Abstract
We revisit the efficiency of Schwinger mechanism in creating charged pairs during inflation. We consider a minimal setup of inflation in which the inflaton field is a complex scalar field charged under a $U(1)$ gauge field. There is a time dependent conformal coupling which pumps energy from the inflaton field to the gauge field to furnish a nearly constant background electric field energy density to drive the Schwinger mechanism. The coupling between the gauge field and the scalar field induces a time dependent effective mass for the inflaton field. The requirement of a long period of slow-roll inflation causes the Schwinger mechanism to be highly inefficient during inflation. The non-perturbative Schwinger mechanism can be relevant only towards the end of inflation and only on very small scales. This is in contrast to hypothetical models studied in literature in which the complex scalar field is a test field and a constant electric field is imposed on the dS background by hand. We calculate the number of pairs of charged particles created perturbatively during inflation. We show that it is proportional to the amplitude of the quadrupolar statistical anisotropy and it is very small. Consequently, the back-reactions of created particles on magnetogenesis on large scales are negligible.
Highlights
The time dependent nature of the background, whether originating from gravitation or electric fields, leads to particle creation from vacuum [1]
II we review the model of charged anisotropic inflation and explain how a nearly constant electric field in quasi–de Sitter background arises in this model
This analysis shows that the nonperturbative Schwinger pair production does not take place during most of period of inflation and may be relevant only towards the end of inflation. This conclusion is the key difference of our model compared to other less realistic scenarios studied in previous works on Schwinger mechanism during inflation. This is because we took the complex scalar field to be the inflaton field itself which is responsible for curvature perturbations, and not a hypothetical test field decoupled from inflation
Summary
The time dependent nature of the background, whether originating from gravitation or electric fields, leads to particle creation from vacuum [1]. Several attempts were made in order to study Schwinger pair production by electric field coupled to inflaton and its backreaction to the background geometry [17,21,22] This leads to some difficulties in solving the equations of motion of a charged scalar field to find the mode functions and interpret them in terms of positive and negative frequency modes [21]. The charged particle production rate depends on the direction of these particles with respect to the background electric field and leaves a unique angular dependence on the primordial spectra In all of these studies the complex scalar field, which is responsible for the pair production, is considered to be a test field during inflation while the dS spacetime is driven by the real inflaton field.
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