Quark, lepton and right-handed neutrino production via inflation

Inflationary expansion of space-time provides us with an efficient particle production mechanism in the Early Universe. The fermion production efficiency depends critically on the particle mass, which is generated via the Yukawa coupling and sensitive to the corresponding scalar field value. During inflation, scalar fields experience large quantum fluctuations driving the average field values to the Hubble scale and above. This applies, in particular, to the Higgs field, making the Standard Model fermions very heavy and facilitating their production. Using the Bogolyubov coefficient approach, we compute the corresponding fermion abundance taking into account time dependence of the mass term. We find that the Standard Model fermion and the right-handed neutrino production grows dramatically compared to the naive estimate based on the low energy masses. The inflationary production mechanism can be the leading source of the right handed neutrinos, if they gain a Majorana mass from the Yukawa coupling to a light scalar. We also find a lower bound on the mass of fermionic dark matter, which can be produced by inflation.

💡 Research Summary

The paper investigates how the rapid expansion of space during cosmic inflation can act as a highly efficient source of fermionic particles, including Standard Model (SM) quarks and leptons as well as right‑handed (sterile) neutrinos, which are potential dark‑matter candidates. The key observation is that fermion masses in the SM arise from Yukawa couplings to the Higgs field, (M_f = Y_f \langle h\rangle/\sqrt{2}). During inflation, light scalar fields experience large de Sitter‑induced quantum fluctuations, driving their vacuum expectation values (VEVs) to the order of the Hubble scale, (\langle h\rangle \sim H), unless a strong positive coupling to the inflaton or curvature suppresses this growth. Consequently, SM fermions become enormously heavy—by up to eleven orders of magnitude compared to their low‑energy values—during the inflationary epoch.

To quantify particle production, the authors employ the Bogoliubov‑coefficient formalism. In a conformally flat Friedmann‑Lemaître‑Robertson‑Walker (FLRW) background, the Dirac equation reduces to a flat‑space equation with a time‑dependent mass term, (i\gamma^\mu\partial_\mu\Psi - a(\eta)M(\eta)\Psi = 0). The time dependence of (M(\eta)) originates from the evolving Higgs (or singlet scalar) VEV. By solving the mode equations for the spinor components, they derive expressions for the Bogoliubov coefficients (\beta_k), whose squared magnitude gives the occupation number of each momentum mode after inflation.

Two representative mass‑evolution profiles are considered: (i) a sharp step‑function drop at the end of inflation, modeling an abrupt Higgs relaxation, and (ii) a smooth, adiabatic decrease, representing a more gradual relaxation. In the sharp case, the derivative term ((Ma)’) in the second‑order mode equations introduces a delta‑function‑like feature that significantly enhances particle production across a broad range of momenta. In the smooth case, the adiabaticity condition is partially broken for low‑momentum modes, still yielding a sizable (\beta_k). Both analytical approximations and full numerical integrations (with a smooth scale‑factor transition between inflation and radiation domination) confirm that the resulting fermion abundance scales far more steeply than the conventional estimate for a constant mass, \