Relativistic cosmology and large-scale structure

TL;DR

The work surveys relativistic cosmology with a covariant 1+3 framework, unifying the dynamics and perturbations of the FLRW background and its generalisations. It develops a comprehensive, gauge-invariant treatment of linear and nonlinear perturbations, multi-fluid and magnetised cosmologies, scalar-field dynamics, and kinetic theory for neutrinos and the CMB, all within a single covariant formalism. Key contributions include the Weyl curvature decomposition into $E_{ab}$ and $H_{ab}$, generalized Friedmann and Raychaudhuri equations, Jeans scales for various components, and the full Boltzmann treatment of CMB and neutrino perturbations. The framework clarifies the interpretation of observational probes (CMB, LSS, SN) and provides a robust platform for exploring departures from FLRW, early-universe physics, and the interplay between gravity, fluids, and radiation in cosmology.

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.

Figures (5)

• Figure 1: Observational constraints in the $(\Omega_{(m)},\Omega_\Lambda)$ plane: joint constraints (left) (from 2003ApJ...598..102K); recent compilation of supernova constraints (right) (from 2007ApJ...666..694W).
• Figure 2: Left: Power spectrum of CMB temperature anisotropies, showing data from WMAP5 2008arXiv0803.0593N, the 2003 flight of BOOMERANG 2006ApJ...647..823J, CBI 2004ApJ...609..498R and the full ACBAR dataset 2008arXiv0801.1491R. The red line is the best-fit LCDM model to the data. Right: Matter power spectrum, showing data from the SDSS 2006 data release and the best-fit LCDM curve; the inset shows the imprint (in Fourier space) of the CMB acoustic peaks, known as the baryon acoustic oscillations (from 2007ApJ...657..645P).
• Figure 3: In a multi-component system, the 4-velocity $u_a^{(i)}$ of the $i$-th fluid makes a hyperbolic angle $\beta^{(i)}$ with the fundamental 4-velocity field $u_a$, normal to the hypersurfaces of homogeneity $S(t)$. The unit vectors $e_a$ and $e_a^{(i)}$ are orthogonal to $u_a$ and $u_a^{(i)}$ respectively. Following definition (\ref{['Lboost']}), the peculiar velocity of the $i$-th species is $v_a^{(i)}=v^{(i)}e_a$, with $v_{(i)}^2= v_a^{(i)}v_{(i)}^a$.
• Figure 4: Power spectra produced by adiabatic scalar perturbations (left) and tensor perturbations (right) for a tensor-to-scalar ratio $r=0.20$ and optical depth to reionization of $0.08$. The power spectrum of the $B$-modes produced by gravitational lensing of the scalar $E$-mode polarization is also shown on the left.
• Figure 5: Phase plane with $\Sigma_+\equiv X$ and $\Sigma_-\equiv Y$. The lines $L_1$, $L_2$ and $L_3$ that form the central triangle correspond to $\sigma_i=-\bar{\Theta}/3$ ($i=1,2,3$), with the three pancakes located at $P_1$, $P_2$ and $P_3$ where these lines intersect. The points $F_1$, $F_2$, $F_3$ represent filamentary solutions and spindle-like singularities, while $O$ corresponds to spherically symmetric, isotropic collapse (see 2002PhRvD..66l4015E and also 1996ASPC...94...31B).