Amplifying quantum discord during inflationary magnetogenesis through violation of parity

Abstract

It is well known that, during inflation, the conformal invariance of the electromagnetic action has to be broken in order to produce magnetic fields of observed strengths today. Often, to further enhance the strengths of the magnetic fields, parity is also assumed to be violated when the fields are being generated. In this work, we examine the evolution of the quantum state of the Fourier modes of the non-conformally coupled and parity violating electromagnetic field during inflation. We utilize tools such as the Wigner ellipse, squeezing parameters and quantum discord to understand the evolution of the field. We show that the violation of parity leads to an enhancement of the squeezing amplitude and the quantum discord (or, equivalently, in this context, the entanglement entropy) associated with a pair of opposite wave vectors for one of the two states of polarization (and a suppression for the other state of polarization), when compared to the case wherein parity is conserved. We highlight the similarities between the evolution of the Fourier modes of the electromagnetic field when parity is violated during inflation and the behavior of the modes of a charged, quantum, scalar field in the presence of a constant electric field in a de Sitter universe. We briefly discuss the implications of the results we obtain.