Large-scale perturbations on the brane and the isotropy of the cosmological singularity

We present the complete set of propagation and constraint equations for the kinematic and nonlocal first order quantities which describe general linear inhomogeneous and anisotropic perturbations of a flat Friedmann-Robertson-Walker braneworld with vanishing cosmological constant and decompose them in the standard way into their scalar, vector and tensor contributions. A detailed analysis of the perturbation dynamics is performed using dimensionless variables that are specially tailored for the different regimes of interest; namely, the low energy general relativity regime, the high energy regime and the dark energy regime. Tables are presented for the evolution of all the physical quantities, making it easy to do a detailed comparison of the past asymptotic behavior of the perturbations of these models. We find results that exactly match those obtained in the analysis of the spatially inhomogeneous G2 braneworld cosmologies presented recently; i.e., that isotropization towards the Fb model occurs for γ>4/3