GW231123 mass gap event and the primordial black hole scenario

We investigate the possibility that the recently reported GW231123 event, with component masses ${M}_{1}=13{7}_{\ensuremath{-}17}^{+22}{M}_{\ensuremath{\bigodot}}$ and ${M}_{2}=10{3}_{\ensuremath{-}52}^{+20}{M}_{\ensuremath{\bigodot}}$ and a local merger rate ${R}_{\text{local}}=0.0{8}_{\ensuremath{-}0.07}^{+0.19}\text{ }\text{ }{\mathrm{Gpc}}^{\ensuremath{-}3}\text{ }{\mathrm{yr}}^{\ensuremath{-}1}$, originates from primordial black holes (PBHs) formed during an early matter-dominated era. We compute the PBH mass function, abundance, spin distribution, and merger rate density and find a set of choices for the parameters to reproduce the key properties of GW231123. While PBHs formed in such a scenario can acquire large spins through sustained tidal torques, the spin distribution remains uncertain, and additional accretion might lead to extreme spin values inferred in GW231123. We also show that the resulting PBH abundance ${f}_{\mathrm{pbh}}=1.6{4}_{\ensuremath{-}1.59}^{+5.00}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}1}$ lies close to the exclusion bounds from cosmic microwave background accretion limits and other probes, highlighting a potential tension with current constraints. Finally, we estimate the scalar-induced gravitational waves that are inevitably generated during PBH formation. PBHs that interpret GW231123 are accompanied by negligible scalar-induced gravitational waves in the nanohertz band, indicating no conflict with current pulsar timing array data.