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  • Open Access

Analytic approximations for fermionic preheating

Heather E. Logan*, Daniel Stolarski†, and Fazlul Yasin‡

  • Ottawa-Carleton Institute for Physics, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario K1S 5B6, Canada

  • *Contact author: logan@physics.carleton.ca
  • †Contact author: stolar@physics.carleton.ca
  • ‡Contact author: FAZLULYASIN@cmail.carleton.ca
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Phys. Rev. D 114, 076012 – Published 6 October, 2026

DOI: https://doi.org/10.1103/p5hl-gkxv

Abstract

Nonthermal fermions can be produced nonperturbatively in the early Universe during coherent oscillations of a scalar field. We explore fermion production in λϕ4 inflation through this mechanism and analyze the momentum spectrum of the fermions produced, which depends on a coupling parameter q. For q≳0.01, the main contribution to the total number density comes from an approximately half-filled Fermi sphere as a result of nonadiabaticity. For q≲0.01, we find that the major contributions instead come from resonance peaks at higher momentum values. We find a simple relation to predict the momentum values corresponding to resonance peaks for any q. We observe power-law behavior for the total number density of fermions as a function of q and find numerical approximations for the integrals describing the total number density. We find that it is proportional to q1/2 for q≲0.01 and proportional to q3/4 for q≳10. If fermions produced by this mechanism make up the entirety of dark matter, we estimate lower bounds on their mass.

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Phys. Rev. D 114, 076012– Published 6 October, 2026
  • Received 20 April 2026
  • Accepted 14 September 2026
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