This dissertation is an investigation into some properties of vacuum states in curved space-time. The energy spectrum of zero-point field of a massless scalar field in many particle state and in the presence of both uniform acceleration and temperature, and nontrival topology and acceleration is obained using zero-point field method. If uniformly accelerated observer``s proper time goes to infinity, then the vacuum state and many particle state are indistingushable. But in the case of thermal state, though the energy spectrum is not thermal, this is distinguishable from the vacuum state as observer``s time goes to infinity. Finally, using functional Schrodinger formalism, Unruh effect on deSitter space-time is investigated.