Inflationary cosmology- A new approach using Non-linear electrodynamics

Abstract

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 $\alpha$ and $\beta$. We investigate the classical stability and causality aspects of this model by demanding that the speed ($C_s=\frac{dP}{d\rho }$) of the sound wave $C_s^2>0$ and $C_s\le 1$ and find that $0<C_s^2<1$ corresponds to $0.25\le \alpha \le 0.4$ and $0.6\le \beta B^2\le 1$. A study of the deceleration parameter($q=\frac{1}{2}(1+3\omega )$, $\omega =P/\rho$ being the equation of state parameter) suggests that the value $q<0$ (i.e. $\omega <-1/3$ and $\ddot{a}(t)>0$ ( the accelerating universe)) requires $\beta B^2\ge 0.13$. During inflation, the energy density ${\rho }_B$ is found to be maximum and is given by ${\rho }_B^{max}=0.65/\beta$ corresponding to $\alpha =0.3$. The magnetic field necessary to trigger the inflation, is found to be $B(=B_{max})\simeq \sqrt{\frac{0.4{\rho }_B^{max}}{0.65}}=4\times 10^{51}\mathrm{Gauss}$, where ${\rho }_B^{max}(=10^{64}{\mathrm{GeV}}^4$) 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.

Comments: 11 pages, 17 figures