Reheating with Axion-SU(2) and Gravitational Chern-Simons Couplings

Abstract

We study the early stages of an oscillatory reheating phase in an inflaton plus spectator axion-SU(2) system, including both an axion-gauge Chern-Simons coupling $χF\tilde{F}$ and a gravitational Chern-Simons coupling $χR\tilde{R}$. Assuming an isotropic SU(2) background configuration of chromo-natural type and quadratic potentials, we numerically solve the coupled background and tensor perturbation equations during the first e-fold of reheating. The gravitational Chern-Simons term induces a helicity-dependent modification of the tensor kinetic coefficient, yielding a chiral enhancement of the tensor power spectrum on the order of tens of percent for a representative benchmark. We illustrate how such an early-time enhancement can map to a narrow feature in the present-day stochastic gravitational wave spectrum, potentially relevant for upcoming and proposed space-based detectors, while a fully self-consistent determination of the peak scale requires scanning comoving wavenumbers and specifying the reheating history.

Figures (9)

• Figure 1: Background reheating dynamics for the parameter choice and initial conditions in Table \ref{['tab:params']}. Left: oscillations of the inflaton $\varphi$ and spectator axion $\chi$. Right: effective equation of state $w_{\rm eff}=p_{\rm tot}/\rho_{\rm tot}$ and the short running average; we see that$\langle w\rangle\simeq 0$.
• Figure 2: Energy fractions showing that the spectator axion--SU(2) sector remains subdominant, for the parameter choice in Table \ref{['tab:params']}.
• Figure 3: Tensor mode evolution during reheating, using the parameter values in Table \ref{['tab:params']}. Left:$\sqrt{2k}\,|x\,h_A|$ for $A=R,L$ with (solid) and without (dashed) the GCS coupling. Right: power ratios relative to $\lambda_2=0$. The GCS interaction produces a chiral enhancement that accumulates over the reheating evolution.
• Figure 4: The present-day $\Omega_{\rm GW,0}(f)$ from Eqs. \ref{['eq:OmegaGW_simple']} and \ref{['eq:Pt_param']}, using the parameters and initial conditions in Table \ref{['tab:params']}. Unlike inflationary production, the enhancement is localized because it is generated during the first e-fold of reheating. Left: Illustrative sensitivities of LISA, the Advanced Laser Interferometer Antenna (ALIA), the Deci-hertz Interferometer Gravitational Wave Observatory (DECIGO) and Big Bang Observatory (BBO) in an order-of-magnitude detectability sketch. The LISA curve shows an approximate power-law integrated sensitivity (PLS) curve (SNR=10, 4-year mission), using the noise model of Robson2019 and the PLS construction in Caprini2019. Sensitivity curves for ALIA, DECIGO and BBO follow the mission concepts described in Crowder2005Seto2001Kawamura2011Corbin2006. The bump amplitude/width and peak frequency are chosen for demonstration rather than derived from a full $k$-scan of the reheating dynamics. The plotted effect should therefore be interpreted as an order-unity rescaling of the bump amplitude, via Eq. (\ref{['eq:tensor-power-ratios']}), rather than as a parameter-free forecast. Right: Same as the left panel, but for a SKA-like PTA, using a simplified white-noise model and the analytic sensitivity formalism of Moore2015.
• Figure 5: Reheating-era GCS enhancement as a frequency-dependent factor for the LISA-band benchmark. For a narrow reheating bump, the GCS term effectively rescales the peak amplitude of the dominant helicity by a factor of order unity (here $\sim1.27$), leaving the spectrum unchanged away from the reheating feature.