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Primordial gravitational waves (GWs) carry the imprints of the dynamics ofthe universe during its earliest stages. With a variety of GW detectors beingproposed to operate over a wide range of frequencies, there is greatexpectation that observations of primordial GWs can provide us with anunprecedented window to the physics operating during inflation and reheating.In this work, we closely examine the effects of the regime of reheating on thespectrum of primordial GWs observed today. We consider a scenario wherein thephase of reheating is described by an averaged equation of state (EoS)parameter with an abrupt transition to radiation domination as well as ascenario wherein there is a gradual change in the effective EoS parameter tothat of radiation due to the perturbative decay of the inflaton. We show thatthe perturbative decay of the inflaton leads to oscillations in the spectrum ofGWs, which, if observed, can possibly help us decipher finer aspects of thereheating mechanism. We also examine the effects of a secondary phase ofreheating arising due to a brief epoch driven possibly by an exotic,non-canonical, scalar field. Interestingly, we find that, for suitable valuesof the EoS parameter governing the secondary phase of reheating, the GWs can beof the strength as suggested by the recent NANOGrav observations. We concludewith a discussion of the wider implications of our analysis.

Decoding the phases of early and late time reheating through imprints on primordial gravitational waves