Weyl invariance and the conductivity of the protoinflationary plasma

TL;DR

This paper investigates how Weyl invariance in a protoinflationary plasma influences initial electromagnetic conditions, affecting large-scale magnetic field amplification during inflation, especially when the number of efolds is minimal.

Contribution

It introduces a new framework for initial conditions based on plasma conductivity influenced by Weyl invariance breaking, contrasting with traditional vacuum assumptions.

Findings

Conductivity remains approximately constant during protoinflation due to Weyl invariance.

Breaking of Weyl invariance causes conductivity to decrease to zero after protoinflation.

Conducting initial conditions significantly impact magnetic field amplification when inflation is minimal.

Abstract

We consider a globally neutral Lorentzian plasma as a possible remnant of a preinflationary stage of expansion and pose the problem of the suitable initial conditions for the evolution of the large-scale electromagnetic inhomogeneities. During the protoinflationary regime the Weyl invariance of the Ohmic current guarantees that the comoving conductivity is approximately constant. The subsequent breaking of Weyl invariance by the masses of the charge carriers drives the conductivity to zero. The newly derived conducting initial conditions for the amplification of large-scale magnetic fields are contrasted with the conventional vacuum initial conditions. It is shown, in a specific class of examples, that when the number of inflationary efolds is close to minimal the effects of the conducting initial conditions cannot be neglected.