Relativistic cosmology and large-scale structure

Abstract

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

The linear growth of structure in theRh=ctuniverse

“…Note that for the application we are considering in this paper, we have explicitly used the constant value w − 1/3, so terms proportional toẇ have been omitted from these expressions (cf. Tsagas et al 2008). …”

A non-perturbative study of the evolution of cosmic magnetised sources

“…Such a perturbative approach of a frozen magnetic field is fully justified if the latter is tangled on scales smaller than the Hubble horizon [21] and has lead to a comprehensive literature [20,21,22,23,24,25] in which the perturbations are covariant and gauge invariant.…”

“…However, a classical Maxwellian electromagnetic interaction (not necessarily restricted to early cosmic times) can also be incorporated into the full dynamics of General Relativity through an elegant first order system based on covariant objects defined in a 4-velocity frame (the 1+3 formalism [9,20,21]). In particular, this formalism is useful to study (following a perturbative or non-perturbative approach) the dynamics of a "frozen" magnetic field without electric currents through the limit of infinite conductivity [20,21,22,23,24,25].…”

“…However, a classical Maxwellian electromagnetic interaction (not necessarily restricted to early cosmic times) can also be incorporated into the full dynamics of General Relativity through an elegant first order system based on covariant objects defined in a 4-velocity frame (the 1+3 formalism [9,20,21]). In particular, this formalism is useful to study (following a perturbative or non-perturbative approach) the dynamics of a "frozen" magnetic field without electric currents through the limit of infinite conductivity [20,21,22,23,24,25]. Whenever a spatially flat FLRW background is assumed in a perturbative treatment, a "weak field approximation" can be defined in which the anisotropic stresses of the the magnetic field (associated with vector perturbations) are neglected and the latter field is described (at first order) as a sort of scalar source that dilutes as B ∼ a −2 [20,21,22,23,24,25,26].…”

“…In particular, this formalism is useful to study (following a perturbative or non-perturbative approach) the dynamics of a "frozen" magnetic field without electric currents through the limit of infinite conductivity [20,21,22,23,24,25]. Whenever a spatially flat FLRW background is assumed in a perturbative treatment, a "weak field approximation" can be defined in which the anisotropic stresses of the the magnetic field (associated with vector perturbations) are neglected and the latter field is described (at first order) as a sort of scalar source that dilutes as B ∼ a −2 [20,21,22,23,24,25,26]. While this approximation is not gauge invariant, it leads to the same results (see proof in [26]) as gauge invariant perturbations when infinite conductivity is assumed.…”