosmological model has suggested to many that its ingredients are all that one needs to explain galaxies and their systems. I summarize a number of known problems with this programme. They might signal the failure of ...

The combination of general relativity (GR) and the Standard Model of particle physics disagrees with numerous observations on scales from our Solar System up. In the canonical concordance model of Lambda cold dark matter (ΛCDM) cosmology, many of these ...

I summarize various tests of general relativity on astrophysical scales, based on the large-scale structure of the universe but also on other systems, in particular the constants of physics. I emphasize the importance of hypotheses on the geometric ...

Comparing measurements of redshift-space distortions (RSDs) with geometrical observations of the expansion of the Universe offers tremendous potential for testing general relativity on very large scales. The basic linear theory of RSDs in the distant-...

We review the effects of modified gravity on large-scale structure in the nonlinear regime, focusing on f(R) gravity and the Dvali–Gabadadze–Porrati model, for which full N-body simulations have been performed. In particular, we discuss the abundance of ...

Modified gravity theories may provide an alternative to dark energy to explain cosmic acceleration. We argue that the observational programme developed to test dark energy needs to be augmented to capture new tests of gravity on astrophysical scales. ...

In this article, we review model selection predictions for modified gravity scenarios as an explanation for the observed acceleration of the expansion history of the Universe. We present analytical procedures for calculating expected Bayesian evidence ...

In this paper, we discuss what we truly know about dark energy. I shall argue that, to date, our single indication for the existence of dark energy comes from distance measurements and their relation to redshift. Supernovae, cosmic microwave background ...

The standard model of cosmology is based on the existence of homogeneous surfaces as the background arena for structure formation. Homogeneity underpins both general relativistic and modified gravity models and is central to the way in which we interpret ...

The Copernican principle remains largely unproven at Gpc radial scale and above. Generally, violations of this type cause a first-order anisotropic kinetic Sunyaev Zel'dovich (kSZ) effect. Here we show that, if large-scale radial inhomogeneities have ...