The cosmological constant of emergent spacetime in the Newtonian approximation

TL;DR

This paper provides a quantum-mechanical estimate of the cosmological constant within a Newtonian approximation, linking matter states to the cosmological constant through an operator expectation value.

Contribution

It introduces a novel quantum approach to estimate the cosmological constant in a Newtonian universe using nonrelativistic quantum mechanics.

Findings

Existence of a quantum state with the operator's expectation value equal to the cosmological constant.

A simple quantum estimate of the cosmological constant in a Newtonian framework.

Demonstration of a correspondence between matter states and the cosmological constant.

Abstract

We present a simple quantum-mechanical estimate of the cosmological constant of a Newtonian Universe. We first mimic the dynamics of a Newtonian spacetime by means of a nonrelativistic quantum mechanics for the matter contents of the Universe (baryonic and dark) within a fixed (i.e., nondynamical) Euclidean spacetime. Then we identify an operator that plays, on the matter states, a role analogous to that played by the cosmological constant. Finally we prove that there exists a quantum state for the matter fields, in which the above mentioned operator has an expectation value equal to the cosmological constant of the given Newtonian Universe.