Implication of preheating on gravity assisted baryogenesis in $R^2$-Higgs inflation

Abstract

We investigate the impact of preheating on baryogenesis in $R^2$-Higgs inflation. In this scenario, the inclusion of a dimension-six operator $(R/{\Lambda }^2)B_{\mu \nu }{\tilde{B}}^{\mu \nu }$ abundantly generates helical hypermagnetic fields during inflation, leading to a baryon asymmetric Universe at the electroweak crossover. Focusing on the $R^2$-like regime, we first derive the relevant dynamics of preheating using a doubly-covariant formalism. We find that preheating can happen for the Higgs, transverse gauge and Goldstone bosons, however, it is dependent on the value of the non-minimal coupling ${\xi }_H$ between the Standard Model Higgs field and the Ricci scalar. We identify the preheating temperature to determine the appropriate scale $\Lambda$ for driving baryogenesis, which is around $\Lambda \sim 2.2(2.6)\times 10^{-5}{M}_{\mathrm{P}}$ for ${\xi }_H\sim 1(10)$. Our results represent the most accurate estimation of the scale of gravity induced baryogenesis in $R^2$-Higgs inflation to date. Areas for further improvement are identified.

Comments: 37 pages, 16 figures