COSMOLOGICAL PERTURBATIONS IN GENERALIZED GRAVITY THEORIES - SOLUTIONS

We have derived second-order differential equations for cosmological perturbations, using gauge-invariant variables in a Friedmann-Lemaître- Robertson-Walker background, for each of the following gravity theories: f(R) gravity, generalized scalar-tensor gravity, gravity with nonminimally coupled scalar field, and induced gravity. Assuming a spatially flat background, each equation is put into a form suggested by Mukhanov, and asymptotic solutions are derived for the large- and small-scale limits. We also present conservation quantities which remain constant in the large-scale limit. © 1990 The American Physical Society.