Spontaneous baryogenesis with large misalignment

Abstract

We investigate particle production by a pseudo-Nambu-Goldstone boson (pNGB) in the spontaneous baryogenesis scenario for large misalignment angles. Since the fermionic backreaction is intrinsically nonlocal in time, the large-angle problem is in general difficult to treat directly. We argue that the adiabaticity conditions are parametrically satisfied in the model, allowing the backreaction to be described by a local Markovian approximation while retaining the nonlinear dependence of the pNGB potential on the angular field. Through a numerical study of arbitrary initial phases, we reproduce the cubic dependence of the baryon asymmetry for small oscillations and demonstrate that this behavior breaks down for large oscillations, especially for initial phases close to $\pi$. Our calculations indicate that particle production saturates as the initial phase approaches $\pi$ in Minkowski spacetime. The analysis is then extended to conformal Friedmann--Lema\^itre--Robertson--Walker (FLRW) spacetime, where the generated asymmetry shows a pronounced dependence on the damping rate of the pNGB motion. We further discuss the baryon-isocurvature bound on the ratio $H_\star/f$ and present sample parameter sets that satisfy this constraint at large misalignment. We also discuss the probability distribution of the baryon asymmetry.