Most of the matter in the universe is invisible, meaning that it hardly interacts with ordinary (baryonic) matter. In particular, it doesn't emit photons, so we cannot see it directly. We can only infer its existence from the gravitational effects it has on galaxies and the universe as a whole.
While the evidence for the existence of dark matter so far stems purely from its gravitational influence, the dark matter particle is usually assumed to have other-than-gravitational interactions. In other words, the physics beyond the Standard Model responsible for dark matter is typically assumed to emerge much below the Planck scale. In the WIMP scenario, for example, new particles and symmetries are expected to arise around the TeV scale. This also makes it reasonably feasible to see the dark matter particle in direct detection experiments.
However, new physics below the Planck scale is not a necessity. There is nothing fundamentally wrong in having an extended desert between the electroweak scale and the Planck scale, or possibly the GUT scale. New physics is bound to emerge close to the Planck scale to restore unitarity in gravitational scattering, but in principle no new fundamental scale is needed to make sense of our world. In a minimal approach to the dark matter problem, no new scale should be added to solve the problem if it’s not needed. Thus, the most minimal dark matter model is one in which the dark matter particle is connected to the new degrees of freedom that emerge at the Planck scale to unitarize gravity. In this new paradigm, the dark matter particle is intimately linked to the theory of quantum gravity; it has a natural mass close to the Planck scale, and has only gravitational (planck-suppressed) interactions. We call this scenario Planckian Interacting Dark Matter (PIDM).
The PIDM scenario has a natural string theory realization as the Kaluza-Klein excitation of the graviton in orbifold compactifications of string theory, as well as in models of monodromy inflation and in Higgs inflation. In these setups, dark matter is, in a sense, both a particle and a modification of gravity.
I wrote my PhD thesis on PIDM at the Center for Cosmology and Particle Physics of SDU.
Conventional wisdom says that you can't have gravitational atoms because gravity is weak: electric and nuclear forces always dominate at microscopic scales. This is not necessarily true. While it is true that gravity is weak for visible particles, it could be strong for a heavy particle that we haven't found yet. It could even be the dark matter particle, as in the PIDM scenario. In fact, in the minimal PIDM scenario, purely gravitational atoms are naturally produced by thermal scattering in the SM plasma, the same mechanism responsible for dark matter genesis.
By their very nature, gravitational atoms are incredibly heavy. In our paper we derive a lower bound on their mass based on tidal disruption in galaxies. It turns out that the mass has to be at least 10^-8 in natural units. That's approximately the mass of a bacterium! The heaviest atoms are not much bigger than the Planck length and they weigh almost as much as a grain of sand. These heaviest atoms are usually unstable and decay to gravitons in the early universe, sourcing a highly energetic, isotropic, and nearly monochromatic gravitational wave signal. In the paper we derive a lower bound on the frequency of the signal, it's 10^13 Hz. We don't know of any other process in nature that would give such a strong monochromatic signal at such high frequencies.
Below you can find a poster on gravitational atoms that I made for the Annual Danish Astronomy Meeting, and here the slides of a talk I gave in Freiburg.