Revisiting Isocurvature Bounds on the Minimal QCD Axion

TL;DR

This work shows that the conventional isocurvature exclusion for high $f_a$ and high $H_I$ in the minimal QCD axion is not generic: if the PQ-breaking sector has a small quartic coupling and couples to gravity via a positive $R$-term, the inflationary decay constant $f_a^{(inf)}$ can exceed the late-time $f_a$, suppressing isocurvature perturbations. The authors model the saxion-axion system with the $2\xi R|\Phi|^2$ coupling, derive the inflationary evolution of $f_a^{(inf)}$, and numerically solve the coupled equations of motion to assess parametric resonance across UV-parameter space. They find sizable regions where isocurvature is avoided without overproducing axions, illustrating the UV sensitivity of the bounds and highlighting the role of inflation and reheating dynamics. These results open substantial portions of the previously excluded $H_I$–$f_a$ parameter space for pre-inflationary axion DM and motivate further UV model-building and potential friction mechanisms to widen viable regions.

Abstract

The QCD axion has important connections to early universe cosmology. For example, it is often said that isocurvature limits rule out a combination of high axion decay constant, $f_a$, and high inflationary Hubble scale, $H_I$. High scales are theoretically motivated, so it is important to ask how robust this constraint is. We demonstrate that this constraint is naturally evaded when the quartic coupling of the complex $U(1)_\mathrm{PQ}$-breaking field is small. In this case, $f_a$ changes from a larger value during inflation to a smaller value in the later universe, suppressing isocurvature perturbations. Importantly, we show that in large parts of parameter space this solution is not jeopardised by overproduction of the axion through parametric resonance. The isocurvature bounds are thus dependent on UV physics. We have found that, even for the minimal QCD axion, large parts of UV parameter space at both high $f_a$ and high $H_I$ are in fact allowed, not ruled out by isocurvature constraints.

Figures (13)

• Figure 1: A rough sketch of axion parameter space in the axion decay constant $f_a$ vs the inflationary Hubble scale $H_I$. The left figure shows the region of parameter space which has conventionally been claimed to be ruled out by isocurvature constraints (grey). However we demonstrate in this paper that a significant fraction of that region is in fact allowed, shown as the yellow region in the right plot. Whether the isocurvature fluctuations are too large in this region is determined by parameters of the underlying PQ-breaking potential and the model of inflation and reheating. Both figures show the parts of parameter space that would be in the pre-inflationary (blue) and post-inflationary (red) regimes, as well as bounds from B-modes and superradiance (light grey).
• Figure 2: Parameter space in the plane $(H_I,f_a)$ where the QCD axion can be the DM respecting the isocurvature constraint, which can exclude the grey-shaded area. The region shaded in light blue (plus the grey region) corresponds to the Pre-inflationary regime, and the left-axis marks the initial misalignment $\theta_\text{i}$ for the axion to be DM (solid line for the quadratic regime, and dashed for the large misalignment). In the red region, assuming that the maximum temperature is equal to 10% of the one achieved in instantaneous reheating ($0.1\,T_\mathrm{inst.\,RH}$, where $T_\mathrm{inst.\,RH}$ is also marked on the upper axis), PQ symmetry is restored and we fall in the Post-inflationary regime. The upper limits for $H_I$ and $f_a$ are due respectively to the constraints from B-modes in the CMB and black-hole superradiance.
• Figure 3: Same as \ref{['fig:baseline isocurvature']}, showing the amplification of axion fluctuations for all the points of our scan in $(H_I,f_a,\xi,\lambda_\Phi)$ for our model of Warm Inflation. The color of each point indicates how much parametric resonance drives the axion modes, as shown in the legend on the right. Blue and light blue points do not feature a strong parametric resonance, and successfully avoid the isocurvature constraint without overproducing axions. For light-orange points, axion strings are formed due to parametric resonance.
• Figure 4: Growth of the axion fluctuations due to parametric resonance as a function of the enhancement of $f_a$ during inflation, $f_a^\text{(inf)}\approx\sqrt{24 \xi/\lambda_\Phi} H_I$, for our scenario of warm inflation. The red horizontal line marks $f_a^\text{(inf)}/f_a\approx 700$, which roughly divides the points featuring inefficient or short parametric resonance (in blue) and string formation (light orange). Points which display an amplification $\tfrac{1}{\pi}\delta\theta_\text{(par.res.)} <10^{-9}$, or $>10^{2}$, are all marked on the respective threshold. Some points on the lower left align on diagonal lines because of our sampling of integer powers of $\xi/\lambda_\Phi$.
• Figure 5: The blue and green regions show the parameter space for fixed values of $f_a^\text{(inf)}/H_I\approx \sqrt{24 \xi/\lambda_\Phi}$ where the QCD axion can be the DM and not violate the isocurvature constraint (with the $2\xi R|\Phi|^2$ coupling and a small quartic coupling $\lambda_\Phi$). The plot shows the regions, in the parameter space typically subject to isocurvature, where $f_a^\text{(inf)} >f_a$ suppresses isocurvature without sourcing a parametric resonance for the axion, for the model of Warm inflation. In general the whole region that is rescued from the isocurvature constraints is the one enclosed by the purple and orange (as well as grey and red) lines.