Gravitons and Lightcone Fluctuations II: Correlation Functions

TL;DR

This paper models how a bath of gravitons causes lightcone fluctuations, leading to correlated photon flight time variations that could be constrained by pulsar timing observations.

Contribution

It derives a correlation function for photon flight times affected by graviton-induced lightcone fluctuations, enhancing understanding of their observational implications.

Findings

Photon flight times follow a Gaussian distribution centered on classical time.

Photon pairs exhibit correlated flight time fluctuations due to gravitons.

Potential to constrain quantum graviton states using pulsar timing data.

Abstract

A model of a fluctuating lightcone due to a bath of gravitons is further investigated. The flight times of photons between a source and a detector may be either longer or shorter than the light propagation time in the background classical spacetime, and will form a Gaussian distribution centered around the classical flight time. However, a pair of photons emitted in rapid succession will tend to have correlated flight times. We derive and discuss a correlation function which describes this effect. This enables us to understand more fully the operational significance of a fluctuating lightcone. Our results may be combined with observational data on pulsar timing to place some constraints on the quantum state of cosmological gravitons.