Viable inflationary models ending with a first-order phase transition

We investigate the parameter space of two-field inflation models where inflation terminates via a firstorder phase transition causing nucleation of bubbles. Such models experience a tension from the need to ensure nearly scale-invariant density perturbations, while avoiding a near scale-invariant bubble size distribution which would conflict observations. We perform an exact analysis of the different regimes of the models, where the energy density of the inflaton field ranges from being negligible as compared to the vacuum energy to providing most of the energy for inflation. Despite recent microwave anisotropy results favoring a spectral index less than 1, we find that there are still viable models that end with bubble production and can match all available observations. As a by-product of our analysis, we also provide an up-to-date assessment of the viable parameter space of Linde’s original second-order hybrid model across its full parameter range.