Cosmological probes of grand unification: Primordial black holes and scalar-induced gravitational waves
Anish Ghoshal, Ahmad Moursy, Qaisar Shafi
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 $r\ensuremath{\simeq}0.025$ 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 ${10}^{17}--{10}^{18}\text{ }\text{ }\mathrm{g}$ (${10}^{\ensuremath{-}16}--{10}^{\ensuremath{-}15}{M}_{\ensuremath{\bigodot}}$). 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 ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{GW}}{h}^{2}\ensuremath{\sim}5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}--{10}^{\ensuremath{-}8}$ and peak frequency ${f}_{\mathrm{peak}}\ensuremath{\sim}(0.1--300)\text{ }\text{ }\mathrm{Hz}$, 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.