Cosmic birefringence from a stiff axion field and its cosmological implications

We propose a model in which the observed cosmic microwave background birefringence arises from the interaction of photons with a stiff ($w=1$) pseudo-scalar field that today contributes a subdominant fraction of the total energy density, distinct from both dark matter and dark energy. Big Bang Nucleosynthesis constrains the cosmological density of the stiff field, leading to a lower bound for its coupling with photons, $g_{\phi \gamma }>8.9\times {10}^{-14}{\mathrm{G}\mathrm{e}\mathrm{V}}^{-1}$. Photon conversion in cluster-hosted quasars sets an upper bound, $g_{\phi \gamma }<5.0\times {10}^{-13}{\mathrm{G}\mathrm{e}\mathrm{V}}^{-1}$. Therefore, there is a narrow window for the discovery of this cosmological component that can be explored in the forthcoming years with astrophysical axion searches. Moreover, we show that this scenario leads to gravitational-wave signals that can be tested with planned experiments.