Scalar Curvature Fluctuations on the Four-Sphere

TL;DR

This paper analyzes scalar curvature fluctuations on the four-sphere by calculating two-point functions using spacetime foam methods, providing a bridge between continuum quantum gravity and lattice approaches.

Contribution

It introduces a method to compute two-point functions of scalar curvature on the four-sphere, facilitating comparison between continuum and lattice quantum gravity.

Findings

Derived two-point functions for fixed-distance points

Calculated curvature fluctuations for fixed-volume metrics

Provides a basis for comparing different quantum gravity approaches

Abstract

Two-point functions of the scalar curvature for metric fluctuations on the four-sphere are analysed. The two-point function for points separated by a fixed distance and for metrics of fixed volume is calculated using spacetime foam methods. This result can be used for comparison between the continuum approach to quantum gravity and numerical quantum gravity on the lattice. Pacs numbers: 04.60.Gw, 04.60.Nc, 04.62.+v