Solving the Tension between High-Scale Inflation and Axion Isocurvature Perturbations

TL;DR

This work tackles the tension between high-scale inflation, suggested by BICEP2, and astrophysical axion dark matter which generically induces isocurvature perturbations. It introduces a mechanism in which PQ symmetry is explicitly broken to a discrete subgroup in a way that is enhanced during inflation, giving the axion a large mass and suppressing isocurvature fluctuations, while ensuring the breaking fades after inflation so the PQ solution to the strong CP problem remains intact. The authors analyze two realizations: (i) a SUSY-driven scenario where the saxion acquires a large VEV during inflation, amplifying a PQ-breaking operator, and (ii) an inflaton-dependent operator that is active only during inflation. They show this approach can relax the bound on the axion decay constant f_a, permitting f_a in the range ~10^{10}–10^{13} GeV and, in some cases, enabling N_DW > 1 without cosmological catastrophe. The results suggest a broader connection between inflation dynamics and axion phenomenology, with potential UV completions and extensions to axion-like particles.

Abstract

The BICEP2 experiment determined the Hubble parameter during inflation to be about $10^{14}$ GeV. Such high inflation scale is in tension with the QCD axion dark matter if the Peccei-Quinn (PQ) symmetry remains broken during and after inflation, because too large axion isocurvature perturbations would be generated. The axion isocurvature perturbations can be suppressed if the axion acquires a sufficiently heavy mass during inflation. We show that this is realized if the PQ symmetry is explicitly broken down to a discrete symmetry and if the breaking is enhanced during inflation. We also show that, even when the PQ symmetry becomes spontaneously broken after inflation, such a temporarily enhanced PQ symmetry breaking relaxes the constraint on the axion decay constant.

Figures (2)

• Figure 1: Constraint on the inflation scale from the axion CDM isocurvature perturbation. The isocurvature constraint (\ref{['iso']}) is shown by the solid (orange) line, where the anharmonic effect is taken into account Kobayashi:2013nva. The relaxed constraints for $\langle S \rangle_{\rm inf} = 10^{16}{\rm\,GeV}, M_{Pl}$ and $15 M_{Pl}$ are shown by the dashed, solid, and dot-dashed lines, respectively. The horizontal band is the BICEP2 result (\ref{['B']}). If the axion acquires a heavy mass during inflation, all these constraints disappear as shown in the text.
• Figure 2: The lower bound on $N$ as a function of $f_a$. We have set $m_{3/2}=100$TeV, $\lambda = 1$ and $A_\lambda = m_{3/2}$.