Abstract
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.
Highlights
Understanding the universe’s evolution is one of the greatest mysteries in the history of humanity
In this subsection we aim to find the relation between the number of e-folds from the horizon crossing to the end of inflation and the reheating temperature Treh
In the present review we have dealt with some important quintessential inflation scenarios, namely, the original Peebles–Vilenkin one—the first quintessential inflation model introduced at the end of the 90s—and some of its improved versions; exponential scenarios; the Lorentzian quintessential inflation; and quintessential inflation in the context of α-attractors
Summary
Understanding the universe’s evolution is one of the greatest mysteries in the history of humanity. The upper bound may depend on the theory we are dealing with; for instance, many supergravity and superstring theories contain particles such as the gravitino or a modulus field with only gravitational interactions, and the late-time decay of these relic products may disturb the success of the standard BBN [66], but this problem can be successfully removed if the reheating temperature is considered in the order of 109 GeV (see, for instance, [67]).
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