Continuous Bogoliubov formalism for gravitational-wave generation in a unified dark sector warm inflation

In this work, we review gravitational-wave generation in a two-scalar-field cosmological model. The framework relies on a two-field scenario in which warm inflation is unified with the dark sector within a single theoretical description. It has recently been shown that this setup leads to a gravitational-wave spectrum potentially detectable by future experiments. Here we also demonstrate that the resulting spectrum is largely independent of the $\phi$ field initial condition, thereby extending previous findings.