The growing cosmological interest of different entropy functions (like the
Tsallis entropy, the R\'{e}nyi entropy, the Barrow entropy, the Sharma-Mittal
entropy, the Kaniadakis entropy and the Loop Quantum gravity entropy) naturally
raises an important question: "Does there exist a generalized entropy that can
bring all the known entropies proposed so far within a single umbrella?" In
spirit of this, recently a four parameter generalized entropy has been
formulated that reduces to different known entropies for suitable limits of the
parameters. Based on such four parameter generalized entropy (symbolized by
Sgβ), in the present paper, we examine the universe's evolution
during its early phase, particularly from inflation to reheating, in the
context of entropic cosmology where the entropic energy density acts as the
inflaton. It turns out that the entropic energy successfully drives an early
inflationary phase with a graceful exit, and moreover, the theoretical
expectations of the observable indices get consistent with the recent Planck
data for suitable ranges of the entropic parameters. After the inflation ends,
the universe enters to a reheating stage when the entropic energy decays to
relativistic particles with a certain decay rate. Actually the presence of the
entropic parameters in the Sgβ ensures a continuous evolution of the
Hubble parameter from a quasi de-Sitter phase during the inflation to a power
law phase during the reheating stage dominated by a constant EoS parameter.
Consequently we investigate the reheating phenomenology, and scan the entropic
parameters from both the inflation and reheating requirements. We further
address the possibility of instantaneous reheating in the present context of
generalized entropy.Comment: "Physics of the Dark Universe" Accepte