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An improved version of the well-known Peebles-Vilenkin model unifying earlyinflationary era to current cosmic acceleration, is introduced in order tomatch with the theoretical values of the spectral quantities provided by itwith the recent observational data about the early universe. Since the modelpresents a sudden phase transition, we consider the simplest way to reheat theuniverse - via the gravitational production of heavy massive particles - whichassuming that inflation starts at GUT scales $\sim 10^{16}$ GeV, allows us touse the Wentzel-Kramers-Brillouin (WKB) approximation and consequently thisenables us to perform all the calculations in an analytic way. Our results showthat the model leads to a maximum temperature at the TeV regime, and passes thebounds to ensure the success of the Big Bang Nucleosynthesis. Finally, we haveconstrained the quintessence piece of the proposed improved version of thePeebles-Vilenkin model using various astronomical datasets available atpresent.

Reheating in quintessential inflation via gravitational production of heavy massive particles: A detailed analysis