Gravitational waves with generalized holonomy corrections

TL;DR

This paper derives a generalized dispersion relation for gravitational waves incorporating holonomy corrections from loop quantum gravity, analyzes the constraint algebra for vector modes, and estimates the effective graviton mass with implications for future detection.

Contribution

It introduces a new framework for gravitational wave propagation with generalized holonomy corrections and explores anomaly cancellation constraints in loop quantum gravity.

Findings

Derived a generalized dispersion relation for gravitational waves.

Identified constraints on holonomy correction functions from anomaly cancellation.

Estimated the effective graviton mass and discussed its observational prospects.

Abstract

The cosmological tensor perturbation equation with generalized holonomy corrections is derived in the framework of effective loop quantum gravity. This results in a generalized dispersion relation for gravitational waves, encompassing holonomy corrections. Furthermore, we conduct an examination of the constraint algebra concerning vector modes with generalized holonomy corrections. The requirement of anomaly cancellation for vector modes imposes constraints on the possible functional forms of the generalized holonomy corrections. What's more, we estimate the theoretical value of the effective graviton mass and discuss the potential detectability of this effective mass in future observations.