Unified treatment of cosmological perturbations from super-horizon to small scales
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We study the evolution of cosmological perturbations, using a hybrid approximation scheme which upgrades the weak-field limit of Einstein's field equations to account for post-Newtonian scalar and vector metric perturbations and for leading-order source terms of gravitational waves, while including also the first and second-order perturbative approximations. Our equations, which are derived in the Poisson gauge, provide a unified description of matter inhomogeneities in a Universe filled with a pressureless and irrotational fluid and a cosmological constant, ranging from the linear to the highly non-linear regime. The derived expressions for scalar, vector and tensor modes can have a wide range of cosmological applications, ranging from secondary CMB anisotropy and polarization effects, cosmographic relations in a inhomogeneous Universe, gravitational lensing effects and the stochastic gravitational-wave backgrounds generated by non-linear cosmic structures.
LaTeX file, 13 pages, typos corrected, improved calculations, new section added, matches published version
LaTeX file, 13 pages, typos corrected, improved calculations, new section added, matches published version