Low-Energy Effective Field Theory for Chromo-Natural Inflation

TL;DR

Chromo-natural inflation couples an axion to an SU(2) gauge field, generating an extra damping term that enables slow-roll without a super-Planckian decay constant. In a slow-roll hierarchy scaling (SRHS) limit where the gauge fields are heavy ($m_g\gg H$), the gauge fluctuations can be integrated out, yielding a single-field EFT with a non-minimal kinetic term: $S_{\chi}=\int d^4x\sqrt{-g}\left[ \frac{M_{Pl}^2}{2}R - \frac{1}{2}(\partial\chi)^2 + \frac{1}{4\Lambda^4}(\partial\chi)^4 - \mu^4\left(1+\cos(\chi/f)\right)\right]$, with $\Lambda^4=8 f^4 g^2/\lambda^4$. The EFT reproduces the background evolution and perturbations, remains technically natural under loops, and yields observable predictions with $c_s^2=1/3$ and modest equilateral non-Gaussianity, while the heavy gauge sector decouples. Beyond SRHS, a more general $P(X,\chi)$ structure emerges with higher-order corrections, and the EFT’s validity imposes conditions such as $\epsilon_2 \gtrsim 4\epsilon_1$ to ensure gauge-field decoupling. Overall, the model provides a stable, UV-insensitive mechanism for inflation with predictive cosmological signatures.

Abstract

Chromo-natural inflation is a novel model of inflation which relies on the existence of non-abelian gauge fields interacting with an axion. In its simplest realization, an SU(2) gauge field is assumed to begin inflation in a rotationally invariant VEV. The dynamics of the gauge fields significantly modifies the equations of motion for the axion, providing an additional damping term that supports slow-roll inflation, without the need to fine tune the axion decay constant. We demonstrate that in an appropriate slow-roll limit it is possible to integrate out the massive gauge field fluctuations whilst still maintaining the nontrivial modifications of the gauge field to the axion. In this slow-roll limit, chromo-natural inflation is exactly equivalent to a single scalar field effective theory with a non-minimal kinetic term, i.e. a P(X,χ) model. This occurs through a precise analogue of the gelaton mechanism, whereby heavy fields can have unsuppressed effects on the light field dynamics without contradicting decoupling. The additional damping effect of the gauge fields can be completely captured by the non-minimal kinetic term of the single scalar field effective theory. We utilize the single scalar field effective theory to infer the power spectrum and non-gaussianities in chromo-natural inflation and confirm that the mass squared of all the gauge field fluctuations is sufficiently large and positive that they completely decouple during inflation. These results confirm that chromo-natural inflation is a viable, stable and compelling model for the generation of inflationary perturbations.