  We investigate the production of gravitational waves due to quantum
fluctuations of the vacuum during the transition from the inflationary to the
radiation-dominated eras of the universe, assuming this transition to be
dominated by the phenomenon of parametric resonance. The energy spectrum of the
gravitational waves is calculated using the method of continuous Bogoliubov
coefficients, which avoids the problem of overproduction of gravitons at large
frequencies. We found, on the sole basis of the mechanism of quantum
fluctuations, that the resonance field leaves no explicit and distinctive
imprint on the gravitational-wave energy spectrum, apart an overall upward or
downward translation. Therefore, the main features in the spectrum are due to
the inflaton field, which leaves a characteristic imprint at frequencies of the
order of MHz/GHz.
