Abstract
The author presents cosmological perturbation equations for a theory with the Lagrangian L approximately f(R)+ gamma RR;c;c, where the second term leads to a sixth-order theory in the metric. Equations for both density and gravitational wave perturbations are derived in a gauge-invariant way where the density perturbation equation becomes a fourth-order differential equation. The integral form solution of the gravitational wave perturbations in the large scale is shown and it can be applied to a wide variety of gravity theories.
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