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

Abstract

Abstract Quantum behavior of scalar fields and vacuum energy density in the inflationary universe are investigated using SU(1,1) Lie algebraic approach. Wave functions describing the evolution of scalar fields that have been 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 the SU(1,1) coherent states. In particular, we focus in this research on two important classes of the SU(1,1) coherent states, which are the so-called even and odd coherent states and the Perelomov coherent state. It is shown in the 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 the vacuum energy density became faster as the matter era began after the end of the early dominance of radiation. This consequence is, indeed, in agreement with the results of our previous researches in cosmology (for example, see [Chin. Phys. C 35 (2011) 233] and references there in).