A Step in Flux to Suppress Axion Isocurvature

TL;DR

This work introduces a novel mechanism to suppress axion isocurvature in the pre-inflation QCD axion scenario by endowing the axion with a large BF-type monodromy mass during inflation, controlled by a dynamical integer flux that turns off abruptly via a first-order phase transition. The authors construct a 4D EFT framework with a thin-brane (flux) tunneling process mediated by $B$-brane domain walls, analyze bubble nucleation and percolation during inflation, and provide a case study of tunneling occurring during inflation to quantify the impact on the axion power spectrum and isocurvature. They demonstrate that this mechanism can substantially enlarge the allowed region in the $(H_I,f_a)$ plane across fractional-DM, anthropic, and dilution scenarios, thereby easing tension with high-scale inflation. The paper also outlines UV completions in extra dimensions and string theory (including a Type IIA realization where chirality can emerge after the transition) and discusses possible observational signals such as gravitational waves and reheating effects. Altogether, the proposal offers a concrete, testable route to reconcile high-scale inflation with axion dark matter in the pre-inflation paradigm and motivates further exploration of brane-based flux tunneling in cosmology and UV completions.

Abstract

The QCD axion in the pre-inflation scenario faces a stringent isocurvature constraint, which requires a relatively low Hubble scale during inflation. If the axion was heavier than the Hubble scale during inflation, its isocurvature is suppressed and the constraint disappears. We point out a novel mechanism for achieving this, relying on the topological nature of a BF-type (monodromy) mass for the axion. Such a mass term has an integer coefficient, so it could naturally have been very large during inflation and exactly zero by the time of the QCD phase transition. This integer can be viewed as a quantized flux, which is discharged in a first-order phase transition that proceeds by the nucleation of charged branes. This mechanism can be embedded in cosmology in several different ways, with tunneling during, at the end of, or after inflation. We provide a detailed case study of the scenario in which the tunneling event occurs during inflation. We also comment briefly on possible UV completions within extra-dimensional gauge theories and string theory. Intriguingly, the phase transition could be accompanied by the emergence of the chiral Standard Model field content from a non-chiral theory during inflation.

Figures (9)

• Figure 1: Axion potential schematically: An axion 3-form coupling generates a BF type monodromy potential $V_{\mathrm{tree}}$ (blue). It traps the axion field around its minimum $\theta_0$ and suppresses isocurvature perturbations during inflation. The QCD phase transition turns off the monodromy mass and generates $V_{\mathrm{QCD}}$ (red). The minima of the two potentials are misaligned by an angle $\theta_0 - {\bar{\theta}}$, which seeds axion dark matter after inflation.
• Figure 2: Axion monodromy potential in effective theory: $V_{\mathrm{eff}}(\theta,j)=\frac{1}{2}m_{\theta}^2f^2\left((\theta-\theta_0) - 2\pi j/n\right)^2$. The potential exhibits monodromy when $\theta \to \theta + 2\pi/n$, $j \to j+1$. Dynamical $A$-branes interpolate between branches with different $j$.
• Figure 3: The axion monodromy potential for different flux levels $n$, for fixed $j=0$. The potential has the form $V_{\mathrm{eff}}(\theta,0,n) = \frac{1}{2} n^2 \left[\frac{e_A}{2\pi}(\theta - \theta_0)\right]^2 + V_n$. Our solution to the axion isocurvature problem relies on a cosmological phase transition connecting the $n = 1$ branch with the $n=0$ branch, effectuated by dynamical $B$-branes. The constant offset $V_n$ can differ for different choices of $n$.
• Figure 4: The process of $B$-brane bubble mergers. As explained in Blanco-Pillado:2009lan, when bubbles merge, the overlap region will have a different flux ($n = -1$ in this example). Left panel: the state immediately after bubbles collide. Arrows indicate the direction of pressure on the bubble walls due to vacuum energy differences, assuming that the $n = 0$ state has lowest vacuum energy. Right panel: we expect that the branes will reconnect and interior regions with $n \neq 0$ will collapse, eventually leading to a universe in the $n = 0$ state everywhere.
• Figure 5: We plot the axion power spectrum $P_\theta(k)$ and show how its response as we change each parameter that determines its shape. For reference, we mark $k_c$ for the base case in the black dashed line. The base set of parameters are $k_c=10^{-2}\,h {\rm Mpc}^{-1}$, $\nu_\theta=3$, $(f_a/H_I)=10$ and $\xi=0.99$, which is shown in solid black in each subplot. The variation in each parameter is shown sequentially in blue.