  Thermal freeze-out is a prominent example of dark matter (DM) production
mechanism in the early Universe that can yield the correct relic density of
stable weakly interacting massive particles (WIMPs). At the other end of the
mass scale, many popular extensions of the Standard Model predict the existence
of ultra-light scalar fields. These can be coupled to matter, preferentially in
a universal and shift-symmetry-preserving way. We study the impact of such
conformal and disformal couplings on the relic density of WIMPs, without
introducing modifications to the thermal history of the Universe. This can
either result in an additional thermal contribution to the DM relic density or
suppress otherwise too large abundances compared to the observed levels. In
this work, we assume that the WIMPs only interact with the standard model via
the light scalar portal. We use simple models of fermionic or scalar DM,
although a similar discussion holds for more sophisticated scenarios, and
predict that their masses should be between $\sim 100~\textrm{GeV}$ and several
$\textrm{TeV}$ to comply both with the DM abundance and current bounds on the
couplings of the light scalars to matter at the LHC. Future searches will
tighten these bounds.
