On the cosmological constant as a quantum operator

Abstract

We regard the cosmological fluid within an exponentially expanding FLRW spacetime as the probability fluid of a nonrelativistic Schroedinger field. The scalar Schroedinger particle so described has a mass equal to the total (baryonic plus dark) matter content of the Universe. This procedure allows a description of the cosmological fluid by means of the operator formalism of nonrelativistic quantum theory. Under the assumption of radial symmetry, a quantum operator proportional to [Formula: see text] represents the cosmological constant [Formula: see text]. The experimentally measured value of [Formula: see text] is one of the eigenvalues of [Formula: see text]. Next we solve the Poisson equation [Formula: see text] for the gravitational potential [Formula: see text], with the cosmological constant [Formula: see text] playing the role of a source term. It turns out that [Formula: see text] includes, besides the standard Newtonian potential [Formula: see text], a correction term proportional to [Formula: see text] identical to that appearing in theories of modified Newtonian dynamics.