A Tale of Two Timescales: Mixing, Mass Generation, and Phase Transitions in the Early Universe

Light scalar fields such as axions and string moduli can play an important role in early-universe cosmology. However, many factors can significantly impact their late-time cosmological abundances. For example, in cases where the potentials for these fields are generated dynamically --- such as during cosmological mass-generating phase transitions --- the duration of the time interval required for these potentials to fully develop can have significant repercussions. Likewise, in scenarios with multiple scalars, mixing amongst the fields can also give rise to an effective timescale that modifies the resulting late-time abundances. Previous studies have focused on the effects of either the first or the second timescale in isolation. In this paper, by contrast, we examine the new features that arise from the interplay between these two timescales when both mixing and time-dependent phase transitions are introduced together. First, we find that the effects of these timescales can conspire to alter not only the total late-time abundance of the system --- often by many orders of magnitude --- but also its distribution across the different fields. Second, we find that these effects can produce large parametric resonances which render the energy densities of the fields highly sensitive to the degree of mixing as well as the duration of the time interval over which the phase transition unfolds. Finally, we find that these effects can even give rise to a "re-overdamping" phenomenon which causes the total energy density of the system to behave in novel ways that differ from those exhibited by pure dark matter or vacuum energy. All of these features therefore give rise to new possibilities for early-universe phenomenology and cosmological evolution. They also highlight the importance of taking into account the time dependence associated with phase transitions in cosmological settings.