The first-order confinement transition of a strongly
coupled composite dark matter theory can provide a possible source
of gravitational waves in the early universe. In this work, on
behalf of the Lattice Strong Dynamics (LSD) Collaboration, we
present our recent investigation on the finite temperature
confinement transition of the one-flavor SU(4) dark gauge theory named
Hyper Stealth Dark Matter (HSDM). The dark matter candidate in this
theory is a composite bosonic baryon and can have a remarkably low
mass of a few GeV. We expect the finite temperature transition
to be first-order over at least
in some finite range of fermionic masses
and to be a potential source of observable gravitational
radiation. The finite temperature simulation of one-flavor SU(4) is
done by using M\"{o}bius Domain wall fermions.
The order of the transition and its fermionic mass
dependence are explored
by monitoring the Polyakov loop, chiral
condensate and topological charge
using three lattice volumes at $N_t=8$.