A post-inflationary kinetic axion

TL;DR

This work investigates axion DM production via kinetic misalignment in a post-inflationary kination era, where a negative Ricci scalar induces tachyonic growth of a non-minimally coupled complex field and triggers spontaneous $U(1)$ breaking. A higher-dimensional $U(1)$-breaking operator imparts a kick that generates a conserved $U(1)$ charge, sustaining rotation as the symmetry is restored and then translating domain charges into axion abundance when the axion potential becomes relevant. The authors provide a domain-averaged linear analysis and identify two thermal histories: (i) Ricci reheating through saxion decays to Higgs bosons, and (ii) external reheating with damping of saxion energy via Higgs/fermion scatterings; both pathways enable DM production in regions underproduced by standard misalignment, with implications for next-generation axion searches. The scenario also naturally yields axion-rich domains with distinctive phenomenology, including topological defects and a relaxed isocurvature constraint relative to pre-inflationary models, and makes concrete predictions for the axion mass-decay constant parameter space that can be probed by upcoming experiments.

Abstract

We present a novel realization of axion kinetic misalignment, triggered by a Hubble-induced phase transition during a post-inflationary stiff (kination) era. A negative Ricci scalar flips the sign of a non-minimally coupled mass term for a non-minimally coupled complex field $Φ$, driving its radial mode to large amplitudes via a tachyonic instability. At large $|Φ|$, higher-dimensional $U(1)$-breaking operators become relevant and impart a kick in the angular direction, generating a conserved $U(1)$ charge that sustains rotation as the symmetry is approximately restored. Because phases randomize across causally disconnected regions, multiple domains with distinct charges form. The subsequent axion potential converts the domain charges into an axion abundance, yielding dark matter even when the net global charge vanishes. We analyze the dynamics through a linear, domain-averaged treatment and identify two thermal histories: (i) Ricci reheating via saxion decays to Higgs bosons; (ii) external reheating with efficient damping of saxion energy by Higgs/fermion scatterings. The mechanism populates regions underabundant in standard misalignment, which are accessible to next generation axion searches.

Figures (11)

• Figure 1: Left: Evolution of the saxion field $S$. The numerical result is shown in red, the analytic solution of Eq. \ref{['growing solution']} is displayed with a dashed brown line, showing a good agreement during the tachyonic growth. The two dashed purple lines represent Eqs. \ref{['Hmax']} and \ref{['Smax']}, while the position of the minimum Eq. \ref{['Smin']} is displayed in grey. On the right, the same evolution in the complex plane, where the rotating dynamics of $\Phi$ is showed. The parameters used are $H_I=10^{12}\,\text{GeV},\,f_a=10^{10}\,\text{GeV},\,\lambda=10^{-12},\,\xi=5,\,n=7$.
• Figure 2: Evolution of the components of the energy density, in the scenario in which the saxion reheats the universe. At the end of inflation, a period of kination starts at $H_{\text{ks}}$, during which the field $S$ grows until it reaches a maximum value at $H_\mathrm{max}$, and then scales as $\rho_S\sim a^{-4}$. At $H_\mathrm{ke}$ it overtakes the inflaton energy density. At $H_\mathrm{rh}$ the saxion decays and reheats the thermal bath. The energy in the axion condensate scales as $a^{-6}$ (kination) until the field gets trapped in the potential at $H_\text{trap}$, and the dark-matter behaviour begins.
• Figure 3: Same plot as the one showed in Fig. \ref{['fig:energy evolution']}, but in this scenario the $\Phi$ does not dominate the energy density and reheating is achieved via some other mechanism.
• Figure 4: In these plots we show the allowed parameter space to achieve an efficient tachyonic growth and a subsequent kick. The parameter $f_a$ is left free, $m_a$ is related to $\lambda$ by requiring the correct dark matter abundance (see Sec. \ref{['sec:Axion Dark Matter Abundance']}) and $A$ is fixed in order to get $\epsilon\sim1$. Gravitational Backreaction refers to the saxion dominating the energy density during the tachyonic growth as computed in Eq. \ref{['GB lowerbound']}. In the region indicated with Kination Bound the duration of kination is too long violating Eq. \ref{['kination bound']}. The upper bound is provided by requiring $A>M_{\text{Pl}}$ in order to have an efficient kick, see Eq. \ref{['boundA']}. Finally, the upper bound on $H_I$ is provided by Planck observations Planck:2018jri.
• Figure 5: Parameter space $[m_a,f_a^{-1}]$ for $\xi=3, n=7, H_I=10^{13}\,\text{GeV}$. The constraints Astrophysics and Haloscopes have been taken from AxionLimits. We show where the axion abundance is given by the string-DW decay, for large $f_a$ dark matter is achieved via standard misalignment, where the saxion mass is smaller than the Higgs mass, so reheating can not occur via decay into Higgs, conversely if the saxion mass is too large it will early decay into axions resulting in a cold universe, in which BBN never happened. Finally the Strong CP Problem is not solved in any point of the QCD axion line, for this reason it is colored in dark blue. We show contours of reheating temperature, achieved via decay into Higgs bosons, Eq. \ref{['Reheating Temperature']}. With dashed lines we show projectionts of future experiments like IAXO2002clme.book.....GArmengaud:2014gea and a combination of Haloscope searches like BREAD BREAD:2021tpx, MADMAX Beurthey:2020yuq, ADMX ADMX:2018ghoADMX:2018ogsADMX:2019uokADMX:2021mioADMX:2021nhdStern:2016bbwCrisosto:2019fcjADMX:2025vom.