Big Bang Nucleosynthesis with an Inhomogeneous Primordial Magnetic Field Strength

Big Bang Nucleosynthesis (BBN) agrees well with the observational abundances of light elements 2H, 3He and 4He except for 7Li. We find that the abundances of these elements can be affected strongly by a stochastic primordial magnetic field (PMF) whose strength is spatially inhomogeneous. We assume an uniform total energy density with a large-scale stochastic PMF and a gaussian distribution of field strength. We show that in such case, the effective distribution function of particle velocities averaged over domains of different temperature is deviates from the Maxwell-Boltzmann (MB) distribution. We perform BBN network calculations taking account the PMF strength distribution and find that the fluctuation of the PMF reduces the 7Be production and enhances 2H production. Finally, we constrain the parameters ρBc and σ for our fluctuating PMF model from observed abundances of 4He and 2H. In this model, the 7Li abundance is significantly reduced. We also discuss the possibility that the baryon-to-photon ratio decreased after the BBN epoch. In this case, we find that for η larger than the present-day value, all light elements can be consistent with observational data.