Slow and fast light dynamics in a chiral cold and hot atomic medium

We study Chiral Based Electromagnetically Induced Transparency (CBEIT) of a light pulse and its associated subluminal and superluminal behavior through a cold and a hot medium of 4-level \textit{double-Lambda type} atomic system. The dynamical behavior of this chiral based system is temperature dependent. The magnetic field based chirality and dispersion is always opposite as compared with the electric field ones. Contrastingly, the response of the chiral effect along with the incoherence Doppler broadening mechanism enhances the superluminal behavior as compared with its traditional degrading effect. Nevertheless, the intensity of a coupled microwave field destroys the coherence of the medium and degrade superluminality and subluminality of the sysmtem. The undistorted retrieved pulse from a hot chiral medium delays by $896 ns$ than from a cold chiral medium under same set of parameters. Nevertheless, it advances by $-31n s$ in the cold chiral medium when a suitably different spectroscopic parameters are selected. The corresponding group index of the medium and the time delay/advance, are studied and analyzed explicitly [Note: A revise version is under preparation