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arXiv · 2207.14611

On the cosmological constant as a quantum operator

P. Fernandez de Cordoba·R. Gallego Torrome·S. Gavasso·J. M. Isidro
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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 $1/r^2$ represents the cosmological constant $\Lambda$. The experimentally measured value of $\Lambda$ is one of the eigenvalues of $1/r^2$. Next we solve the Poisson equation $\nabla^2U=\Lambda$ for the gravitational potential $U(r)$, with the cosmological constant $\Lambda(r)=1/r^2$ 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.

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P. Fernandez de Cordoba, R. Gallego Torrome, S. Gavasso, J. M. Isidro. 2022-07-29. On the cosmological constant as a quantum operator. https://arxiv.org/abs/2207.14611

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