Raychaudhuri-based reconstruction of anisotropic Einstein-Maxwell equation in 1+3 covariant formalism of $f(R)$-gravity

Abstract: Recently, a new strategy to the reconstruction of $f(R)$-gravity models based on the Raychaudhuri equation has been suggested by Choudhury et al. In this paper, utilizing this method, the reconstruction of anisotropic Einstein-Maxwell equation in the $1+3$ covariant formalism of $f(R)$-gravity is investigated in four modes: $i.$ Reconstruction from a negative constant deceleration parameter refereeing to an ever-accelerating universe; $ii.$ Reconstruction from a constant jerk parameter $j=1$ which recovers celebrated $\Lambda \text{CDM}$ mode of evolution; $iii.$ Reconstruction from a variable jerk parameter $j=Q(t)$; and $iv.$ Reconstruction from a slowly varying jerk parameter. Furthermore, two suggestions for enhancing the method are proposed.