Quantum generations of cosmological perturbations in generalized gravity

We present a unified way of analysing the quantum generation process of cosmological perturbations in generalized gravity theories. We consider a situation where an accelerated expansion phase of the early universe is realized in a particular generic phase of the generalized gravity. We take the perturbative semiclassical approximation, which treats the perturbed parts of the metric and matter fields as quantum mechanical operators. Our generic results include the conventional power-law and exponential inflations in Einstein gravity, and the pole-like inflations available in a class of generalized gravity theories without potential as special cases. Using a conserved variable in the large scale, independent of the changes in the underlying gravity, we can derive the generated classical spectra of the hydrodynamic variables in the recent Einstein era. We also show that the conformal transformation properly reduces the (quantum) results derived in the original frame of generalized gravity to the ones in Einstein gravity.