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Production of Massless Fermions during Inflation

T. Prokopec, R. P. Woodard

TL;DR

This work examines whether inflation can generate massless fermions when they interact via a Yukawa coupling with a massless, minimally coupled scalar in a de Sitter background. The authors compute the one-loop fermion self-energy and, using the Schwinger-Keldysh formalism, derive a nonlocal quantum-corrected Dirac equation to study late-time mode evolution; their initial claim of faster-than-exponential growth is later corrected by an Addendum, which shows the asymptotics are oscillatory with a decaying envelope rather than unbounded growth. The results illuminate how inflation’s energy nonconservation can enable the spontaneous appearance of a scalar and a fermion–anti-fermion pair, driving nonconformal particle production while conformally invariant fermions remain massless at one loop. The analysis clarifies differences from photon production in similar backgrounds and discusses higher-order effects such as Pauli blocking.

Abstract

We compute the one loop self energy, in a locally de Sitter background, for a massless fermion which is Yukawa-coupled to a massless, minimally coupled scalar. We then solve the modified Dirac equation resulting from inclusion of the self energy. We find faster-than-exponential growth in the fermion wave function, consistent with the production of fermions through a process in which a scalar and a fermion-anti-fermion pair are ripped out of the vacuum by inflation.

Production of Massless Fermions during Inflation

TL;DR

This work examines whether inflation can generate massless fermions when they interact via a Yukawa coupling with a massless, minimally coupled scalar in a de Sitter background. The authors compute the one-loop fermion self-energy and, using the Schwinger-Keldysh formalism, derive a nonlocal quantum-corrected Dirac equation to study late-time mode evolution; their initial claim of faster-than-exponential growth is later corrected by an Addendum, which shows the asymptotics are oscillatory with a decaying envelope rather than unbounded growth. The results illuminate how inflation’s energy nonconservation can enable the spontaneous appearance of a scalar and a fermion–anti-fermion pair, driving nonconformal particle production while conformally invariant fermions remain massless at one loop. The analysis clarifies differences from photon production in similar backgrounds and discusses higher-order effects such as Pauli blocking.

Abstract

We compute the one loop self energy, in a locally de Sitter background, for a massless fermion which is Yukawa-coupled to a massless, minimally coupled scalar. We then solve the modified Dirac equation resulting from inclusion of the self energy. We find faster-than-exponential growth in the fermion wave function, consistent with the production of fermions through a process in which a scalar and a fermion-anti-fermion pair are ripped out of the vacuum by inflation.

Paper Structure

This paper contains 7 sections, 66 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The one loop self energy
  3. Solving the modified Dirac equation
  4. The physics behind our result
  5. Massless minimally coupled scalars
  6. Production of fermions
  7. Discussion

Figures (1)

  • Figure 1: The one loop fermion self energy. Fermion lines have an arrow, scalar lines do not. The final diagram gives the contribution of field strength renormalization.