New Source for QCD Axion Dark Matter Production: Curvature Induced

Abstract

We discuss a novel mechanism for generating dark matter from a fast-rolling scalar field, relevant for both inflation and rotating axion models, and apply it specifically to the (QCD) axion. Dark matter comes from scalar field fluctuations generated by the product of the curvature perturbation and the fast-rolling background field. These fluctuations can explain the totality of dark matter in a vast axion parameter space, particularly for the QCD axion, which will be targeted by upcoming experiments. We review the constraints on this mechanism and potential gravitational-wave signatures.

Figures (4)

• Figure 1: Cartoon of the energy-density evolution of a fast-moving scalar field condensate in blue, which behaves as radiation $\sim a^{-4}$, kination $\sim a^{-6}$, and matter $\sim a^{-3}$, consecutively, during the radiation era of the Universe. The second stage starts at $a_{\rm kin}$ when the field dynamics is kinetic-energy dominated. The last stage happens when the field gets trapped and oscillates inside the potential barrier at $a_{\rm osc}$, leading to DM via kinetic misalignment or fragmentation. The red line shows the energy-density evolution of scalar-field fluctuations $\rho_{\rm fluct}$ induced by primordial curvature perturbations. Initially produced relativistically, they become non-relativistic at $a_{\rm NR}$, and can serve as DM. The orange line shows the Standard Model radiation. Another possible scenario is if the scalar field is the inflaton itself and fast-rolls after inflation, that would correspond to setting $a_{\rm kick}=a_{\rm kin}$. Plot is schematic and not to scale.
• Figure 2: The rotating axion with quartic potential \ref{['eq:complex_scalar_potential']} produces the observed DM abundance in the region above the green line, via curvature-induced production and kinetic misalignment, i.e., $\Omega_{\rm DM}^0 = \Omega_{\rm fluct}^0 + \Omega_{\rm zero}^0$. For each $\lambda$, DM is overproduced on the right of each dashed blue line. The top panel assumes ${\mathcal{P}_{\mathcal{R}}(k)}$ using Eq. \ref{['eq:Delta_R_k']}. Red lines show the fraction of curvature-induced DM to zero-mode DM. The bottom panel assumes $\mathcal{P}_{\mathcal{R}}(k_{\rm kin}) = 10^{-3}$. The purple region is ruled out by the second inflation bound \ref{['eq:second_inflation_bound']}, while the warmness constraint \ref{['eq:warmness_bound']} does not appear. The gray regions are the combined bounds for ALP DM from haloscopes and ALP-decay searches Wang:2023imiTodarello:2023hdkNakayama:2022jzaCarenza:2023qxhTodarello:2024qciJanish:2023kviPinetti:2025owqSaha:2025anyLiu:2023nctCapozzi:2023xieWadekar:2021qae, while the orange constraints apply to any ALP. The bounds from ALP-decay would become weaker if axion does not form DM Langhoff:2022bij. Regions above gray and orange dotted and dot-dashed will be probed by future experiments. All constraints are compiled from AxionLimits, assuming $g_{\phi \gamma \gamma} \simeq 1.02\alpha_{\rm em}/(2\pi f_a)$ as motivated by the KSVZ model Kim:1979ifShifman:1979if.
• Figure 3: Detectability of the kination peak of inflationary gravitational waves at LISA (green), BBO (brown), and ET (blue), using the scalar potential (\ref{['quadraticpotential']}) with $\{\kappa,l\} = \{10^{-4},13\}$. Yellow region violates perturbativity ($m_a/f_a>\sqrt{4\pi}$). Purple region is excluded by the second inflation bound (Eq.(8.22) of Gouttenoire:2021jhk). Pink region has DM too warm [$\omega_{\rm fluct}^{\rm eq}\simeq k_{\rm kin}/(3a_{\rm eq}m_a)>10^{-8}$]. Red lines represent the ratio $\Omega_{\rm fluct}^0/\Omega_{\rm zero}^0$. Below the black dotted line, there is no kination era; the curvature-induced DM is produced in radiation era and becomes less abundant due to $\Omega_\phi(\eta_{\rm kin})<1$ in Eq. \ref{['eq:yield_ratio']}.
• Figure S1: Same as Fig. \ref{['fig:uv_complete']} of the main text with $H_{\rm inf} = 6 \times 10^{13}\,{\rm GeV}$, but with other values of $\mathcal{P}_{\mathcal{R}}(k_{\rm kin})$.