Domain wall and isocurvature perturbation problems in axion models

Abstract

Axion models have two serious cosmological problems, domain wall and isocurvature perturbation problems. In order to solve these problems we investigate the Linde's model in which the field value of the Peccei-Quinn (PQ) scalar is large during inflation. In this model the fluctuations of the PQ field grow after inflation through the parametric resonance and stable axionic strings may be produced, which results in the domain wall problem. We study formation of axionic strings using lattice simulations. It is found that in chaotic inflation the axion model is free from both the domain wall and the isocurvature perturbation problems if the initial misalignment angle θ a is smaller than O(10 −2 ). Furthermore, axions can also account for the dark matter for the breaking scale v 10 12−16 GeV and the Hubble parameter during inflation H inf 10 11−12 GeV in general inflation models.

Saxion cosmology for thermalized gravitino dark matter

“…Once the fluctuation of the axion field becomes much larger than V PQ , the axion field takes spatially varying random values, leading to the formation of domain walls after the QCD phase transition [47][48][49][50][51][52][53][54]. If N DW = 1, these domain walls are unstable and decay into axions.…”

Axion dark matter from topological defects

“…In particular, the cosmological scenario becomes different according to whether the PQ symmetry is broken after inflation or not. If the PQ symmetry is restored during inflation, the isocurvature perturbations induced by the quantum fluctuations of the axion field during inflation affect the observational results of the cosmic microwave background, putting a stringent constraint on the axion models if the inflationary scale is sufficiently high [10][11][12][13][14][15][16][17]. On the other hand, if the PQ symmetry is broken after inflation, topological defects such as strings and domain walls are formed, and we must take account of their evolution in the early universe.…”

Nonthermal axion dark radiation and constraints

“…Due to large amplitude, σ 0 ≫ f PQ , the initial oscillations will take place around σ ¼ 0. This can result in large quantum amplification of the fluctuations in the PQ field especially along the massless angular direction [24], which may lead to the restoration of the PQ symmetry and consequently the formation of potentially dangerous topological defects unless σ ≲ 10 4 f PQ [21]. Note that we shall adhere to this bound on σ ≲ 10 4 f PQ here.…”

“…On the other hand, if the initial amplitude of the oscillation satisfies σ 0 ≳ 10 4 f PQ , the PQ symmetry can get restored nonthermally, which leads to the formation of topological defects [21]. In order to avoid this, we require that…”

“…This can lead to the restoration of the PQ symmetry and formation of dangerous topological defects [16,17]. 2 The nonthermal restoration of the PQ symmetry can be avoided if the amplitude of the PQ field at the beginning of the oscillation phase is less than ≲10 4 f PQ [21] or, if there is a coupling between the PQ field and the total energy density of the inflaton, and the oscillation of the PQ field is driven by a higher order term in the potential [22,23]. Note that similar constraints would follow, if we had considered a moduli field instead of an inflaton field.…”