Cosmological perturbations in generalized gravity theories: inflationary spectrum

Classical evolution of density perturbations, while the scale remains in the large scale limit, is clarified in the following generalized gravity theories: f(R) gravity, generalized scalar tensor theory, gravity with non-minimally coupled scalar field and induced gravity. The author uses gauge-invariant potential and field variables and shows that the result can be expressed in a similar form to a conventional result derived in Einstein gravity with a minimally coupled scalar field. The author rederives the solutions in the large scale in a simple way using the conformal transformation properties of these theories. The author gives a general prescription for calculating the inflationary spectrum in these gravity theories which can be applicable to specific models.