The Expectation Value of the Cosmological Constant

TL;DR

This paper explores the idea that the cosmological constant might exist in a quantum superposition of two natural values, leading to an expected value consistent with current observations, by extending quantum principles to fundamental parameters.

Contribution

It proposes a novel approach applying quantum superposition to the cosmological constant, linking topological spacetime features to its expected value.

Findings

Expected cosmological constant matches observed value

Superposition principle applied to fundamental parameters

Topological effects influence the cosmological constant

Abstract

The possibility of extending the quantum mechanical superposition principle to free parameters such as the cosmological constant appearing in the Lagrangian of physical theories is examined. If the cosmological constant is subject to a quantum mechanical superposition principle, its observed value is a weighted average of its two natural values, one at the Planck scale and the other at zero. As zero and nonzero values of the cosmological constant leads to topologically distinct spacetimes, the amplitude for the cosmological constant to take a Planck scale value is weighted over a topological Euclidean action and the expectation value of the cosmological constant is found to be of the order of its present observed value.