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Increasingly accurate observations of the cosmic microwave background and thelarge scale distribution of galaxies necessitate the study of nonlinearperturbations of Friedmann-Lemaitre cosmologies, whose equations arenotoriously complicated. In this paper we present a new derivation of thegoverning equations for second order perturbations within the framework of themetric-based approach that is minimal, as regards amount of calculation andlength of expressions, and flexible, as regards choice of gauge andstress-energy tensor. Because of their generality and the simplicity of theirstructure our equations provide a convenient starting point for determining thebehaviour of nonlinear perturbations of FL cosmologies with any givenstress-energy content, using either the Poisson gauge or the uniform curvaturegauge.

A simplified structure for the second order cosmological perturbation equations