We study the consequences of reheating in quintessential inflation. From simple inflationary quintessential models introduced in [1,2], we show that when the reheating is due to the production of heavy massive particles conformally coupled with gravity, a viable model which matches with the current observational data [3][4][5] is only possible for reheating temperatures that range between 1 GeV and 10 4 GeV. On the other hand, when the universe reheats via the production of massless particles, the viability of the model is only possible when those particles are nearly conformally coupled with gravity, leading to a reheating temperature between 1 MeV and 10 4 GeV. INTRODUCTIONIn two recent papers [1, 2] some families of quintessential inflation models have been obtained, coming from very simple polynomial potentials which fit well with the current observational data provided by Planck's team [3,4] and the BICEP/Keck-Planck Collaboration [5]. The models unify the early inflationary period with the current cosmic acceleration and contain a phase transition from the inflationary phase to a kination regime, which is essential to produce enough particles to thermalize the universe with a reheating temperature compatible with the bounds coming from nucleosynthesis.In the present work we explore the consequences and constraints that one obtains from the relation that exists between the spectral index and the reheating temperature. This relation comes from the fact that the number of efolds could be obtained in two completely different ways: by definition through an expression that only depends on the spectral index or using the whole history of the universe that leads to a function of the reheating temperature and the spectral index. On the other hand, to obtain simple expressions of the reheating temperature one can consider either the production of heavy massive particles conformally coupled with gravity or massless particles nearly conformally coupled with gravity.Therefore, for a given reheating temperature between 1 MeV and 10 9 GeV, which is required in order to have a successful nucleosynthesis [6], one obtains the corresponding value of the spectral index and, thus, the value of the ratio of tensor to scalar perturbations. Since this ratio must be less than 0.12 [5], this constrains the reheating temperature to range between 1 MeV and 10 4 GeV. Moreover, since in the case of creation of heavy particles the mass of these produced particles must be less than Planck's mass -in the opposite case these particles would become micro black holes-, the model only supports temperatures greater than 1 GeV and less than 10 4 GeV. Finally, dealing with massless particles, we have shown that the viability of the model is only possible when the coupling constant is very close to 1/6, i.e., the created particles have to be nearly conformally coupled with gravity.This low reheating temperature coming from the constraints that have been found in this paper leads to ensure a successful baryogenesis with thermal equilibrium [7] (1...

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We have tested some simple quintessential inflation models, imposing the requirement that they match with the recent observational data provided by the BICEP and Planck team and leading to a reheating temperature, which is obtained via gravitational particle production after inflation, supporting the nucleosynthesis success. Moreover, for the models coming from supergravity one needs to demand low temperatures in order to avoid problems such as the gravitino overproduction or the gravitational production of moduli fields, which are obtained only when the reheating temperature is due to the production of massless particles with a coupling constant very close to its conformal value.

Some of the most important quintessential inflation scenarios, such as the Peebles–Vilenkin model, are described in detail. These models are able to explain the early- and late-time accelerated expansions of our universe, and the phase transition from the end of inflation to the beginning of kination where the adiabatic evolution of the universe was broken in order to produce enough particles to reheat the universe with a viable temperature, thereby aligning with the Hot Big Bang universe. In addition, while considering the reheating to be due to the gravitational production of superheavy particles conformally coupled to gravity, we checked that the considered scenarios do not suffer problems due to the overproduction of gravitational waves at the end of inflation, and thus the validity of Big Bang nucleosynthesis is preserved.