Electromagnetic waves propagation in time-varying dielectric media and in a de Sitter spacetime

In this work we investigate the propagation of electromagnetic waves in a homogenous dielectric linear medium with a time-varying electric permittivity modulated exponentially at a constant rate and in a de Sitter spacetime. We demonstrate that the classical and quantum dynamics of this propagation for both cases are equivalent and can be mapped into damped harmonic oscillators which are be generated by similar Hamiltonians. By making use of the Lewis and Riesenfeld invariant theory together with the Fock states we solve the time-dependent Schrödinger equation for this problem and evaluate some important properties of quantized light, such as coherent states, expectation values of the amplitude and momentum of each mode, their quantum variances and the corresponding uncertainty principle