Structure of the graviton self-energy at finite temperature

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 $\mathrm{log}(T).$ We verify explicitly the gauge independence of the leading ${T}^{4}$ term and obtain a compact expression for the subleading ${T}^{2}$ 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.