Cosmological probes of grand unification: Primordial black holes and scalar-induced gravitational waves

Abstract

We investigate the inflationary cosmology involving an SU(5) GUT (grand unified theory) singlet scalar with nonminimal coupling to the Ricci scalar. In this scenario the scale of grand unification is set by the inflaton vacuum expectation value when the inflaton rolls down its potential towards its minimum v, thereby relating inflationary dynamics to GUT symmetry breaking with a prediction of r≃0.025 for the tensor-to-scalar ratio to be tested by the next generation of CMB experiments. We show in this inflationary framework involving an inflection point how a suitable choice of parameters in SU(5) leads to a bump in the scalar power spectrum with the production of primordial blackholes (PBH) of masses 1017-1018 g (10-16-10-15M⊙). We derive the constraints on the self-quartic and mixed-quartic couplings of the inflaton in SU(5) that are consistent with the inflationary analysis. Moreover, we also show that this scenario leads to large amplitude induced second-order tensor perturbations propagating as gravitational waves (GWs) with an amplitude ωGWh2∼5×10-10-10-8 and peak frequency fpeak∼(0.1-300) Hz, which can be detected in the next-generation GW observatories like LISA, BBO, ET, etc. Thus, we unify the SU(5) framework with PBH via inflection-point inflation showing how the upcoming measurements of PBH and GW will enable us to probe the scale of SU(5) symmetry breaking, and thereby complementing the laboratory-based experiments. We also discuss scenarios involving the Pati-Salam and trinification gauge groups and its impact on quartic and mixed-quartic couplings that may lead to PBH and detectable GW signals.