On Non-Minimal Couplings to Gravity and Axion Isocurvature Bounds

TL;DR

This work analyzes how simultaneous non-minimal couplings of the inflaton and PQ field to gravity modify axion isocurvature bounds in inflationary scenarios. It shows that a large inflaton non-minimal coupling ξ_σ inherently lowers the inflationary axion decay constant f_a^(inf), tightening isocurvature constraints, while a sufficiently strong radial PQ coupling ξ_ρ can lift f_a^(inf) above the bare decay constant f_a, alleviating the bounds. The lifting mechanism yields f_a^(inf) ≈ √(12 ξ_ρ/λ_ρ) H in the appropriate parameter window, with backreaction and reheating history imposing nontrivial upper limits on ξ_ρ; these results persist in both Palatini and metric formulations and across Palatini Higgs and Starobinsky inflation. The paper delineates the viable parameter space for alleviating isocurvature constraints and highlights model-dependent upper bounds on ξ_ρ, suggesting careful consideration of reheating dynamics in future studies. Overall, non-minimal gravity couplings provide a controllable handle on axion isocurvature, but their effectiveness is tightly constrained by inflationary dynamics and the gravity formulation chosen.

Abstract

For axions present during inflation, it has been shown that a non-minimal coupling $ξ_σ$ of the inflaton to gravity worsens isocurvature bounds, while a non-minimal coupling $ξ_ρ$ of the radial Peccei-Quinn field can alleviate them. We analyze the simultaneous presence of both couplings and determine when one effect dominates the other, in both the metric and Palatini formulations of gravity. The two tendencies interpolate smoothly, but introducing a non-minimal inflaton coupling reduces the viable interval of $ξ_ρ$ in which isocurvature bounds can be alleviated while avoiding backreaction on the inflationary dynamics. We illustrate our findings in Palatini Higgs inflation and Starobinsky inflation.

Figures (2)

• Figure 1: Constraints on $\xi_\rho$ in Palatini Higgs inflation as a function of $f_a$, for $H=10^{9}$ GeV and some choices of $\lambda_\rho$. The green line represents the lower bound on $\xi_\rho$ for which the inflationary decay constant \ref{['faInfNonMinimal']} fulfills the isocurvature bound \ref{['isocurvatureBound']}. The red curve shows the would-be lower bound on $\xi_\rho$ if the inflaton were minimally coupled, which is found by plugging Eq. \ref{['faInfMinimalApprox']} into Eq. \ref{['isocurvatureBound']}. Furthermore, the solid black line represents the upper bound on $\xi_\rho$ from imposing the non-backreaction condition of Eq. \ref{['boundPalatini']} (with $\Omega_0 \sim 2 \cdot10^4$) and the dashed black line corresponds to the would-be upper bound for the minimally coupled case. In the green region, isocurvature bounds are obeyed and the red region would only be viable if the influence of the inflaton non-minimal coupling on axions were neglected. That the red region on the right extends down to vanishing $\xi_\rho$ reflects the fact that Palatini Higgs inflation would obey isocurvature bound if the effect of the inflaton non-minimal coupling were not taken into account Tenkanen:2019xzn.
• Figure 2: Constraints on $\xi_\rho$ in Starobinsky inflation as a function of $f_a$, for $H=10^{13}$ GeV and some choices of $\lambda_\rho$. The green line represents the lower bound on $\xi_\rho$ for which the inflationary decay constant \ref{['fInfStarobinskyNonminimal']} fulfills the isocurvature bound \ref{['isocurvatureBound']}. The red curve show the would-be lower bound on $\xi_\rho$ if the inflaton were minimally coupled, which is found by plugging Eq. \ref{['faInfMinimalApprox']} into Eq. \ref{['isocurvatureBound']}. Furthermore, the solid black line represents the upper bound on $\xi_\rho$ from imposing the non-backreaction condition of Eq. \ref{['boundXiStarobinskyExact']} (with $\Omega^2_0=N=50$) and the dashed black line corresponds to the would-be upper bound for the minimally coupled case. In the green region, isocurvature bounds are obeyed and the red region would only be viable if the influence of the inflaton non-minimal coupling on axions were neglected.