The quantum cosmological constant

TL;DR

This paper extends general relativity by making the cosmological constant dynamical and conjugate to the Chern-Simons invariant, offering new insights into quantum gravity and the nature of the cosmological constant.

Contribution

It introduces a framework where the cosmological constant is dynamical and conjugate to Chern-Simons time, providing a novel interpretation of the Kodama state in quantum gravity.

Findings

The inverse cosmological constant and Chern-Simons time are conjugate operators.

The Kodama state is reinterpreted as a family of transition functions.

An uncertainty relation between $ abla$ and Chern-Simons time is proposed.

Abstract

We present an extension of general relativity in which the cosmological constant becomes dynamical and turns out to be conjugate to the Chern-Simons invariant of the Ashtekar connection on a spatial slicing. The latter has been proposed in \cite{Chopin-Lee} as a time variable for quantum gravity: the Chern-Simons time. In the quantum theory the inverse cosmological constant and Chern-Simons time will then become conjugate operators. The "Kodama state" gets a new interpretation as a family of transition functions. These results imply an uncertainty relation between $\Lambda$ and Chern-Simons time; the consequences of which will be discussed elsewhere.