  Conformal and Disformal couplings between a scalar field and matter occur
naturally in general scalar-tensor theories. In D-brane models of cosmology and
particle physics, these couplings originate from the D-brane action describing
the dynamics of its transverse (the scalar) and longitudinal (matter)
fluctuations, which are thus coupled. During the post-inflationary regime and
before the onset of big-bang nucleosynthesis (BBN), these couplings can modify
the expansion rate felt by matter, changing the predictions for the thermal
relic abundance of dark matter particles and thus the annihilation rate
required to satisfy the dark matter content today. We study the D-brane-like
conformal and disformal couplings effect on the expansion rate of the universe
prior to BBN and its impact on the dark matter relic abundance and annihilation
rate. For a purely disformal coupling, the expansion rate is always enhanced
with respect to the standard one. This gives rise to larger cross-sections when
compared to the standard thermal prediction for a range of dark matter masses,
which will be probed by future experiments. In a D-brane-like scenario, the
scale at which the expansion rate enhancement occurs depends on the string
coupling and the string scale.
