Brane World Cosmology

TL;DR

This review surveys brane world cosmology, focusing on RS-type models with an AdS bulk and extensions that include a bulk scalar field, as well as two-brane systems. It develops the modified Friedmann dynamics, notably the $ρ^2$-dominant regime and dark-radiation effects, and contrasts two main analytic approaches: the bulk-derived (Gauss–Codazzi) projection and the moduli-space effective action for low-energy two-brane systems. It discusses inflation, primordial perturbations, graviton backreaction, and the CMB implications, highlighting how bulk physics introduces nonlocal effects via the projected Weyl tensor and radion dynamics. The review also covers brane collisions in cyclic and born-again scenarios, the challenges posed by bulk singularities, and the observational constraints on brane-induced variation of constants, delineating the path toward connecting brane cosmology with data. Overall, brane-world models offer intriguing mechanisms for cosmology and gravity but require deeper understanding of bulk dynamics and robust observational tests to establish their viability."

Abstract

Recent developments in the physics of extra dimensions have opened up new avenues to test such theories. We review cosmological aspects of brane world scenarios such as the Randall--Sundrum brane model and two--brane systems with a bulk scalar field. We start with the simplest brane world scenario leading to a consistent cosmology: a brane embedded in an Anti--de Sitter space--time. We generalise this setting to the case with a bulk scalar field and then to two--brane systems. We discuss different ways of obtaining a low--energy effective theory for two--brane systems, such as the moduli space approximation and the low--energy expansion. A comparison between the different methods is given. Cosmological perturbations are briefly discussed as well as early universe scenarios such as the cyclic model and the born--again brane world model. Finally we also present some physical consequences of brane world scenarios on the cosmic microwave background and the variation of constants.

Figures (6)

• Figure 1: As can be seen, increasing $\alpha$ results in a decrease of $n_R$, the power law index of the curvature perturbation power spectrum and in an increase of $r_T= P_T/16 P_R$. Taken from ashcroft2.
• Figure 2: Constraints on the parameter $\alpha$ and $\beta$, using the results from quasar spectra (hyperbolic curves) and different values for $\theta$. It is interesting to note that the observations, taken at face value, imply that $\alpha$ and $\beta$ are of the same order. Taken from palma.
• Figure 3: Effects of the bulk gravitational field in brane worlds for constant radion and adiabatic perturbations. The quantity $\delta C_{\rm Weyl}$ quantifies the amplitude of the perturbations in the Weyl fluid. $\zeta_*$ denotes here the curvature perturbation due to dark radiation. Taken from koyamacmb.
• Figure 4: Influence of the radion on the CMB anisotropies in a two brane system in which the radion is allowed to move. The values in the legend denote the initial value of the radion in Planck units. During cosmological evolution, the radion is driven towards zero. The spectra are normalised to COBE. Taken from chriscmb.
• Figure 5: Damping of tensor modes in the Randall--Sundrum brane world due to the creation of massive modes. Here, $\epsilon_* = \rho_0/\lambda$ at the start of integration and $\gamma$ is a parameter specifying the brane position. Taken from tensor4.