Quantum de Sitter Spacetime and Energy Density Contributed from the Cosmological Constant

Previously we introduce a new way to quantize the static Schwarzschild black hole (SSBH), there the SSBH was first treated as a single periodic Euclidean system and then the Bohr--Sommerfeld quantum condition of action was used to obtain a quantum theory of Schwarzschild black hole [Chin. Phys. Lett. (2004) 21 1887]. Here we try to extend the above method to quantize the static de Sitter (SDS) spacetime and establish a quantum theory of both SDS space and the energy density contributed from the cosmological constant.