After reading the book Das Dunkle Universum by Adalbert Pauldrach ( which btw is very well written) questions remain regarding the Higgs field and it's role in the early universe. According to the hypothesis by Tulin and Servant, initially Higgs and anti-Higgs Bosons formed. Since the former interacted and produced mass particles, anti-Higgs Bosons had no more partners to interact and are sitting around as dark matter.
Question: Can anti-Higgs particles have formed before any baryonic matter existed or is the Higgs boson always its own anti-particle ? Is it plausible that a particle with a half-life of $1.56 × 10^{−22}s$ can stay around for 14 billion years because it has no reaction partners ?
Regarding the Higgs field: does it have the size of the universe or are there innumerable individual fields in the universe?