Light-Cone Fluctuations in the Cosmic String Spacetime

TL;DR

This paper investigates how the nontrivial topology of a cosmic string spacetime causes light-cone fluctuations, analyzing graviton correlations and light pulse delays, with implications for detecting such effects.

Contribution

It provides a detailed calculation of light-cone fluctuations caused by cosmic string topology, including the graviton two-point function and geodesic interval fluctuations.

Findings

Fluctuations depend on the cosmic string's conical parameter.

Fluctuations vanish without the cosmic string.

Large distances yield extremely small fluctuations, increasing logarithmically at short distances.

Abstract

In this paper we consider light-cone fluctuations arising as a consequence of the nontrivial topology of the locally flat cosmic string spacetime. By setting the light-cone along the z-direction we are able to develop a full analysis to calculate the renormalized graviton two-point function, as well as the mean square fluctuation in the geodesic interval function and the time delay (or advance) in the propagation of a light-pulse. We found that all these expressions depend upon the parameter characterizing the conical topology of the cosmic string spacetime and vanish in the absence of it. We also point out that at large distances from the cosmic string the mean square fluctuation in the geodesic interval function is extremely small while in the opposite limit it logarithmically increases, improving the signal and thus, making possible the detection of such quantity.