Baryogenesis in Conformally Flat Spacetimes
Felix Finster, Marco van den Beld-Serrano
TL;DR
This work extends a causal-fermion-systems baryogenesis mechanism from Minkowski space to conformally flat spacetimes by introducing a regularizing timelike vector field $u$ and a symmetrized Hamiltonian $A_t$ that drives locally rigid spinor dynamics. Through a perturbative spectral calculus in $ ext{Δ}A(t)=A_t- ilde{H}_{ ilde{η}}$, the authors derive a leading second-order expression for the baryogenesis rate $B_t^{(2)}$ that depends on the conformal factor $ ext{Ω}$, the particle mass $m$, and the regularizing field $u$, with the kernel $G_{ ext{Ω},m,u}$ encoding the geometric and dynamical data. They show $B_t^{(0)}=B_t^{(1)}=0$ under general conditions and analyze two key scenarios: a trivial regularization $u=∂_t$ where baryogenesis vanishes for massless states and reduces to specific $ ext{Ω}$-dependent form for $m≠0$, and a general $u$ where multiple operator contributions yield a richer, nonzero second-order rate even when $m=0$. The results provide a rigorous framework for quantitative predictions in cosmological spacetimes (FLRW, Milne, Milne-like) and pave the way for confronting the mechanism with the observed baryon asymmetry in the early universe.
Abstract
Based on a baryogenesis mechanism originating from the theory of causal fermion systems, we analyze its main geometric and analytic features in conformally flat spacetimes. An explicit formula is derived for the rate of baryogenesis in these spacetimes, which depends on the mass $m$ of the particles, the conformal factor $Ω$ and a future directed timelike vector field $u$ (dubbed the regularizing vector field). Our analysis covers Friedmann-Lema{î}tre-Robertson-Walker, Milne and Milne-like spacetimes. It sets the ground for concrete, quantitative predictions for specific cosmological spacetimes.