Abstract
We have derived second-order differential equations for cosmological perturbations, using gauge-invariant variables in a Friedmann-Lema\^{\i}tre-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.
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