The paper commences by examining the geometric properties of de-Sitter space-time, with a specific focus on the isometries generated by Killing vectors. It also investigates various metrics that are applicable to specific regions of space-time, revealing that in the distant future, the symmetries exhibit a similar local structure to that of
Furthermore, the classical Klein-Gordon equation is solved within this space-time, leading to the discovery that energy is not conserved. The solutions to the Klein-Gordon equation yield intriguing outcomes that have the potential to enable observations from the early inflationary era. Finally, the primary objective of the paper is to comprehensively examine a quantized scalar field in the de-Sitter background, exploring the solutions for the two-point function and analyzing their behavior during both early and late time periods.