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Quark, lepton and right-handed neutrino production via inflation

Duarte Feiteira, Fotis Koutroulis, Oleg Lebedev, Stefan Pokorski

Abstract

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.

Quark, lepton and right-handed neutrino production via inflation

Abstract

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.

Paper Structure

This paper contains 26 sections, 143 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Basics of fermion production in an expanding Universe
  3. Fermion production with a time-dependent mass: inflation followed by radiation domination
  4. Fermion masses via Yukawa couplings: the Early Universe
  5. Radiation dominated era
  6. Step-function mass term
  7. Slow effective mass decrease and thermal effects
  8. Standard Model fermion and right-handed neutrino production via inflation
  9. Quark and lepton production
  10. Sharp effective mass decrease
  11. Slow effective mass decrease
  12. Top-quark production
  13. No Higgs condensate
  14. Inflationary production of the right-handed neutrinos due to the Higgs coupling
  15. Production of $\nu_R$ due to the background evolution
  16. ...and 11 more sections

Figures (5)

  • Figure 1: Hubble rate evolution assumed in this work. Inflation ends at $a\sim a_e$ and is followed by the radiation or matter domination epochs.
  • Figure 2: Bogolyubov coefficient squared for a constant fermion mass (blue) and piece-wise constant mass (grey). Radiation domination after inflation is assumed and $m= 10^{-5} H_e\,,\, M= 10^{-2} H_e\,, N=6\,.$
  • Figure 3: Effective fermion mass evolution: (1) abrupt, (2) smoothed by thermal effects.
  • Figure 4: Bogolyubov coefficient squared for a fermion with a thermal mass during radiation domination. Left: The orange, blue, green curves correspond to $M/H_e= 10^{-2}, 10^{-3}, 10^{-4} \;,$ respectively, and $m/H_e = 10^{-5}$. The occupation number drops above $k_*^{\rm th}$. Right: Comparison of the results for different thermal mass scaling laws: $M(T)\propto a^{-1}$ vs $M(T)\propto a^{-1/2 }$, with the other parameters fixed.
  • Figure 5: Bogolyubov coefficient squared for $N=6,20,100$ and step-function mass variation. Radiation domination after inflation is assumed and $m= 10^{-5} H_e\,,\, M= 10^{-2} H_e\,.$ At large $N$, the curves approach the single mass $|\beta_k|^2$ with the momentum cutoff $M^{1/2} H_e^{1/2} a_e$.