Multiple Axions Save High-Scale Inflation

TL;DR

The paper tackles the mismatch between high-scale inflation and axion dark matter by exploiting multiple axions to remove the domain-wall problem. It shows that the domain-wall number in a multi-axion system is controlled by the determinant of the anomaly matrix ${\cal N}$, with a unique minimum achieved when $|\det {\cal N}|=1$, allowing post-inflationary PQ breaking without cosmological walls. The authors provide concrete SUSY-DFSZ constructions and anomaly choices that yield $N_{DW}=1$, discuss cosmological evolution of string-wall networks, and explore phenomenological consequences including ALP decays, BBN constraints, and possible gravitational-wave signals. This framework opens the possibility of high-scale inflation with detectable tensor modes while preserving axion dark matter, and it offers testable predictions for upcoming axion searches and gravitational-wave observations.

Abstract

Many models of dark matter QCD axion requires inflation at a scale $H_{\text{inf}} \lesssim 10^{6}$~GeV and hence does not allow for a detectable tensor mode fluctuation. This is because the domain wall problem forces the Peccei--Quinn symmetry to be broken during the inflation and the axions to be produced by the misalignment mechanism. We point out that theories with multiple axions can evade this constraint and allow for a high-scale inflation with detectable tensor mode. It only requires a condition on the anomaly coefficients so that there is a unique minimum for the axion potential without a fine-tuning or small parameters.

Figures (5)

• Figure 1: The contour plots of the two-axion potential with ${\cal N}$ given in \ref{['eq:N0']}. On the left plot, only $V_1$ is turned on. The minima are ${g_1 = \rm gcd}(4,6)=2$ disconnected lines. Even though the domain wall number ${\rm det}{\cal N}/g_1=1$ according to definitions in Benabou:2023npnLee:2024toz, there are ${\rm det}{\cal N}=2$ degenerate minima after turning on $V_2$ at $(\theta_1, \theta_2) = (0,0)$ and $(0, \pi)$. Here, we took $\Lambda_1 = \Lambda_2 = 1$.
• Figure 2: The plot of the potential which realizes $N_{DW}=1$ with ${\cal N}$ given in \ref{['eq:N1']} taking $\Lambda_1 = \Lambda_2$ to make the minimum clearly visible. We can see that the minimum is unique at $(\theta_1, \theta_2) = (0,0)$.
• Figure 3: The plot of the potential which realizes $N_{DW}=1$ with ${\cal N}$ given in \ref{['eq:N2']} taking $\Lambda_1 = \Lambda_2$ to make the minimum clearly visible. We can see that the minimum is unique at $(\theta_1, \theta_2) = (0,0)$.
• Figure 4: The phenomenology of the potential with a "string bundle" for $f_a=10^{11}$GeV as an example. The white region is the viable parameter space. The middle section in orange is excluded because ALPs decay late and destroys the success of the Big-Bang Nucleosynthesis Cadamuro:2011fd. The lower left region in yellow is excluded because the excessively rapid cooling of SN1987A Cadamuro:2011fd. The lower right region in dark gray is excluded because it theoretically does not make sense for an ALP if $m_\phi > f_\phi$.
• Figure 5: The phenomenology of the potential with a string-wall network for $f_a=10^{11}$GeV as an example. The white region is the viable parameter space. The upper left region in blue-gray is excluded because ALPs decay late and destroys the success of the Big-Bang Nucleosynthesis Cadamuro:2011fd. The lower left region in yellow is excluded because the too-rapid cooling of SN1987A Cadamuro:2011fd. The upper right region in cyan is excluded because the string-wall network persists down to the BBN era \ref{['eq:collapse2']}. The lower right region in dark gray is excluded because it theoretically does not make sense for an ALP if $m_\phi > f_\phi$. Finally, the region below the orange dashed line is preferred to avoid axion overproduction from the collapse of string-wall network \ref{['eq:fratio']}. We also show other implications for a reference. The orange line is the upper bound on decay constant from the tensor mode \ref{['eq:RH']}. The magenta dashed line shows the $f_a$ and the pink dashed line represents $10^{-3}f_a$ to avoid the overproduction of axion DM from DW collapse. The magenta dashed line is $f_a = 10^{11}$ GeV for a comparison and we assumed $f_\phi < f_a$ and hence is below this line. The purple band roughly corresponds to the region where PTA signal can be explained ($10^{15}$GeV$^3\lesssim \sigma \lesssim 10^{16}$GeV$^3$) Lee:2024xjb.