A general proof of the conservation of the curvature perturbation.

Lyth, David H. and Malik, Karim A. and Sasaki, Misao (2005) A general proof of the conservation of the curvature perturbation. Journal of Cosmology and Astroparticle Physics, 0505. 004. ISSN 1475-7516

Abstract

Without invoking a perturbative expansion, we define the cosmological curvature perturbation, and consider its behaviour assuming that the universe is smooth over a sufficiently large comoving scale. The equations are simple, resembling closely the first-order equations, and they lead to results which generalize those already proven in linear perturbation theory and (in part) in second-order perturbation theory. In particular, the curvature perturbation is conserved provided that the pressure is a unique function of the energy density.