  We compute numerically the reheating temperature due to the gravitational
production of conformally coupled superheavy particles during the phase
transition from the end of inflation to the beginning of kination in two
different Quintessential Inflation (QI) scenarios, namely Lorentzian
Quintessential Inflation (LQI) and $\alpha$-attractors in the context of
Quintessential Inflation ($\alpha$-QI). Once these superheavy particles have
been created, they must decay into lighter ones to form a relativistic plasma,
whose energy density will eventually dominate the one of the inflaton field in
order to reheat after inflation our universe with a very high temperature, in
both cases greater than $10^7$ GeV, contrary to the usual belief that heavy
masses suppress the particle production and, thus, lead to an inefficient
reheating temperature. Finally, we will show that the over-production of
Gravitational Waves (GWs) during this phase transition, when one deals with our
models, does not disturb the Big Bang Nucleosynthesis (BBN) success.

General Relativity and Quantum Cosmology;High Energy Physics - Theory