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Cosmological Constant in the Imaginary-Time Field Theory

The origins of the cosmological constant are discussed from the perspective of the imaginary-time field theory. The concept of the thermal time, which is related to the Tolman-Ehrehfest relation, and the conformal invariance of the actions are applied to account for the relation between the scale factor of the FRW metric and the temperature of the vacuum. Finite values of the cosmological constant from the DeWitt-Schwinger representation and the Casimir effect with a large separation between two plates are derived. The induced energy density is found to be uniform over the space and independent of the evolution of the universe, and the equation of state ratio is indeed $w=-1$. From the point of view presented here, the largest discrepancy of the vacuum energy between the theoretical and the experimental sides can be conciliated. And the value of the cosmological constant corresponds to a characteristic temperature of vacuum determined by the history of the universe.