  A minimal model of Cold Dark Matter (CDM) is a very massive particle with
only gravitational interactions, also called Planckian Interacting Dark Matter
(PIDM). Here we consider an extension of the PIDM framework by an unbroken
$U(1)$ gauge symmetry under which the PIDM is charged, but remains only
gravitationally coupled to the Standard Model (SM). Contrary to "hidden charged
dark matter", the charged PIDM never reaches thermal equilibrium with the SM.
The dark sector is populated by freeze-in via gravitational interactions at
reheating. If the dark fine-structure constant $\alpha_D$ is larger than about
$10^{-3}$, the dark sector thermalizes within itself, and the PIDM abundance is
further modified by freeze-out in the dark sector. Interestingly, this largely
reduces the dependence of the final abundance on the reheating temperature, as
compared to an uncharged PIDM. Thermalization within the dark sector is driven
by inelastic radiative processes, and affected by the Landau-Pomeranchuk-Migdal
(LPM) effect. The observed CDM abundance can be obtained over a wide mass range
from the weak to the GUT scale, and for phenomenologically interesting
couplings $\alpha_D\sim 10^{-2}$. Due to the different thermal history, the
charged PIDM can be discriminated from "hidden charged dark matter" by more
precise measurements of the effective number of neutrino species $N_{\rm eff}$.
