Gauge Fields and Inflation: Chiral Gravitational Waves, Fluctuations and the Lyth Bound

TL;DR

The paper analyzes Chromo-Natural Inflation with a non-Abelian SU(2) gauge background that intrinsically violates parity, enabling chiral gravitational waves without requiring super-Planckian field excursions. It derives the coupled tensor and scalar perturbation dynamics, revealing a tachyonic growth of left-handed gauge-field tensors that amplifies one GW polarization and a suppressed axion perturbation modulated by a large magnetic-drift parameter Λ. A key finding is a scalar instability for small m_ψ and a tension between achieving observable chirality and satisfying scalar and tensor constraints, rendering the model observationally inviable in its current form. The work clarifies how gauge-field-induced chirality interacts with standard inflationary perturbations and informs constraints on Lyth-bound-like behavior in gauge-field-driven inflation models.

Abstract

Models of inflation involving non-Abelian gauge field backgrounds can produce gravitational waves at an observable level with a preferred handedness. This asymmetry comes about because the non-Abelian background generates parity-violation in the action for perturbations. In the specific model we study, Chromo-Natural Inflation, these gravitational waves can be produced at observable levels even when no field makes a super-Planckian field excursion, thus evading a common formulation of the Lyth bound. Unfortunately, when considered in concert with the scalar fluctuations, this chiral enhancement of the gravitational waves makes the model observationally inviable.

Figures (3)

• Figure 1: In the upper panel, we plot in blue and black curves the real and imaginary parts, respectively, of the physical left-handed gravitational wave perturbation $\gamma^+/a$ in units of the Hubble rate. In green and red curves we plot the real and imaginary parts of the physical left-handed spin-2 gauge field fluctuations $t^+$. In dashed lines show the numerical integration of the equations resulting from the action, Eqn. (\ref{['eqn:tensoraction']}). Solid lines show the result of the approximation of Eqns. (\ref{['eqn:metricfull']}) and (\ref{['eqn:gaugeapprox']}). The values of the parameters are chosen so that $m_{\psi} \approx 2.1$ and $\psi \approx 0.048$. The lower panel shows the ratio of the power in the two gravitational wave helicities as a function of $m_\psi$ holding $\psi$ fixed.
• Figure 2: In this figure, we show the late-time value of ${\boldsymbol\varphi}$ obtained from exact numerical integration of the reduced system as a function of $(m_{\psi}-\sqrt{2})$.
• Figure 3: Comparison of the tensor-to-scalar ratio, r, evaluated at $k=0.002$ h/Mpc and the spectral tilt, $n_s$ (evaluated at $k=0.05$ h/Mpc) for models drawn from a numerical exploration of the $g, f, \mu, \lambda$ parameter space with the corresponding parameter constraints from Planck. The value for $r$ presented here includes the contributions from both gravitational wave helicities and is computed numerically using the gravitational wave mode functions. The open black circles represent parameter combinations whose scalar power spectrum amplitudes are outside of the Planck error bars; blue stars represent models with acceptable power spectrum amplitudes. The Planck one and two sigma contours are plotted in red and pink, respectively. Note that the y-axis is logarithmic, and that in this model it is possible to have $r>1$ due to the chirally enhanced gravitational wave spectrum.