Unifying inflation and dark matter with the Peccei-Quinn field: observable axions and observable tensors

TL;DR

The paper tackles the tension between high-scale inflation and axion dark matter by proposing that the radial part of the Peccei-Quinn field acts as the inflaton with a non-minimal coupling to gravity, flattening the potential and enabling successful inflation at large field values. This setup suppresses axion isocurvature perturbations by effectively replacing the decay constant $f_a$ with the inflaton radius $s_*$ during inflation, thereby permitting a broad window for $f_a$ between $10^{12}$ and $10^{15}$ GeV to coexist with observable tensor modes $r$. A key result is the prediction of a minimum tensor-to-scalar ratio $r$ of order $10^{-3}$, with the exact window depending on the reheating efficiency parameter $\epsilon_{\rm eff}$. The work maps out the $f_a$–$r$ plane, identifies regions excluded by isocurvature, photon-axion couplings, and DM from string decays, and highlights experimental prospects for Spider, CASPEr, and ADMX-HF to test the scenario. The approach provides a concrete path to reconcile high-scale inflation with high-$f_a$ axion DM and offers testable predictions for upcoming cosmology and axion-detection experiments.

Abstract

A model of high scale inflation is presented where the radial part of the Peccei-Quinn (PQ) field with a non-minimal coupling to gravity plays the role of the inflaton, and the QCD axion is the dark matter. A quantum fluctuation of $\mathcal{O}(H/2π)$ in the axion field will result in a smaller angular fluctuation if the PQ field is sitting at a larger radius during inflation than in the vacuum. This changes the effective axion decay constant, $f_a$, during inflation and dramatically reduces the production of isocurvature modes. This mechanism opens up a new window in parameter space where an axion decay constant in the range $10^{12}\text{ GeV}\lesssim f_a\lesssim 10^{15}\text{ GeV}$ is compatible with observably large $r$. The exact range allowed for $f_a$ depends on the efficiency of reheating. This model also predicts a minimum possible value of $r=10^{-3}$. The new window can be explored by a measurement of $r$ possible with \textsc{Spider} and the proposed CASPEr experiment search for high $f_a$ axions.

Figures (4)

• Figure 1: Schematic of our mechanism. Isocurvature fluctuations in the axion field, $\delta \theta$, are reduced if the radial field, $s$, lies at higher values during inflation, $s_\star$, compared to the low energy minimum, $f_a$.
• Figure 2: The dependence of the self-coupling, $\lambda$, and the tensor-to-scalar ratio, $r$, on the non-minimal couping to gravity, $\xi$, for $N=60$ (solid) and $N=50$ (dashed). Here $\lambda$ is fixed using $A_s=2.196 \times 10^{-9}$ and we take the limit $f_a \rightarrow 0$.
• Figure 3: The variation of the model prediction in the $n_s$-$r$ plane for different values of $\xi$. We show the 1 and 2$\sigma$ constraints from Planck with WMAP bennett/etal:2012 polarisation (WP) and BAO from various surveys (see Ref. PlanckCosmo for details). Our model is consistent with the data for $\xi\gtrsim \mathcal{O}(\text{few})\times 10^{-3}$ depending on $N$, the number of $e$-folds of observable inflation.
• Figure 4: Axion DM constraints for non-minimal PQ inflation model showing the new window unavailable to other axion models. The red region is ruled out by isocurvature constraints. The orange region is rule out by astrophysical constraints on the photon-axion coupling. The blue region is ruled out by overproduction of DM from cosmic strings (shown for three different reheating temperatures parameterised by $\epsilon_{\text{eff}}$). The green region is excluded by direct searches for DM axions by ADMX. The purple lines show the projected lower bounds of the CASPEr experiment. Together, Spider and CASPEr/ADMX-HF can probe a large part of the parameter space of our model.