Primordial black holes in Gauss-Bonnet gravity

Abstract

In this paper, we investigate the production of primordial black holes (PBHs) during the preheating era. Indeed, the amplification of field fluctuations can lead to the amplification of curvature perturbations. The overproduction of primordial black holes can occur if curvature perturbations on small scales are sufficiently large. In this study, we explore the Gauss-Bonnet inflation model with Power-law potential, V ( ϕ ) = V 0 ϕ n , and monomial Gauss-Bonnet coupling function, ξ ( ϕ ) = ξ 0 ϕ n . Additionally, we examine a two-field preheating model with a quadratic inflaton potential. After that, we calculate and present the mass variance and the fraction of the total energy density collapsing into PBHs taking into account some specific values of the parameter, α , relating the dimensionless constants of the power-law potential and the monomial coupling function, for n = 2 . Our findings indicate that the PBHs production is influenced by the model parameter with an increasing probability of PBHs production as α increases. Furthermore, the duration of preheating, m Δ t , affects the range of k / k end within which PBHs production is consistent with observations. Finally, we study the abundance of PBHs produced. In the case where m Δ t = 10 and n = 2 , we find that PBHs can constitute a fraction of the present dark matter in the Universe for the three considered values of α , namely α = − 1.5 × 10 − 6 , − 2 × 10 − 6 and − 2.5 × 10 − 6 .