Varying vacuum energy of a self-interacting scalar field

Abstract

Understanding mechanisms capable of altering the vacuum energy is currently of interest in field theories and cosmology. We consider an interacting scalar field and show that the vacuum energy naturally takes any value between its maximum and zero because interaction affects the number of operating field modes, the assertion that involves no assumptions or postulates. The mechanism is similar to the recently discussed temperature evolution of collective modes in liquids. The cosmological implication concerns the evolution of scalar field $\phi$ during the inflation of the Universe. $\phi$ starts with all field modes operating and maximal vacuum energy in the early inflation-dominated epoch. As a result of inflation, $\phi$ undergoes a dynamical crossover and arrives in the state with one long-wavelength longitudinal mode and small positive vacuum energy predicted to be asymptotically decreasing to zero in the late epoch. Accordingly, we predict that the currently observed cosmological constant will decrease in the future, and comment on the possibility of a cyclic Universe.