  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.
