Taking the recently reported non-zero rotation angle of the cosmic microwave background (CMB) linear polarization $beta=0.35pm0.14{rm, deg}$ as the hint for a pseudo Nambu-Goldstone boson quintessence dark energy (DE), we study the electroweak (EW) axion quintessence DE model where the axion mass is generated by the EW instantons. We find that the observed value of $beta$ implies a non-trivial $U(1)$ electromagnetic anomaly coefficient ($c_{gamma}$), once the current constraint on the DE equation of state is also taken into account. With the aid of the hypothetical high energy structure of the model inspired by the experimentally inferred $c_{gamma}$, the model is shown to be able to make prediction for the current equation of state ($w_{rm DE,0}$) of the quintessence DE. This is expected to make our scenario distinguishable in comparison with the cosmological constant ($w=-1$) and testable in future when the error in the future measurement of $w_{rm DE,0}$ is reduced to $mathcal{O}(1)%$ level ($delta w=mathcal{O}(10^{-2})$).
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