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# Big Bang Nucleosynthesis with an Inhomogeneous Primordial Magnetic Field Strength

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### Abstract

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 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 $$\rho_{\rm Bc}$$ and the fluctuation parameter $$\sigma_{\rm B}$$. 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 $$\eta$$, $$\rho_{\rm Bc}$$, and $$\sigma_{\rm B}$$. We find that the fluctuations of the PMF reduces the $$^7$$Be production and enhances 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 $$\rho_{\rm Bc}$$ and $$\sigma_{\rm B}$$ for our fluctuating PMF model from observed abundances of $$^4$$He and D. In this model, the $$^7$$Li 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 if the $$\eta$$ value during BBN was larger than the present-day value, all produced light elements are consistent with observational constraints.

### Most cited references5

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### Compilation and R-matrix analysis of Big Bang nuclear reaction rates

(2004)
We use the R-matrix theory to fit low-energy data on nuclear reactions involved in Big Bang nucleosynthesis. A special attention is paid to the rate uncertainties which are evaluated on statistical grounds. We provide S factors and reaction rates in tabular and graphical formats.
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### Primordial nucleosynthesis

(2017)
Primordial nucleosynthesis, or big bang nucleosynthesis (BBN), is one of the three evidences for the big bang model, together with the expansion of the universe and the cosmic microwave background. There is a good global agreement over a range of nine orders of magnitude between abundances of 4He, D, 3He and 7Li deduced from observations, and calculated in primordial nucleosynthesis. However, there remains a yet-unexplained discrepancy of a factor 3, between the calculated and observed lithium primordial abundances, that has not been reduced, neither by recent nuclear physics experiments, nor by new observations. The precision in deuterium observations in cosmological clouds has recently improved dramatically, so that nuclear cross-sections involved in deuterium BBN needs to be known with similar precision. We will briefly discuss nuclear aspects related to the BBN of Li and D, BBN with nonstandard neutron sources, and finally, improved sensitivity studies using a Monte Carlo method that can be used in other sites of nucleosynthesis.
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### Introduction to Big Bang Nucleosynthesis and Modern Cosmology

Primordial nucleosynthesis remains as one of the pillars of modern cosmology. It is the testing ground upon which many cosmological models must ultimately rest. It is our only probe of the universe during the important radiation-dominated epoch in the first few minutes of cosmic expansion. This chapter reviews the basic equations of space-time, cosmology, and big bang nucleosynthesis. We also summarize the current state of observational constraints on primordial abundances along with the key nuclear reactions and their uncertainties. We summarize which nuclear measurements are most crucial during the big bang. We also review various cosmological models and their constraints. In particular, we analyze the constraints that big bang nucleosynthesis places upon the possible time variation of fundamental constants, along with constraints on the nature and origin of dark matter and dark energy, long-lived supersymmetric particles, gravity waves, and the primordial magnetic field.
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### Author and article information

###### Journal
20 October 2018
###### Article
1810.08803