Accelerating Universe from constraints

Abstract

We introduce a framework of constrained scalar fields that can give rise to cosmological evolution of the Universe independent of the values of the cosmological constant. Focusing on the simplest realization involving a scalar field with non-minimal coupling, we first study the analytical solutions in the Jordan frame. We show that such solutions include evolution from a radiation dominated-like universe to an exponential expansion, as well as evolution that starts with super-Hubble expansion and then relaxes towards an exponential expansion of the Universe, while describing well-behaved scalar perturbations. We then also relate the theory to the Einstein frame, and analyze the corresponding accelerating solutions. We then consider the model in the presence of external matter. We find that the matter does not affect the evolution of the universe if minimally coupled to the scalar field. In other words, in the Jordan frame, in order to influence the evolution of the space-time, the matter should be non-minimally coupled to the constrained scalar, while it may be minimally coupled to gravity. We show that in this case, the solutions are similar to the free case, and, in addition, allow for the phantom-like equation of state. Finally, we introduce the minimal frame, a frame in which the matter is minimally coupled to both gravity and the constrained scalar, and show that among other possibilities, the phantom-like equation of state can still be realized.