The structure of the graviton self-energy at finite temperature

TL;DR

This paper analyzes the graviton self-energy at finite temperature using a gauge-invariant approach, revealing the structure of thermal corrections and their implications for graviton plasma behavior.

Contribution

It provides a detailed calculation of the graviton self-energy at finite temperature, including gauge independence and the structure of thermal terms, which was not previously fully understood.

Findings

Gauge independence of the leading T^4 term confirmed

Compact expression for the sub-leading T^2 contribution derived

Logarithmic term matches the ultraviolet pole of T=0 self-energy

Abstract

We study the graviton self-energy function in a general gauge, using a hard thermal loop expansion which includes terms proportional to T^4, T^2 and log(T). We verify explicitly the gauge independence of the leading T^4 term and obtain a compact expression for the sub-leading T^2 contribution. It is shown that the logarithmic term has the same structure as the ultraviolet pole part of the T=0 self-energy function. We argue that the gauge-dependent part of the T^2 contribution is effectively canceled in the dispersion relations of the graviton plasma, and present the solutions of these equations.