In a series of papers Boyanovsky et al. have studied the evolution of an inflaton with a negative mass squared and a quartic self coupling using the Closed Time Path (CTP) formalism relevant for out-of-equilibrium dynamics. In this paper we comment on various aspects of these works. We first compare their approach to alternate approaches to study inflaton dynamics and point out that the use of the CTP formalism gives the same results as standard field theory in the Hartree and leading order large N approximations. We then rederive using the WKB approximation the large momentum mode functions of the inflaton needed for renormalisation and point out some differences with the previously obtained results. We also argue that the WKB approximation is valid only for large $k/a$ and not for large $k$ as apparently assumed in the above mentioned works. We comment on the renormalisation prescription adopted in these works and finally discuss how it differs from another more commonly used prescription.
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