Conformal symmetry of the cosmological constant and the cosmological constant vacuum

In this paper we analyze the relationship between the cosmological constant and the cosmological constant vacuum. We investigate the formation of the cosmological constant in the presence of a massless scalar field. After introducing the appropriate positive and negative limits, we show that the formation of the cosmological constant is always possible in the presence of a massless scalar field. We also demonstrate that the formation of the cosmological constant is in agreement with the second order noncommutative Lagrangian of the common scalar fields.