A note on the semiclassicality of cosmological perturbations

TL;DR

This paper argues that cosmological perturbations should be described using the semiclassical limit of quantum fields, extending from scalar to Dirac fermion fields, emphasizing their fundamental quantum nature.

Contribution

It demonstrates that cosmological perturbations can be consistently described by the expectation values of quantum fields, including Dirac fermions, within the semiclassical framework.

Findings

Cosmological perturbations are best described by the semiclassical limit of quantum fields.

Expectation values of Dirac fermion bilinears can serve as scalar quantities under diffeomorphisms.

The work extends the treatment of cosmological perturbations from scalar to fermionic quantum fields.

Abstract

Moving from the consideration that matter fields must be treated in terms of their fundamental quantum counterparts, we show straightforward arguments, within the framework of ordinary quantum mechanics and quantum field theory, in order to convince readers that cosmological perturbations must be addressed in term of the semiclassical limit of the expectation value of quantum fields. We first take into account cosmological perturbations originated by a quantum scalar field, and then extend our treatment in order to account for the expectation values of bilinears of Dirac fermion fields. The latter can indeed transform as scalar quantities under diffeomorphisms, as well as all the other bilinear of the Dirac fields that belong to the Clifford algebra. This is the first of a series of works that is intended to prove that cosmological quantum perturbations can actually be accounted for in terms of Dirac fermion fields, which must be treated as fundamental quantum objects, and their dynamics.