Gravitational Atoms
  Particles in a yet unexplored dark sector with sufficiently large mass and
small gauge coupling may form purely gravitational atoms (quantum gravitational
bound states) with a rich phenomenology. In particular, we investigate the
possibility of having an observable signal of gravitational waves or ultra high
energy cosmic rays from the decay of gravitational atoms. We show that if
ordinary Einstein gravity holds up to the Planck scale, then, within the
$\Lambda \text{CDM}$ model, the frequency of the gravitational wave signal
produced by the decays is always higher than $10^{13} \, \text{Hz}$. An
observable signal of gravitational waves with smaller frequency from such
decays, in addition to probing near Planckian dark physics, would also imply a
departure from Einstein gravity near the Planck scale or an early epoch of
non-standard cosmology. As an example, we consider an early universe cosmology
with a matter-dominated phase, violating our assumption that the universe is
radiation dominated after reheating, which gives a signal in an interesting
frequency range for near Planckian bound states. We also show how gravitational
atoms arise in the minimal PIDM scenario and compute their gravitational wave
signature.
