Exact non-linear equations for cosmological perturbations

Abstract

We present a complete set of exact and fully non-linear equations describing all three types of cosmological perturbations -- scalar, vector and tensor perturbations. We derive the equations in a thoroughly gauge-ready manner, so that any spatial and temporal gauge conditions can be employed. The equations are completely general without any physical restriction except that we assume a flat homogeneous and isotropic universe as a background. We also comment briefly on the application of our formulation to the non-expanding Minkowski background.

(v1) 10 pages, 1 table; (v2) important update to employ any spatial gauge condition; (v3) more discussions, to appear in Journal of Cosmology and Astroparticle Physics