Cosmological probes of Grand Unification: Primordial Blackholes & scalar-induced Gravitational Waves

We investigate the inflationary cosmology involving an SU(5) GUT (grand unified theory) singlet scalar with non-minimal coupling to the Ricci scalar. In this scenario the scale of grand unification is set by the inflaton vev when the inflaton rolls down its potential towards its minimum $v$, thereby relating inflationary dynamics to GUT symmetry breaking with a prediction $r \simeq 0.025$ for the tensor-to-scalar ratio to be tested by the next generation CMB experiments. We show in this inflationary framework involving inflection-point how a suitable choice of parameters in $SU(5)$ leads to a bump in the scalar power spectrum with production of Primordial Blackholes (PBH) of masses $10^{17}-10^{18}$g ($ 10 - 100 M_\odot$). 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 (GW) with amplitude $\Omega_{\rm GW}h^2 \sim 10^{-17}$ and peak frequency $f_{\rm peak} \sim$ (0.1 - 1) 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.