Abstract
We study the evolution of axions interacting with primordial magnetic fields (PMFs) starting just from the QCD phase transition in the expanding universe. This interaction is owing to the Primakoff effect. Adopting the zero mode approximation for axions, we derive the system of equations for axions and magnetic fields, where the expansion of the universe and the spectra of magnetic fields are accounted for exactly. We find that the contribution of the Primakoff effect to the dynamics of axions and magnetic fields is rather weak. It confirms some previous estimates leading to analogous conclusions, when accounting here for the Hubble expansion both for an uniform axion field and non-uniform PMFs using Fourier spectra for their energy and helicity densities. We solve the corresponding system of the evolution equations and find that the axion zero mode, when evolving during radiation era, has its amplitude at the level sufficient for that axion to be a good candidate for the cold dark matter.
Highlights
As a solution to the CP problem in quantum chromodynamics (QCD), Peccei and Quinn suggested a mechanism that naturally gives rise to a Nambu-Goldstone boson, the so-called axion [1,2,3]
The axion provides a possible candidate for the cold dark matter (CDM) of the Universe [4]
We adopt that in the Universe cooling TPQ → TQCD, where TPQ ≃ fa 1⁄4 ð1010–1012Þ GeV is the temperature at the Peccei-Quinn phase transition, TQCD ≃ ð100–200Þ MeV is the temperature at the QCD phase transition (QCDPT), and fa is the Peccei-Quinn (PQ) parameter
Summary
As a solution to the CP problem in quantum chromodynamics (QCD), Peccei and Quinn suggested a mechanism that naturally gives rise to a Nambu-Goldstone boson, the so-called axion [1,2,3]. The simultaneous presence of primordial magnetic fields (PMFs) and an axion field in a hot Universe plasma near the QCD phase transition (QCDPT) allows to study their mutual influence during the radiation era. BY which exist before the electroweak phase transition, T > TEW ≃ ð100–160Þ GeV Such PMFs, being a seed for observable galactic magnetic fields B ∼ 10−6 G, can be strong enough at TQCD. B; ð1:2Þ or, vice versa, whether the PMF can influence the evolution of the uniform axion field, ∇φ 1⁄4 0, φþ m2aφ gaγ σcond ð∇. The problem of the mutual influence of axions and PMFs was discussed in Ref.
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