SU(1,1) Lie algebraic approach for the evolution of the quantum inflationary universe

Quantum behavior of scalar fields and vacuum energy density in inflationary universe are investigated using SU(1,1) Lie algebraic approach. Wave functions describing the evolution of scalar fields thought to have driven cosmic inflation are identified in several possible quantum states at the early stage of the universe, such as the Fock state, the Glauber coherent state, and SU(1,1) coherent states. In particular, we focus in this research on two important classes of SU(1,1) coherent states, so-called the even and odd coherent states and the Perelomov coherent state. It is shown in spatially flat universe driven by a single scalar field that the probability densities in all these states have converged to the origin (ϕ = 0, where ϕ is the scalar field) as time goes by. This outcome implies that the vacuum energy density characterized by the scalar field dissipates with time. The probability density in the matter-dominated era converged more rapidly than that in the radiation-dominated era. Hence, we can confirm that the progress of dissipation for vacuum energy density became faster as the matter era began after the end of the early dominance of radiation. This consequence is, indeed, well agree with the results of our previous researches in cosmology (for example, see [Chin. Phys. C 35 (2011) 233] and references there in).