The stochastic gravitational-wave background and the inflation to radiation transition in the early universe

In this paper, we calculate the gravitational-wave power-spectra corresponding to different types of transitions between the inflationary regime and the radiation era. We study four cases, where inflation is followed by a stiff-matter phase, or by a dust-dominated phase, or by a combination of the two, before the universe enters the radiation era. Use is made of differential equations for the Bogoliubov coefficients, allowing us to model all the transitions between the different eras as continuous. New features appear, for frequencies above 10−5 rad s−1, in an otherwise flat part of the spectrum.