Big Bang Nucleosynthesis with an Inhomogeneous Primordial Magnetic Field Strength

Yudong Luo1,2,3, Toshitaka Kajino1,2,3, Motohiko Kusakabe1,3, and Grant J. Mathews1,4
Astrophysical Journal 872, 172 Link to Article [DOI: 10.3847/1538-4357/ab0088 ]
1National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan
2Department of Astronomy, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
3School of Physics and Nuclear Energy Engineering, and International Research Center for Big-Bang Cosmology and Element Genesis, Beihang University 37, Xueyuan Road, Haidian-qu, Beijing 100083, People’s Republic of China
4Center for Astrophysics, Department of Physics, University of Notre Dame, Notre Dame, IN 46556, USA

We investigate the effect on the Big Bang nucleosynthesis (BBN) from the presence of a stochastic primordial magnetic field (PMF) whose strength is spatially inhomogeneous. We assume a uniform total energy density and a Gaussian distribution of field strength. In this case, domains of different temperatures exist in the BBN epoch due to variations in the local PMF. We show that in such a case, the effective distribution function of particle velocities averaged over domains of different temperatures deviates from the Maxwell–Boltzmann distribution. This deviation is related to the scale invariant strength of the PMF energy density ρ Bc and the fluctuation parameter σ B. We perform BBN network calculations taking into account the PMF strength distribution and deduce the element abundances as functions of the baryon-to-photon ratio η, ρ Bc, and σ B. We find that the fluctuations of the PMF reduce the 7Be production and enhance D production. We analyze the averaged thermonuclear reaction rates compared with those of a single temperature and find that the averaged charged-particle reaction rates are very different. Finally, we constrain the parameters ρ Bcand σ B from observed abundances of 4He and D and find that the 7Li abundance is significantly reduced. We also find that if the η value during BBN was larger than the present-day value due to a dissipation of the PMF or a radiative decay of exotic particles after BBN or if the stellar depletion of 7Li occurred, abundances of all light elements can be consistent with observational constraints.

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