On the prospects of thermalization of axion-SU(2) inflation

TL;DR

This work probes whether nonlinear gauge interactions in axion-SU(2) inflation can drive sustained thermalization during inflation. By combining a Boltzmann-occupation-number framework with perturbativity bounds, the authors identify conditions under which a warm inflation regime could emerge and chart the corresponding parameter space for zero and nonzero gauge-field backgrounds. They find that a large portion of the parameter space supports cold inflation, while a notable region with $g\sim\mathcal{O}(0.1-1)$ and moderate to large $\xi$ or $m_Q$ could approach warm inflation, potentially with a dynamically generated gauge-field VEV. Full thermalization remains a lattice-scale problem, but their analysis provides practical criteria and benchmark lines to guide future simulations and phenomenological studies of chiral gravitational waves, PBHs, and lepton asymmetry in these models.

Abstract

Axion inflation models coupled to a gauge sector via a Chern-Simons term exhibit an array of interesting phenomenology including a chiral gravitational wave spectrum and primordial black hole production. They may also provide a useful mechanism for generating lepton asymmetry. The possibility to embed this class of models in UV-finite theories and their intriguing, testable, signatures make for a compelling candidate for early acceleration. Due to the Chern-Simons coupling, gauge modes may undergo a finite tachyonic growth during which non-linearities become important. Naturally, this raises the question of whether such (self) interactions can lead to thermalization during inflation. We provide a set of useful criteria for sustained thermalization in an axion-$SU(2)$ model and chart the parameter space of the model accordingly. We find that the cold inflation regime constitutes a very significant fraction of the parameter space. Our analysis accounts for a initially vanishing as well as non-zero gauge field vacuum expectation value (VEV). We also consider the possibility of a dynamically generated VEV.

Figures (5)

• Figure 1: Scattering diagrams from cubic and quartic interactions
• Figure 2: Comparison of the source-free and sourced contributions to the Boltzmann Eq. \ref{['eq:Boltz001']}. $S_{++}(k)$ is plotted as a function of $-k\tau$ in red and blue solid (dashed) lines for $m_Q=3$ ($m_Q=5$) for $g=10^{-1}$ and $g=10^{-2}$ respectively. Black solid (dashed) plots represent $S_{\rm Free}(k,\tau)$ for $m_Q=3$ ($m_Q=5$). Thick (thin) gray and pink vertical lines denote the position of peak $x_{-}$ and maximum instability $x_m$ for $m_Q=3$ ($m_Q=5$).
• Figure 3: 1-loop diagrams from cubic (left) and quartic (right) interactions
• Figure 4: The various regions in the $(\xi,g)$ plane identifying the conditions for transitioning to the warm inflation regime. Left: Bounds for zero vev case. Interactions are efficient above the light green (cyan) band plotted for $1/2\xi <r<1$, where the gauge modes are estimated at the horizon exit $x=1$ (at maximum instability $x=\xi$). Backreaction bounds are shown in black dashed and dotted vertical lines for $\frac{1}{\lambda}\frac{f}{H}=10^3$ and $10^4$ respectively. Perturbativity bounds from the Chern-Simons contribution and from self-interaction are shown in orange dashed and solid lines respectively. Right: Bounds for non-vanishing vev. Interactions are efficient above the dark green (blue) band plotted for $x_+ <r<1$, where the gauge modes are estimated at the peak $x=x_-$ (at maximum instability $x=x_m$). In both panels, red horizontal solid (dashed) lines signify sustainability of thermalization with $H_{\rm inf}=10^{-10}~M_{\rm Pl}$ ($H_{\rm inf}=10^{-5}~ M_{\rm Pl}$).
• Figure 5: Plot of the bubble nucleation efficiency defined in (\ref{['eq:bub-nuc']}) as a function of the particle production parameter $\xi$ for three different choices of the gauge coupling $g$. The dashed line corresponds to $g=10^0$, dotted line to $g=10^{-1/3}$ and dot-dashed to $g=10^{-2/3}$.