Quantized cosmological constant in 1+1 dimensional quantum gravity with coupled scalar matter

TL;DR

This paper investigates a 2D quantum gravity model with matter, revealing that quantum constraints discretize the cosmological constant and that gravitational fluctuations contribute negatively, offering insights into the cosmological constant problem.

Contribution

It demonstrates that quantum constraints in a 2D gravity-matter model discretize the cosmological constant and highlight the negative role of gravitational fluctuations.

Findings

Quantum constraints discretize the cosmological constant spectrum.

Gravitational fluctuations contribute negatively to the cosmological constant.

Matter field fluctuations contribute positively to the cosmological constant.

Abstract

A two dimensional matter coupled model of quantum gravity is studied in the Dirac approach to constrained dynamics in the presence of a cosmological constant. It is shown that after partial fixing to the conformal gauge the requirement of a quantum realization of the conformal algebra for physical quantum states of the fields naturally constrains the cosmological constant to take values in a well determined and mostly discrete spectrum. Furthermore the contribution of the quantum fluctuations of the single dynamical degree of freedom in the gravitational sector, namely the conformal mode, to the cosmological constant is negative, in contrast to the positive contributions of the quantum fluctuations of the matter fields, possibly opening an avenue towards addressing the cosmological constant problem in a more general context.