  Dark matter (DM) could be a nonthermal relic that freezes in from extremely
weak, sub-Hubble annihilation and decay of Standard Model (SM) particles. The
case of Dirac DM freezing in via a dark photon mediator is a well-studied
benchmark for DM direct detection experiments. Here, we extend prior work to
take into account the possibility that DM is pseudo-Dirac with a small mass
splitting. If the mass splitting is greater than twice the electron mass but
less than the dark photon mass, there will be distinct cosmological signatures.
The excited state $\chi_2$ is initially produced in equal abundance to the
ground state $\chi_1$. Subsequently, the excited state population decays at
relatively late cosmological times, primarily via the three-body process
$\chi_2 \rightarrow \chi_1 e^+ e^-$. This process injects energetic electrons
into the ambient environment, providing observable signatures involving Big
Bang nucleosynthesis, cosmic microwave background spectral distortions and
anisotropies, and the Lyman-$\alpha$ forest. Furthermore, the ground state
particles that are populated from the three-body decay receive a velocity kick,
with implications for DM clustering on small scales. We find that cosmological
probes and accelerator experiments are highly complementary, with future
coverage of much of the parameter space of the model.
