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Molecular oxygen has been confirmed as the fourth most abundant molecule incometary material O$_2$/H$_2$O $\sim 4$ %) and is thought to have a primordialnature, i.e., coming from the interstellar cloud from which our solar systemwas formed. However, interstellar O$_2$ gas is notoriously difficult to detectand has only been observed in one potential precursor of a solar-like system.Here, the chemical and physical origin of O$_2$ in comets is investigated usingsophisticated astrochemical models. Three origins are considered: i) in darkclouds, ii) during forming protostellar disks, and iii) during luminosityoutbursts in disks. The dark cloud models show that reproduction of theobserved abundance of O$_2$ and related species in comet 67P/C-G requires a lowH/O ratio facilitated by a high total density ($\geq 10^5$ cm$^{-3}$), and amoderate cosmic ray ionisation rate ($\leq 10^{-16}$ s$^{-1}$) while atemperature of 20 K, slightly higher than the typical temperatures found indark clouds, also enhances the production of O$_2$. Disk models show that O$_2$can only be formed in the gas phase in intermediate disk layers, and cannotexplain the strong correlation between O$_2$ and H$_2$O in comet 67P/C-Gtogether with the weak correlation between other volatiles and H$_2$O. However,primordial O$_2$ ice can survive transport into the comet-forming regions ofdisks. Taken together, these models favour a dark cloud (or "primordial")origin for O$_2$ in comets, albeit for dark clouds which are warmer and denserthan those usually considered as solar system progenitors.

A primordial origin for molecular oxygen in comets: A chemical kinetics study of the formation and survival of O$_2$ ice from clouds to disks