Large-distance behaviour of the massless vector two-point function in de Sitter spacetime

TL;DR

This paper analyzes the long-distance behavior of the massless vector two-point function in de Sitter spacetime, showing it approaches a gauge-dependent constant at large distances, with specific results in the Landau gauge.

Contribution

It extends the understanding of the massless vector propagator's asymptotic behavior in de Sitter space to arbitrary dimensions and clarifies gauge dependence.

Findings

Propagator tends to a gauge-dependent constant at large distances.

In Landau gauge, the constant is zero.

Results agree with previous 4D analyses.

Abstract

We study the long-distance behaviour of the massless vector propagator in (n)-dimensional de Sitter spacetime, where $n \geq 4$. Specifically, we consider the massless limit of the vector propagator in the Stueckelberg theory, which is an extension of Proca theory, with an additional gauge-fixing term. We work to leading order in the de Sitter-invariant distance $Z$ to show that, in the large $Z$ limit, this propagator tends to a gauge dependent constant, where the gauge worked in is described by the Stueckelberg parameter $\xi$. In the Landau gauge, where $\xi=0$, this constant is found to be 0. This result is in agreement with the 4 dimensional case discussed by Youssef.