Tracking Dark Energy from Axion-Gauge Field Couplings

We propose a toy model of Dark Energy in which the degrees of freedom currently dominating the energy density of the universe are described by a pseudo-scalar "axion field" linearly coupled to the Pontryagin density, $ \text{tr}(F \wedge F)$, i.e., the exterior derivative of the Chern-Simons form, of a gauge field. We assume that the axion has self-interactions corresponding to an exponential potential. We argue that a non-vanishing magnetic helicity of the gauge field leads to slow-rolling of the axion at field values far below the Planck scale. Our proposal suggests a "Tracking Dark Energy Scenario" in which the contribution of the axion energy density to the total energy density is constant (and small), during the early radiation phase, until a secular growth term proportional to the Pontryagin density of the gauge field becomes dominant. The initially small contribution of the axion field to the total energy density is related to the observed small baryon-to-entropy ratio.