  We study a simple extension of the Standard Model featuring a dark sector
with an ultralight pseudo Nambu-Goldstone boson as dark matter candidate. We
focus on the mass range $\mathcal{O}(10^{-20} - 10^{-10})$ eV, relevant for
strong gravity applications, and explore its production and evolution in the
early Universe. The model is formulated in such a way that dark matter does not
couple directly to photons or other Standard Model particles avoiding some of
the most stringent cosmological bounds related to axion-like particles. In this
work, two different scenarios are considered depending on whether dark matter
is produced in a pre-inflationary or post-inflationary regime. We also discuss
the effect from emergent topological defects such as cosmic strings and domain
walls, and estimate the spectrum of stochastic gravitational waves produced by
their decay, enabling to test the model at current and future
gravitational-wave experiments.
