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(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-Planckian 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 O(100).

Inflation and String Theory

“…The maximum number of e-folds that can be achieved while the axion rolls to the minimum of its potential is found to be [797] (N e ) max ≈ 3 5 λ . The crucial question is whether such a large coupling can be achieved in a controlled string compactification.…”

“…We explain how trapped inflation could plausibly arise in the class of string compactifications discussed in the context of axion monodromy inflation in §5.4.2, albeit in a slightly different parameter regime. Then, in §5.6.2 and §5.6.3, we present two very recent ideas: inflation via flux cascades [623] and via magnetic drift [797]. Both are imaginative additions to the string inflation literature, so we include them here even though, at the time of writing, the models still lack explicit embeddings into fully specified string compactifications including moduli stabilization.…”

“…The top-down naturalness of this mechanism remains to be established, and in particular no complete string theory realization has been constructed. 99 Another recent proposal, which we will now describe in some detail, is that inflation can be achieved by coupling an axion to non-Abelian gauge fields with suitable vevs [625,797] (see [815][816][817] and the review article [818] for 99 One way to achieve large α is to fine-tune two axion decay constants to be nearly coincident [767].…”

Cosmological consequences of classical flavor-space locked gauge field radiation

“…The prediction, borne out by numerical integration, is that the gravitational wave and tensor modes of the gauge field are damped out. (We note that such suppression could modify the predictions of the gauge-flation and chromo-natural inflation scenarios [36,37,39] or other inflationary models that traditionally overproduce gravitational waves. This effect has not been explored before and might mitigate the shortcomings of these theories that ultimately led to the predictions that ruled them out.…”

“…An origin for this small coupling as well as the flavor-space locked configuration might be devised in an inflationary epoch along the lines of [34,35], although that is beyond the scope of our present investigation. Inflationary scenarios based on a similar gauge field that include self interactions with couplings to matter fields, have been studied elsewhere [36,37].…”