Scalar Field Perturbations with Arbitrary Potentials in Quantum Backgrounds

Understand

In this paper it is shown how to obtain, without ever using the background classical equations of motion, a simple second order Hamiltonian involving the Mukhanov-Sasaki variable describing quantum linear scalar perturbations for the case of scalar fields with arbitrary potentials and arbitrary spacelike hyper-surfaces.

• It is a generalization of previous works, where the scalar field potential was absent and the spacelike hypersurfaces were flat.
• This was possible due to the implementation of a new method, together with the Faddeev-Jackiw procedure for the constraint reduction.
• The resulting Hamiltonian can then be used to study the evolution of quantum cosmological perturbations in quantum backgrounds.