A toy model of quantum gravity with a quantized cosmological constant

TL;DR

This paper presents a simplified quantum gravity model where the cosmological constant is quantized, offering insights into its potential implications within a quantum gravitational framework.

Contribution

It introduces a toy model coupling one-dimensional quantum gravity with matter fields, demonstrating the quantization of the cosmological constant as an energy eigenvalue.

Findings

The cosmological constant is quantized in the model.

The model links quantum gravity with matter field dynamics.

Implications for understanding the cosmological constant are discussed.

Abstract

The path integral for the hydrogen atom, for example, is formulated as a one-dimensional quantum gravity coupled to matter fields representing the electron coordinates. The (renormalized) cosmological constant, which corresponds to the energy eigenvalue, is thus quantized in this model. Possible implications of the quantized cosmological constant are briefly discussed.