The status of the Lambda term in quantum geometrodynamics in extended phase space

TL;DR

This paper explores quantum geometrodynamics in extended phase space as a framework to derive the cosmological constant Lambda from quantum principles, linking it to the state of the gravitational vacuum and cosmological evolution.

Contribution

It introduces a novel approach to quantum geometrodynamics that incorporates reference frames and predicts Lambda's values through the Schrödinger equation for the Universe.

Findings

Lambda eigenvalues depend on cosmological models

The approach links Lambda to gravitational vacuum states

Predictions of Lambda vary with cosmological evolution

Abstract

S. Weinberg pointed out a way to introduce a cosmological term by modifying the theory of gravity. This modification would be justified if the Einstein equations with the cosmological term could be obtained in the classical limit of some physically satisfied quantum theory of gravity. We propose to consider quantum geometrodynamics in extended phase space as a candidate for such a theory. Quantum geometrodynamics in extended phase space aims at giving a selfconsistent description of the integrated system ``the physical object (the Universe) + observation means'', observation means being represented by a reference frame. The Lambda term appears in classical equations under certain gauge conditions and characterizes the state of gravitational vacuum related to a chosen reference frame. The eigenvalue spectrum of Lambda depends on a concrete cosmological model and can be found by solving the Schrodinger equation for a wave function of the Universe. The proposed version of quantum geometrodynamics enables one to make predictions concerning probable values of the Lambda term at various stages of cosmological evolution.