On the cosmological constant as a quantum operator

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 1/r2 represents the cosmological constant.. The experimentally measured value of. is one of the eigenvalues of 1/r2. Next we solve the Poisson equation.2U =. for the gravitational potential U(r), with the cosmological constant.(r) = 1/r2 playing the role of a source term. It turns out that U(r) includes, besides the standard Newtonian potential 1/r, a correction term proportional to ln r identical to that appearing in theories of modified Newtonian dynamics.