Introduction to the Line-of-Sight Approach to CMB and Refine It to Incorporate Effects from Reionization

Cosmic Microwave Background (CMB) is the relic microwave radiation emitted at last scattering surface and fills all space in our universe. The FriedmannLematreRobertsonWalker metric predicts a homogeneous and isotropy CMB temperature distribution, but in fact people observe some anisotropic temperature fluctuation of CMB across the universe. This paper will provide history of exploring CMB and discuss anisotropic property of CMB across the sky. A possible explanation of this anisotropy behaviour of free CMB photons, the Line-of-Sight (LoS) approach of Boltzmann equation, including Sachs Wolfe effect, gravitational Doppler effect and Integrated Sachs Wolfe effect, and mathematical derivation of LoS from Boltzmann equation will also be included. Then this paper will provide a possible way to modify the LoS to include effects from the Reionization and include error propagation analysis. Finally this paper will discuss the importance in studying the anisotropy of CMB, the LoS and why we need to refine it.