General relativity marked the beginning of modern cosmology and it has since been at the centre of many of the key developments in this field. In the present review, we discuss the general-relativistic dynamics and perturbations of the standard cosmological model, the Friedmann-Lemaitre universe, and how these can explain and predict the properties of the observable universe. Our aim is to provide an overview of the progress made in several major research areas, such as linear and non-linear cosmological perturbations, large-scale structure formation and the physics of the cosmic microwave background radiation, in view of current and upcoming observations. We do this by using a single formalism throughout the review, the 1+3 covariant approach to cosmology, which allows for a uniform and balanced presentation of technical information and physical insight.Comment: Several minor changes, typos corrected, references added and updated (Physics Reports in press

Magnetic fields appear everywhere in the universe. From stars and galaxies, all the way to galaxy clusters and remote protogalactic clouds magnetic fields of considerable strength and size have been repeatedly observed. Despite their widespread presence, however, the origin of cosmic magnetic fields is still a mystery. The galactic dynamo is believed capable of amplifying weak magnetic seeds to strengths like those measured in ours and other galaxies, but the question is where do these seed fields come from? Are they a product of late, post-recombination, physics or are they truly cosmological in origin? The idea of primordial magnetism is attractive because it makes the large-scale magnetic fields, especially those found in early protogalactic systems, easier to explain. As a result, a host of different scenarios have appeared in the literature. Nevertheless, early magnetogenesis is not problem free, with a number of issues remaining open and a matter of debate. We review the question of primordial magnetic fields and consider the limits set on their strength by the current observational data. The various mechanisms of pre-recombination magnetogenesis are presented and their advantages and shortcomings are debated. We consider both classical and quantum scenarios, that operate within as well as outside the standard model, and also discuss how future observations could be used to decide whether the large-scale magnetic fields we see in the universe today are truly primordial or not.Comment: 107 pages, 3 figures. Revised and expanded version, to be published in Physics Report

We provide a realization of a singularity-free inflationary universe in the form of a simple cosmological model dominated at early times by a single minimally coupled scalar field with a physically based potential. The universe starts asymptotically from an initial Einstein static state, which may be large enough to avoid the quantum gravity regime. It enters an expanding phase that leads to inflation followed by reheating and a standard hot Big Bang evolution. We discuss the basic characteristics of this Emergent model and show that none is at odds with current observations.

We show using covariant techniques that the Einstein static universe containing a perfect fluid is always neutrally stable against small inhomogeneous vector and tensor perturbations and neutrally stable against adiabatic scalar density inhomogeneities so long as c 2 s > 1 5 , and unstable otherwise. We also show that the stability is not significantly changed by the presence of a self-interacting scalar field source, but we find that spatially homogeneous Bianchi type IX modes destabilise an Einstein static universe. The implications of these results for the initial state of the universe and its pre-inflationary evolution are also discussed.

We provide a fully general-relativistic treatment of cosmological perturbations in a universe permeated by a large-scale primordial magnetic field using the Ellis-Bruni gauge-invariant formalism. The exact non-linear equations for general relativistic magnetohydrodynamic evolution are derived. A number of applications are made: the behaviour of small perturbations to Friedmann universes are studied; a comparison is made with earlier Newtonian treatments of cosmological perturbations and some effects of inflationary expansion are examined.