Dark Energy, Background Independent Quantum Mechanics and the Origin of Cosmological Constant

TL;DR

This paper proposes an extended generalized quantum mechanics framework, linking phase space volume and the cosmological constant, to explore the origin of dark energy and background independence in quantum cosmology.

Contribution

It introduces an expanded phase space volume definition with an uncertainty relation, offering a novel approach to understanding the cosmological constant within quantum mechanics.

Findings

Phase space volume in eight dimensions is a suitable representation.

The relation $( riangle \\Lambda)( riangle V) \\sim h$ connects quantum uncertainty to cosmological constant.

The framework suggests a background independent quantum description of cosmology.

Abstract

We explore the extended framework of the generalized quantum mechanics and discuss various aspects of neighborhood in the construction of space in search of origin of cosmological constant. We propose to expand definition of the volume of the phase space in eight dimensions with an overall constraint in the form of uncertainty relation as: $(\Delta p_{x}\Delta p_{y}\Delta p_{z}\Delta E)(\Delta x\Delta y\Delta z\Delta t)\sim h^{4}$. We argue that the phase space volume in the eight dimensions is an appropriate representation that it should be, and the relation $(\Delta \Lambda)(\Delta V)\sim h$ again brings it down to the reduced phase space.