Kaluza-Klein towers in the early universe: Phase transitions, relic abundances, and applications to axion cosmology

We study the early-universe cosmology of a Kaluza-Klein (KK) tower of scalar fields in the presence of a mass-generating phase transition, focusing on the time development of the total tower energy density (or relic abundance) as well as its distribution across the different KK modes. We find that both of these features are extremely sensitive to the details of the phase transition and can behave in a variety of ways significant for late-time cosmology. In particular, we find that the interplay between the temporal properties of the phase transition and the mixing it generates are responsible for both enhancements and suppressions in the late-time abundances, sometimes by many orders of magnitude. We map out the complete model parameter space and determine where traditional analytical approximations are valid and where they fail. In the latter cases we also provide new analytical approximations which successfully model our results. Finally, we apply this machinery to the example of an axion-like field in the bulk, mapping these phenomena over an enlarged axion parameter space that extends beyond that accessible to standard treatments. An important by-product of our analysis is the development of an alternate “UV-based” effective truncation of KK theories which has a number of interesting theoretical properties that distinguish it from the more traditional “IR-based” truncation typically used in the extra-dimension literature.