  We study the superheavy dark matter (DM) scenario in an extended $B-L$ model,
where one generation of right-handed neutrino $\nu_R$ is the DM candidate. If
there is a new lighter sterile neutrino that co-annihilate with the DM
candidate, then the annihilation rate is exponentially enhanced, allowing a DM
mass much heavier than the Griest-Kamionkowski bound ($\sim10^5$ GeV). We
demonstrate that a DM mass $M_{\nu_R}\gtrsim10^{13}$ GeV can be achieved.
Although beyond the scale of any traditional DM searching strategy, this
scenario is testable via gravitational waves (GWs) emitted by the cosmic
strings from the $U(1)_{B-L}$ breaking. Quantitative calculations show that the
DM mass $\mathcal{O}(10^9-10^{13}~{\rm GeV})$ can be probed by future GW
detectors.

High Energy Physics - Phenomenology;Cosmology and Nongalactic Astrophysics