Schwinger effect in 4D de Sitter space and constraints on magnetogenesis in the early universe

Abstract

We investigate pair creation by an electric field in four-dimensional de Sitter space. The expectation value of the induced current is computed, using the method of adiabatic regularization. Under strong electric fields the behavior of the current is similar to that in flat space, while under weak electric fields the current becomes inversely proportional to the mass squared of the charged field. Thus we find that the de Sitter space obtains a large conductivity under weak electric fields in the presence of a charged field with a tiny mass. We then apply the results to constrain electromagnetic fields in the early universe. In particular, we study cosmological scenarios for generating large-scale magnetic fields during the inflationary era. Electric fields generated along with the magnetic fields can induce sufficiently large conductivity to terminate the phase of magnetogenesis. For inflationary magnetogenesis models with a modified Maxwell kinetic term, the generated magnetic fields cannot exceed 10 −30 G on Mpc scales in the present epoch, when a charged field carrying an elementary charge with mass of order the Hubble scale or smaller exists in the Lagrangian. Similar constraints from the Schwinger effect apply for other magnetogenesis mechanisms.

Schwinger mechanism in electromagnetic field in de Sitter spacetime

“…Since the Bogoliubov coefficient β is independent of the momentum k x , the integral gives eBL y /(2π) from the position of the center of the wave packet. Under the semiclassical condition [2,3] …”

“…the time when most of the particles are created, estimates τk z ∼ −|γ| [2,3], hence the k z integral can be transformed into a τ integral. We then obtain…”

“…Since the early universe scenarios predict the existence of strong electromagnetic fields, it is natural to consider the Schwinger effect in this context. The pioneering works studied this effect in the 1+1 dimensional [2] and 1+3 dimensional [3] de Sitter spacetimes. To describe Schwinger effect in a curved spacetime, the more relevant quantity is the induced current [2,3].…”

“…The pioneering works studied this effect in the 1+1 dimensional [2] and 1+3 dimensional [3] de Sitter spacetimes. To describe Schwinger effect in a curved spacetime, the more relevant quantity is the induced current [2,3]. Indeed, it is not plagued by the notion of particle in the adiabatic future, which allows one to explore a broader parameter space.…”

Pair creation in the early universe

“…One of the simplest curved spacetime is de Sitter spacetime which is believed to be of great importance both for inflationary scenarii and late time acceleration of the expansion of the universe. In the recent litterature, these generalisations of the Schwinger effect in curved spacetime were investigated and permit to be conclusive on many theoretical problems: bubble nucleation, 4 testing the conjecture ER=EPR, 5 constraining magnetogenesis, 6 connecting Hawking and Unruh effect to Schwinger effect.…”