Primordial Gravitational Waves from Scalar Backreaction in Axion-SU(2) Inflation

TL;DR

The paper investigates strong scalar backreaction in spectator axion–SU(2) inflation (SCNI) by numerically evolving the axion and gauge backgrounds as the tachyonic scalar instability activates when $m_Q$ crosses $\sqrt{2}$. It introduces backreaction terms $B_\chi^{\rm BR}$ and $B_Q^{\rm BR}$, shows that a time-dependent quartic contribution in the gauge-background potential drives $Q$ to zero, and produces a brief, large spike in the axion production parameter $\xi$. This spiky $\xi$ generates a localized, chiral stochastic gravitational-wave background that can lie in the LISA band for suitable $f$ and initial conditions, while the inflaton energy remains dominant and scalar-induced PBHs or SIGWs are avoided in the explored regime. The results provide a robust, testable link between strong scalar backreaction in a spectator sector and an observable GW signature, with potential implications for the string axiverse and future non-perturbative analyses such as lattice studies.

Abstract

In this work, we perform the first numerical study of strong scalar backreaction in spectator chromo-natural inflation (SCNI) in the case where the spectator sector decays during inflation. The tachyonic instability in scalar fluctuations, activated as the system crosses the $m_Q = \sqrt{2}$ threshold, amplifies perturbations and may significantly alter the background dynamics. The strong scalar backreaction regime introduces an effective quartic term in the potential for the gauge field background that rapidly drives it to zero, accelerating the axion-gauge system decay. We describe the dynamics of such decay and derive the gravitational wave spectrum for a set of benchmark parameters. Interestingly, the signal may peak at interferometer scales and lie within LISA's projected sensitivity.

Figures (7)

• Figure 1: Typical evolution of the particle production parameters $m_Q$ and $\Lambda$ in SCNI. The maximum is obtained at the inflection point of the potential ($\chi/f=\pi/2$), and $m_Q$ reaches zero when the axion field value reaches the minimum ($\chi/f=\pi$). The red line denotes the onset of the scalar instability $m_Q=\sqrt{2}$. The parameters chosen for this example are $f=3.75\cdot 10^{-2}\;M_p$, $g=4\cdot 10^{-3}$, $\lambda=90$, $\mu=1.5\cdot 10^{-3}\;{M_p}$ and $H=1.69\cdot 10^{-5}\;M_p$. The number of e-folds is defined as $N\equiv\log(a)$ with $a=1$ at the start of the simulation.
• Figure 2: The fractional spectral backreaction defined in eqs.(\ref{['eq:spectralbckchi']}) and (\ref{['eq:spectralbckQ']}). The parameters chosen in this example are the ones listed in the caption of Fig. \ref{['fig:mQ']}. The backreaction is well peaked both in momentum space as well as in time. The lines are only displayed between $k_{\rm IR}$ and $k_{\rm UV}$ as defined in the main text. The colored vertical dashed lines indicate the horizon crossing momentum at each snapshot in time. Note how the integral is typically dominated by scales which cross the horizon at any given time.
• Figure 3: Time evolution of the effective potential for the gauge field background $Q$. Dashed lines correspond to the absence of scalar backreaction, whereas solid lines take into account the effective potential induced by the $B_Q$ term in the equation of motion. The shape of the potential changes over time from purple to red, and the model parameters were chosen to match the ones reported in the caption of Fig. \ref{['fig:mQ']}.
• Figure 4: Particle production parameter $m_Q$ (left panel) and $\xi$ (right panel) with (solid) and without (dashed) the backreaction contribution. We use for our numerical simulation the fiducial values listed in Eq. \ref{['eq:fiducial']}.
• Figure 5: Comparison of the fractional energy density contribution of each component of our system. It is possible to observe that the inflaton energy (black horizontal line) remains the dominant component throughout the time span of our simulation.