Primordial black holes from Higgs inflation with a Gauss-Bonnet coupling
Ryodai Kawaguchi, Shinji Tsujikawa
Abstract
Primordial black holes (PBHs) can be the source for all or a part of today's dark matter density. Inflation provides a mechanism for generating the seeds of PBHs in the presence of a temporal period where the velocity of an inflaton field $\ensuremath{\phi}$ rapidly decreases toward 0. We compute the primordial power spectra of curvature perturbations generated during Gauss-Bonnet (GB) corrected Higgs inflation in which the inflaton field has not only a nonminimal coupling to gravity but also a GB coupling. For a scalar-GB coupling exhibiting a rapid change during inflation, we show that curvature perturbations are sufficiently enhanced by the appearance of an effective potential ${V}_{\mathrm{eff}}(\ensuremath{\phi})$ containing the structures of plateau type, bump type, and their intermediate type. We find that there are parameter spaces in which PBHs can constitute all dark matter for these three types of ${V}_{\mathrm{eff}}(\ensuremath{\phi})$. In particular, models with bump and intermediate types give rise to primordial scalar and tensor power spectra consistent with the recent Planck data on scales relevant to the observations of the cosmic microwave background. This property is attributed to the fact that the number of e-foldings $\mathrm{\ensuremath{\Delta}}{N}_{c}$ acquired around the bump region of ${V}_{\mathrm{eff}}(\ensuremath{\phi})$ can be as small as a few, in contrast to the plateau type, where $\mathrm{\ensuremath{\Delta}}{N}_{c}$ typically exceeds the order of 10.