  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 those 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.
