Light in dielectric media and scalar fields in a de Sitter spacetime

Abstract

Abstract In the present work we discuss the behavior of light in a linear dielectric medium with a time-varying electric permittivity that increases exponentially at a constant rate and of a scalar field in a de Sitter spacetime, in both the classical and quantum contexts. Notably, we find that the behavior of these two systems are identical and can be described by similar Hamiltonians. By using the Lewis–Riesenfeld invariant method together with Fock states we solve the time-dependent Schrödinger equation for this problem and use its solutions to construct coherent states for the scalar field. Finally, we employ both the Fock and coherent states to evaluate some important properties of the quantized scalar field, such as expectation values of the amplitude and momentum of each mode their variances and the respective uncertainty principle.