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arXiv 2005.05568hep-phastro-ph.CO
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暴胀宇宙学--使用非线性电动力学的新方法

Inflationary cosmology- A new approach using Non-linear electrodynamics

Payel Sarkar, Prasanta Kumar Das, Gauranga Charan Samanta

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11 pages, 17 figures
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摘要：

我们探索了一种新的非线性电动力学（NLED）场，它作为引力源，可以在暴胀时代加速宇宙。本文提出了一种新的NLED拉格朗日量，它由两个参数$α$和$β$表征。我们研究了这个模型的经典稳定性和因果关系方面的要求，速度（$C_s = \frac{dP}{dρ}$）的声波$C_s^2 > 0$和$C_s \le 1$，并发现$0 < C_s^2 < 1$对应于$0.25 \le α\le 0.4$和$0.6 \le βB^2 \le 1$。对减速参数（$q = \frac{1}{2}(1 + 3 ω)$，$ω= P/ρ$是状态方程参数）的研究表明，$q < 0$值（即$ω< -1/3$和$\ddot{a}(t) > 0$（加速宇宙））需要$βB^2 \ge 0.13$。在膨胀期间，能量密度$ρ_B$被发现是最大的并且由对应于$α= 0.3$的$ρ_B^{max} = 0.65/β$给出。引发暴胀所需的磁场是$B (= B_{max}) \simeq \sqrt{\frac{0.4 ρ_B^{max}}{0.65}} = 4 \times 10^{51}~{\rm Gauss}$，其中$ρ_{B}^{max}( =10^{64}~{\rm GeV}^4 $是暴胀期间宇宙的能量密度。该模型还预测了e倍数$N = 71$，与实验结果一致。

英文摘要：

We explore a new kind of field of nonlinear electrodynamics(NLED) which acts as a source of gravity and can accelerate the universe during the inflationary era. We propose a new type of NLED lagrangian which is charecterized by two paremetrs $α$ and $β$. We investigate the classical stability and causality aspects of this model by demanding that the speed ($C_s = \frac{dP}{dρ}$) of the sound wave $C_s^2 > 0$ and $C_s \le 1$ and find that $0 < C_s^2 < 1$ corresponds to $0.25 \le α\le 0.4$ and $0.6 \le βB^2 \le 1$. A study of the deceleration parameter($q = \frac{1}{2}(1 + 3 ω)$, $ω= P/ρ$ being the equation of state parameter) suggests that the value $q < 0$ (i.e. $ω< -1/3$ and $\ddot{a}(t) > 0$ ( the accelerating universe)) requires $βB^2 \ge 0.13$. During inflation, the energy density $ρ_B$ is found to be maximum and is given by $ρ_B^{max} = 0.65/β$ corresponding to $α= 0.3$. The magnetic field necessary to trigger the inflation, is found to be $B (= B_{max}) \simeq \sqrt{\frac{0.4 ρ_B^{max}}{0.65}} = 4 \times 10^{51}~{\rm Gauss}$, where $ρ_{B}^{max}( =10^{64}~{\rm GeV}^4 $) is the energy density of the universe during inflation. The model also predict the e-fold number $N = 71$, which agrees with the experimental result.

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