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

An improved version of the well-known Peebles-Vilenkin model unifying early inflationary era to current cosmic acceleration, is introduced in order to match with the theoretical values of the spectral quantities provided by it with the recent observational data about the early universe. Since the model presents a sudden phase transition, we consider the simplest way to reheat the universe - via the gravitational production of heavy massive particles - which assuming that inflation starts at GUT scales $\sim 10^{16}$ GeV, allows us to use the Wentzel-Kramers-Brillouin (WKB) approximation and consequently this enables us to perform all the calculations in an analytic way. Our results show that the model leads to a maximum temperature at the TeV regime, and passes the bounds to ensure the success of the Big Bang Nucleosynthesis. Finally, we have constrained the quintessence piece of the proposed improved version of the Peebles-Vilenkin model using various astronomical datasets available at present.