Large lepton asymmetry from axion inflation and helium abundance hinted by ACT

TL;DR

The work addresses the ACT-indicated lowering of primordial helium by generating a sizable lepton asymmetry through axion inflation coupled to a gauged $U(1)_{L_i-L_j}$ gauge field. It identifies backreaction from Schwinger-produced fermions as the main obstacle to obtaining large asymmetries during inflation, and proposes a mechanism to suppress Schwinger production by employing a spectator sector that dynamically heavyens leptons during inflation. In this suppressed-Schwinger scenario, magnetic helicity generated during inflation survives into the magnetohydrodynamic era and decays after the electroweak transition, transferring helicity into $L_i-L_j$ asymmetries; for the gauged $U(1)_{L_ ext{μ}-L_ ext{τ}}$, this can yield the required electron-neutrino asymmetry to reduce $Y_p$ without conflicting with baryon overproduction, while remaining compatible with laboratory constraints and possibly addressing the muon $g-2$ anomaly. The results thus illustrate a viable pathway to reconcile CMB hints with leptogenesis via a concrete axion-inflationary mechanism, and point to concrete experimental probes of a light $Z'$ boson and gravitational waves from gauge-field dynamics.

Abstract

The generation of helical magnetic fields and the associated chiral asymmetry via the chiral anomaly is a generic feature in pseudoscalar inflation. In the presence of a Chern--Simons coupling between the inflaton and a U(1) gauge field, the homogeneous evolution of the inflaton induces a tachyonic instability in one circular polarization of the gauge field, resulting in the production of helical magnetic fields. In this work, we show that, in the case of a gauged lepton flavor symmetry, U(1)$_{L_i-L_j}$, this mechanism can lead to the generation of a sizable lepton asymmetry. In a simple setup, however, the resulting lepton asymmetry is typically too small to have an observational consequences, even setting aside constraints from baryon overproduction via sphaleron processes, due to the backreaction of the produced gauge fields and fermions on the inflationary dynamics. We demonstrate that this limitation can be overcome by implementing a mechanism to suppress fermion production during inflation. As a result, a much larger lepton asymmetry can be generated from the subsequent decay of magnetic helicity. Remarkably, for the gauged U(1)$_{L_μ-L_τ}$ symmetry, the generated asymmetry can be sufficiently large to suppress the primordial helium abundance, as may be inferred from recent cosmic microwave background observations by ACT.

Figures (4)

• Figure 1: The parameter space excluded by non-negligible backreaction from the energy densities of the produced gauge fields and fermions is shown in the plane of the Hubble parameter during inflation and the helicity-to-entropy ratio, for $g_{L_i-L_j}= 0.1$ (left) and 0.0003 (right). The black solid line correspond to $\rho_{\psi}+\rho_{X}=0.01\rho_{\phi}$, while the black dashed line indicate $\rho_{\psi}+\rho_{X}=0.1 \rho_\phi$ for reference. The yellow-shaded regions to the right of these lines are excluded. The thick and thin blue dashed lines indicate the conditions $\rho_{X}=0.01\rho_{\phi}$ and $\rho_{\psi}=0.01\rho_{\phi}$, respevtively, showing which contribution dominates the backreaction. The thick and thin brown shaded regions denote the parameter space preferred by the ACT and SPT results, assuming that the corresponding electron neutrino asymmetry is generated (Eq. \ref{['eq:nueasymACT']}). Note that the upper bounds of the ACT and SPT results are almost the same.
• Figure 2: Parameter space constraints for the spectator field model. The green line denotes the curvature-induced mass domination condition, $c_S > \dfrac{m_S^2}{12H^2}$ with the region to the right allowed. The blue line corresponds to the lower bound from the Schwinger suppression, $m_\nu > \sqrt{g_{L_i-L_j}E_X/\pi}$, where the region to the right is allowed. The cyan line represents the stabilization condition for a non-zero expectation value of the $S$ field, $\lambda_{SH}^2 < 4 \lambda_S \lambda_H$, with the allowed region lying above the line.. The purple line indicates the backreaction constraint, $\rho_S+\rho_H < \rho_{\phi}$, allowing the region to the left. The black line shows the EFT validity condition, $S_0< \Lambda_W$, with the allowed region to the left. The dark blue line represents the requirement that the $S$ field decays rapidly after inflation $\lambda_S > 3172 \pi^3 c_S \left(\dfrac{H_\mathrm{inf}}{m_S}\right)^3$, again allowing the region to the left. The white region denotes the parameter space simultaneously satisfying all constraints.
• Figure 3: The parameter space constrained by the survival condition of magnetic helicity after inflation, in the absence of the Schwinger effect, is shown in the $\eta_\mathrm{H}$-$H_\mathrm{inf}$ plane for $g_{L_i-L_j} =3\times 10^{-4}$. The purple solid line correspond to $R_m=1$, and the cyan-shaded regions to the left is excluded by the condition $R_m<1$. The black solid line indicates $\rho_{X}=0.01\rho_{\phi}$, while the yellow-shaded regions to the right is excluded by non-negligible backreaction from the energy density of the gauge fields during inflation. The brown and green shaded regions represent the parameter space preferred by the ACT and SPT results, assuming the corresponding electron neutrino asymmetry is generated (Eq. \ref{['eq:nueasymACT']}). The green-shaded regions denote the parameter space accessible in our scenario. The green, gray, and black dashed lines show contours of $\xi=16,17,18$, respectively.
• Figure 4: The parameter space in the $m_{Z'}$-$g_{L_\mu-L_\tau}$ plane in which the the U(1)$_{L_\mu-L_\tau}$ symmetry breaking to occur after EWPT and before BBN is shown, together with existing experimental constraints. The upper gray-shadowed region is excluded by the condition $T_{\mathrm{BBN}}<T_c$, while the lower gray-shadowed region is excluded by $T_c<T_{\mathrm{EW}}$, so that remaining region satisfies Eq. \ref{['eq:gcbbnew']}. Colored regions indicate experimental constrains for $Z'$ parameter space: the bound from the effective number of neutrino species $\Delta N_\mathrm{eff}\leq0.5$, for $g_{\mu\tau}\geq4\times10^{-9}$ and $m_{Z'}\leq0.1\mathrm{GeV}$ (light purple) Escudero:2019gzq; ATLAS searches (thick purple) ATLAS:2023vxgATLAS:2024uvu; hot white dwarf cooling (thick orange) Bell:2025acgFoldenauer:2024cdp; the muon anomalous magnetic moment $\Delta a_\mu$ within $1\sigma$ uncertainty (pink) Muong-2:2025xykAliberti:2025beg; Borexino (light orange) Bellini:2011rx; NA64$\mu$ (yellow) Andreev:2024lps; BaBar & Bell (thick blue) BaBar:2016sciBelle-II:2024wtd; and neutrino trident production from CCFR (light blue) Altmannshofer:2014pba. For the experimental constraints, we use the compiled data in Bernal:2025szh.