  Modified dark matter (MDM) is a phenomenological model of dark matter,
inspired by gravitational thermodynamics. For an accelerating Universe with
positive cosmological constant ($\Lambda$), such phenomenological
considerations lead to the emergence of a critical acceleration parameter
related to $\Lambda$. Such a critical acceleration is an effective
phenomenological manifestation of MDM, and it is found in correlations between
dark matter and baryonic matter in galaxy rotation curves. The resulting MDM
mass profiles, which are sensitive to $\Lambda$, are consistent with
observational data at both the galactic and cluster scales. In particular, the
same critical acceleration appears both in the galactic and cluster data fits
based on MDM. Furthermore, using some robust qualitative arguments, MDM appears
to work well on cosmological scales, even though quantitative studies are still
lacking. Finally, we comment on certain non-local aspects of the quanta of
modified dark matter, which may lead to novel non-particle phenomenology and
which may explain why, so far, dark matter detection experiments have failed to
detect dark matter particles.
