Do we have any hope of detecting scattering between dark energy and
  baryons through cosmology?
  We consider the possibility that dark energy and baryons might scatter off
each other. The type of interaction we consider leads to a pure momentum
exchange, and does not affect the background evolution of the expansion
history. We parametrize this interaction in an effective way at the level of
Boltzmann equations. We compute the effect of dark energy-baryon scattering on
cosmological observables, focusing on the Cosmic Microwave Background (CMB)
temperature anisotropy power spectrum and the matter power spectrum.
Surprisingly, we find that even huge dark energy-baryon cross-sections
$\sigma_{xb} \sim {\cal O}({\rm b})$, which are generically excluded by
non-cosmological probes such as collider searches or precision gravity tests,
only leave an insignificant imprint on the observables considered. In the case
of the CMB temperature power spectrum, the only imprint consists in a
sub-percent enhancement or depletion of power (depending whether or not the
dark energy equation of state lies above or below $-1$) at very low multipoles,
which is thus swamped by cosmic variance. These effects are explained in terms
of differences in how gravitational potentials decay in the presence of a dark
energy-baryon scattering, which ultimately lead to an increase or decrease in
the late-time integrated Sachs-Wolfe power. Even smaller related effects are
imprinted on the matter power spectrum. The imprints on the CMB are not
expected to be degenerate with the effects due to altering the dark energy
sound speed. We conclude that, while strongly appealing, the prospects for a
direct detection of dark energy through cosmology do not seem feasible when
considering realistic dark energy-baryon cross-sections. As a caveat, our
results hold to linear order in perturbation theory.
