Chromo-Natural Inflation: Natural inflation on a steep potential with classical non-Abelian gauge fields

Abstract

We propose a model for inflation consisting of an axionic scalar field coupled to a set of three non-Abelian gauge fields. Our model's novel requirement is that the gauge fields begin inflation with a rotationally invariant vacuum expectation value (VEV) that is preserved through identification of SU(2) gauge invariance with rotations in three dimensions. The gauge VEV interacts with the background value of the axion, leading to an attractor solution that exhibits slow roll inflation even when the axion decay constant has a natural value ($<M_{\mathrm{Pl}}$). Assuming a sinusoidal potential for the axion, we find that inflation continues until the axionic potential vanishes. The speed at which the axion moves along its potential is modulated by its interactions with the gauge VEV, rather than being determined by the slope of its bare potential. For sub-Plankian axion decay constants vanishingly small tensor to scalar ratios are predicted, a direct consequence of the Lyth bound. The parameter that controls the interaction strength between the axion and the gauge fields requires a technically natural tuning of $\mathcal{O}$(100).

v2: 5 pages, no figures. Version accepted to PRL

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