  Rotations of an axion field in field space provide a natural origin for an
era of kination domination, where the energy density is dominated by the
kinetic term of the axion field, preceded by an early era of matter domination.
Remarkably, no entropy is produced at the end of matter domination and hence
these eras of matter and kination domination may occur even after Big Bang
Nucleosynthesis. We derive constraints on these eras from both the cosmic
microwave background and Big Bang Nucleosynthesis. We investigate how this
cosmological scenario affects the spectrum of possible primordial gravitational
waves and find that the spectrum features a triangular peak. We discuss how
future observations of gravitational waves can probe the viable parameter
space, including regions that produce axion dark matter by the kinetic
misalignment mechanism or the baryon asymmetry by axiogenesis. For QCD axion
dark matter produced by the kinetic misalignment mechanism, a modification to
the inflationary gravitational wave spectrum occurs above 0.01 Hz and, for high
values of the energy scale of inflation, the prospects for discovery are good.
We briefly comment on implications for structure formation of the universe.
