Cosmological stasis from dynamical scalars: Tracking solutions and the possibility of a stasis-induced inflation

It has recently been realized that many theories of physics beyond the Standard Model (BSM) give rise to cosmological histories exhibiting extended epochs of cosmological stasis. During such epochs, the abundances of different energy components such as matter, radiation, and vacuum energy each remain fixed despite cosmological expansion. In previous analyses of the stasis phenomenon, these different energy components were modeled as fluids with fixed, unchanging equations of state. In this paper, by contrast, we consider more realistic systems involving dynamical scalars which pass through underdamping transitions as the universe expands. Indeed, such systems might be highly relevant for BSM scenarios involving higher-dimensional bulk moduli and inflatons. Remarkably, we find that stasis emerges even in such situations, despite the appearance of time-varying equations of state. Moreover, this stasis includes several new features which might have important phenomenological implications and applications. For example, in the presence of an additional ``background'' energy component, we find that the scalars evolve into a ``tracking'' stasis in which the stasis equation of state automatically tracks that of the background. This phenomenon exists even if the background has only a small initial abundance. We also discuss the intriguing possibility that our results might form the basis of a new ``stasis inflation'' scenario in which no ad hoc inflaton potential is needed and in which there is no graceful-exit problem. Within such a scenario, the number of $e$-folds of cosmological expansion produced is directly related to the hierarchies between physical BSM mass scales. Moreover, nonzero matter and radiation abundances can be sustained throughout the inflationary epoch.