Probing the initial mass function of the first stars with transients

The emergence of the first, so-called Population III (Pop III), stars shaped early cosmic history in ways that crucially depends on their initial mass function (IMF). However, because absence direct observational constraints, detailed IMF remains elusive. Nevertheless, numerical simulations agree broad terms first were typically massive and should often end lives violent, explosive deaths. These fates include extremely luminous pair-instability supernovae (PISNe) bright gamma-ray bursts (GRBs), latter arising from collapse rapidly rotating progenitor into black holes. high-redshift transients are expected to be within detection limits upcoming space telescope missions, allowing place effective constraints shape primordial is not easily accessible with other probes. This paper presents a framework probe Pop IMF, utilizing cosmological source densities PISNe GRBs. Considering these separately could provide useful but tighter bounds obtainable by combining PISN GRB counts. combined diagnostic more robust as it independent underlying star formation rate density, an unknown prior. Future surveys promise capture most GRBs across entire sky, searches future telescopes, e.g. Roman Space Telescope, will likely substantially incomplete. we demonstrate even such lower count able key particular, if top-heavy or not.