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Assuming axions are potential dark matter (DM) candidate that make up all of the DM abundance, we discuss production of axions via (i) standard misalignment mechanism during the period of reheating and (ii) graviton-mediated 2-to-2 scattering of the inflaton and bath particles, where the inflaton oscillates in a monomial potential V () ^k with a general equation of state. Considering reheating takes place purely gravitationally, mediated by massless gravitons, we explore the viable region of the parameter space that agrees with the observed DM relic abundance, satisfying bounds from big bang nucleosynthesis and cosmic microwave background radiation. We also discuss complementarity between dedicated axion search experiments and futuristic gravitational wave search facilities in probing the viable parameter space, thanks to the presence of detectable primordial gravitational waves with an inflationary origin.
Barman et al. (Mon,) studied this question.