In recent years, I have been investigating gravitational waves of cosmological origin.

I have investigated, together with A. B. Henriques, 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 was calculated using the method of continuous Bogoliubov coefficients. We have 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 [1,2].

I have also investigated, together with A. B. Henriques, the generation of gravitational waves in power-law inflationary models. The energy spectrum of the gravitational waves was calculated using the method of continuous Bogoliubov coefficients. We have shown that, by looking at the interval of frequencies between 10^-5 and 10^5 Hz and also at the GHz range, important information can be obtained, both about the inflationary period itself and about the thermalization regime between the end of inflation and the beginning of the radiation-dominated era [3].

Together with A. B. Henriques and R. Potting, I have investigated a cosmological model, based on the Salam-Sezgin six-dimensional supergravity theory and on previous work by Anchordoqui, Goldberg, Nawata, and Nunez. Assuming a period of warm inflation, we have shown that it is possible to extend the evolution of the model back in time, to include the inflationary period, thus unifying inflation, dark matter, and dark energy within a single framework. Like the previous authors, we were not able to obtain the full dark matter content of the Universe from the Salam-Sezgin scalar fields. However, this work has shown that present-day theories, based on superstrings and supergravity, may eventually lead to a comprehensive modelling of the evolution of the Universe. We have found that the gravitational-wave spectrum of the model has a non-constant negative slope in the frequency range 10^-15 - 10^6 Hz, and that, unlike standard (cold) inflation models, it shows no structure in the MHz/GHz range of frequencies [4].

More recently, together with A. B. Henriques, I have investigated the generation of gravitational waves in the hybrid quintessential inflationary model. The full gravitational-wave energy spectrum was calculated using the method of continuous Bogoliubov coefficients. The post-inflationary kination period, characteristic of quintessential inflationary models, leaves a clear signature on the spectrum, namely, a peak at high frequencies. The maximum of the peak is firmly located at the MHz/GHz region of the spectrum and corresponds to values of the gravitational-wave spectral energy density parameter of the order of 10^(-12) [5,6].