Chromo-Natural Inflation: Natural inflation on a steep potential with classical non-Abelian gauge fields (1202.2366v2)

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 ($<M_{\rm Pl}$). 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).

• The paper introduces a novel inflation model integrating an axionic scalar field with classical SU(2) gauge fields, enabling slow-roll inflation on a steep potential.
• It demonstrates that axion-gauge interactions mediated by the Chern-Simons term effectively slow the axion’s motion and yield a vanishingly small tensor-to-scalar ratio.
• The model requires precise parameter tuning, offering an alternative to traditional inflation scenarios by addressing challenges associated with sub-Planckian axion decay constants.

Chromo-Natural Inflation: An Analysis of Axion and Non-Abelian Gauge Field Interactions

In "Chromo-Natural Inflation: Natural inflation on a steep potential with classical non-Abelian gauge fields," Adshead and Wyman propose a novel inflation model, integrating an axionic scalar field with three non-Abelian SU(2) gauge fields. This model distinctively requires that the gauge fields commence inflation maintaining a rotationally invariant vacuum expectation value (VEV), achieved by identifying SU(2) gauge invariance with three-dimensional spatial rotations. This coupling between the gauge fields and the axion's background results in an attractor solution allowing slow-roll inflation, even when the axion's decay constant is sub-Planckian.

Unlike traditional inflation models, where the axion’s motion is governed by the potential slope and Hubble friction, here the dynamics are modulated by interactions with the gauge VEV. For small axion decay constants, this configuration predicts vanishingly small tensor-to-scalar ratios, compliant with the Lyth bound. Achieving successful inflation in this model necessitates a technically precise tuning of the parameter controlling the interaction between the axion and gauge fields, which is of the order of 100.

The theoretical structure of this model addresses the limitations of typical inflationary models, which often depend on highly tuned scalar field potentials susceptible to quantum corrections. The proposed mechanism uses the axionic shift symmetry for protection, a feature inherent in axions utilized in the Natural Inflation model. However, observations dictate that such a model necessitates large axion decay constants, challenging feasibility within string theory constraints. This model, therefore, emerges amidst a renewed interest in sub-Planckian axionic inflation frameworks.

The inflationary dynamics are driven by axionic energy transferred into classical gauge fields, rather than dissipation through Hubble friction. Axion-gauge interactions mediated via the Chern-Simons term, which respects axionic shift symmetry, enable this energy exchange. Consequently, higher-order corrections to the gauge action are minimal, ensuring a naturally large coefficient for the axion-Chern-Simons operator without extensive fine-tuning.

Within this framework, the axion’s movement is effectively slowed, enhancing the period of inflation. Key conditions for achieving this inflationary phase include a parameter regime where the ratio of gauge coupling squared to the interaction parameter is roughly balanced with the square of the inflationary energy scale. Taking into account that the gauge VEV has an equation of state akin to radiation, it follows that the system inflates only when dominated by axion potential. In the setup analyzed, sufficient inflation corresponds to approximately 60 efoldings, achievable with minimal tuning of the model parameters.

The paper also explores the perturbation dynamics, assuming that fluctuations in the gauge field do not significantly affect the adiabatic perturbations of the model. The curvature and power spectrum perturbations can be roughly estimated under the assumption that the curvature perturbation predominantly arises from quantum fluctuations of the axion along its effective trajectory. This suggests that the dominant tensor fluctuations are those of the metric itself, given the sub-dominant contributions expected from gauge field fluctuations.

Future exploration might include a comprehensive treatment of the perturbation spectrum to better outline the complete contributions to curvature perturbations from gauge fluctuations. Should these additional fluctuations prove significant, they may offer unique signatures or constraints for this inflation model. Given the robust yet concise exploration of axion and SU(2) gauge fields dynamics provided by Adshead and Wyman, their work offers a compelling avenue for expanding our understanding of viable inflationary mechanisms under the umbrella of axion-gauge field frameworks. More detailed results are anticipated from further analysis and simulations, contributing to the discourse on alternative inflation paradigms.