Ground state of the universe and the cosmological constant. A nonperturbative analysis

The physical Hamiltonian of a gravity-matter system depends on the choice of time, with the vacuum naturally identified as its ground state. We study the expanding universe with scalar field in the volume time gauge. We show that the vacuum energy density computed from the resulting Hamiltonian is a non-linear function of the cosmological constant and time. This result provides a new perspective on the relation between time, the cosmological constant, and vacuum energy.