High Reheating Temperature without Axion Domain Walls

TL;DR

The paper tackles the axion domain-wall and isocurvature problems by proposing a Peccei-Quinn non-restoration scenario in which the PQ symmetry remains broken throughout the Universe. It achieves this with a non-supersymmetric two-field PQ sector that yields a flat direction and, via a negative thermal mass from singlet couplings, prevents symmetry restoration at high temperatures. A Daisy-resummed finite-temperature analysis shows a viable parameter space where $v_{ m PQ}(T)$ stays nonzero, allowing arbitrarily high $T_R$ and remaining consistent with observational constraints. This provides a minimal framework that enables high-scale baryogenesis, including thermal leptogenesis, while simultaneously avoiding topological defects and isocurvature constraints.

Abstract

We investigate a cosmological scenario in which the Peccei-Quinn (PQ) symmetry remains broken in the entire history of the Universe, thereby avoiding the formation of axion strings and domain walls. Contrary to the conventional expectation, it is demonstrated that appropriately chosen scalar interactions are able to keep the PQ symmetry broken at arbitrarily high temperatures. We carefully examine the finite-temperature effective potential in a model with two PQ breaking scalar fields. The existence of flat directions plays a vital role in suppressing axion isocurvature perturbations during inflation by stabilizing a PQ field at a large field value. The viable parameter space consistent with theoretical and observational constraints is identified. Our scenario provides a minimal path for PQ symmetry breaking that addresses both the axion domain wall and isocurvature problems while permitting arbitrarily high reheating temperatures accommodating high-scale baryogenesis scenarios such as thermal leptogenesis.

Figures (2)

• Figure 1: The PQ scale $v_{\rm PQ}$ against temperature $T$. Here we take $f_a = 10^{12}$ GeV, $\lambda =0.03$, $m_\psi = 10^{11}$ GeV, $\mu_s = 4\times 10^{12}$ GeV, $\mu_\xi = \mu_\eta = 2 \times 10^{12}$ GeV, $\lambda_s = 0.8$, $N_s = 1$ and $N_{\rm DW} = N_\psi = 10$.
• Figure 2: The parameter space for $|\lambda_{\phi s}|$ and $\lambda$. The shaded regions are excluded by different aspects. The runaway region is where $|\lambda_{\phi s} | > \sqrt{\lambda_s \lambda}/2$. The $v_{\rm PQ}(\infty) \to 0$ indicates an insufficient amount of $|\lambda_{\phi s}|$ to keep the broken phase against high temperature according to Eq. \ref{['eq:high_T_V_1']}. The $\tilde{m}_{\xi,\eta,s}^2<0$ region indicates the instability of expected vacuum solution. Here $\tilde{m}_i^2$ is the second derivative of the zero temperature potential $V_0 + V_1^{(0)}$ evaluated at Eq. \ref{['eq:vacuum_solution']}. Thermal effects will further stabilize them as indicated by their thermal mass corrections \ref{['eq:Pi_s']}. Here we take $m_\psi = 10^{11}$ GeV, $\mu_\xi = \mu_\eta = 2\times 10^{12}$ GeV, $\mu_s = 4\times 10^{10}$ GeV, $\lambda_s=0.8$, $N_s =1$ and $N_{\rm DW} = N_\psi = 10$ as a benchmark. The solid (dashed) lines are limits under $f_a = 10^{12} \, (8\times 10^{11}) \, \rm GeV$. The thermal bounds (blue shaded region) are where $s$ does not have thermal contact with PQ fields; the solid (dotted) line is obtained under reheating temperature $T_{\rm R} = 10^{15} \, (10^{14}) \, \rm GeV$. Here we take the Hubble parameter during radiation-dominated epoch as $H\simeq 3.4 \times T^2/M_{\rm Pl}$.