An M Theory Solution to the Strong CP Problem and Constraints on the Axiverse

TL;DR

The paper embeds a rich axion spectrum within $M$-theory by extending moduli stabilization to include axions, yielding a concrete realization of the String Axiverse with a QCD axion at GUT-scale decay constants. It analyzes two cosmological histories—non-thermal, moduli-dominated pre-BBN and thermal, radiation-dominated—to derive axion relic abundances and cosmological constraints from isocurvature and tensor modes, showing that tensor detections would falsify the Axiverse. It demonstrates that a large, log-spaced axion tower with $f_a \\sim M_{GUT}$ can satisfy cosmological bounds with modest misalignment tuning in non-thermal histories, while providing distinctive observational windows across CMB, structure formation, black hole dynamics, and photon-axion conversions. The results connect high-energy string compactifications to testable cosmological and astrophysical signatures, establishing clear falsifiability criteria and potential multi-messenger probes of the Axiverse.

Abstract

We give an explicit realization of the "String Axiverse" discussed in Arvanitaki et. al \cite{Arvanitaki:2009fg} by extending our previous results on moduli stabilization in $M$ theory to include axions. We extend the analysis of \cite{Arvanitaki:2009fg} to allow for high scale inflation that leads to a moduli dominated pre-BBN Universe. We demonstrate that an axion which solves the strong-CP problem naturally arises and that both the axion decay constants and GUT scale can consistently be around $2\times 10^{16}$ GeV with a much smaller fine tuning than is usually expected. Constraints on the Axiverse from cosmological observations, namely isocurvature perturbations and tensor modes are described. Extending work of Fox et. al \cite{Fox:2004kb}, we note that {\it the observation of tensor modes at Planck will falsify the Axiverse completely.} Finally we note that Axiverse models whose lightest axion has mass of order $10^{-15}$ eV and with decay constants of order $5\times 10^{14}$ GeV require no (anthropic) fine-tuning, though standard unification at $10^{16}$ GeV is difficult to accommodate.

Figures (6)

• Figure 1: Allowed microscopic parameter space (unshaded region) in the $\{\theta_{I_0},H_I\}$ plane for $N_1=10,\,N_2=14$ with a "non-thermal", moduli dominated cosmological history ($H_I > M_{moduli}$) after imposing the current bounds on tensor modes, isocurvature fluctuations and the overall relic abundance. Contours for three allowed values of the isocurvature fluctuations $\alpha_a$ are also plotted.
• Figure 2: Allowed microscopic parameter space (unshaded region) in the $\{\theta_{I_0},H_I\}$ plane for $N_{std}=24$ with a "thermal" cosmological history ($H_I < M_{moduli}$) after imposing the current bounds on tensor modes, isocurvature fluctuations and the overall relic abundance. Contours for three allowed values of the isocurvature fluctuations $\alpha_a$ are also plotted.
• Figure 3: Effect on allowed values of microscopic parameters $\{\theta_{I_0},H_I\}$ by decreasing $\{N_1,N_2\}$, for non-thermal cosmological history ($H_I > M_{moduli}$). Left: $N_1=10,\,N_2=14$; Right: $N_1=1,N_2=2$.
• Figure 4: Effect on allowed values of microscopic parameters $\{\theta_{I_0},H_I\}$ by decreasing $N_{std}$, for thermal cosmological history ($H_I < M_{moduli}$). Left: $N_{std}=24$; Right: $N_{std}=3$.
• Figure 5: Distribution of ${\tilde{a}}_i$ obtained for $200$ randomly generated Kahler potentials consistent with $G_2$ holonomy with $N=50$ moduli. The for each case, the integer parameters $N_i$ were randomly generated sets containing $1$s and $2$s. The mean value is ${\overline {\tilde{a}}}_i=\frac{7}{150}\approx 0.047$ and the standard deviation ${\rm S.D.}({{\tilde{a}}_i})\approx 0.011$.