Curvature fluctuations in a baby quantum gravity model

TL;DR

This paper investigates quantum fluctuations of the Ricci scalar in a simple discrete quantum gravity model, revealing UV-divergent fluctuations that are stable under renormalization but sensitive to a small cosmological constant.

Contribution

It introduces a baby quantum gravity model to analyze Ricci scalar fluctuations and examines their behavior under renormalization and cosmological constant effects.

Findings

Average Ricci scalar vanishes at leading order.

Fluctuations are UV-divergent.

Behavior is stable under renormalization but affected by a small cosmological constant.

Abstract

Understanding the microscopic behavior of spacetime is critical for developing a theory of quantum gravity and perhaps solving the cosmological constant problem. In this context, it has been proposed that the quantity of interest is the quantum uncertainty in the Ricci scalar and here we investigate this for a discrete baby quantum gravity model based a single square cell. We find that the averaged Ricci scalar vanishes to leading order but has UV-divergent fluctuations. While this behavior is stable under renormalization, it appears not to be under the introduction of a small cosmological constant.