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The diagonalization method, introduced by a group of Russian scientists atthe beginning of seventies, is used to compute the energy density of superheavymassive particles produced due to a sudden phase transition from inflation tokination in quintessential inflation models, the models unifying inflation withquintessence originally proposed by Peebles-Vilenkin. These superheavyparticles must decay in lighter ones to form a relativistic plasma, whoseenergy density will eventually dominate the one of the inflaton field, in orderto have a hot universe after inflation. In the present article we show that, inorder that the overproduction of Gravitational Waves (GWs) during this phasetransition does not disturb the Big Bang Nucleosynthesis (BBN) success, thedecay has to be produced after the end of the kination regime, obtaining amaximum reheating temperature in the TeV regime.

Understanding gravitational particle production in quintessential inflation