The Third Structure Function

TL;DR

This paper investigates the graviton self-energy in de Sitter space, deriving a third contribution necessary for cosmological applications, expanding the understanding of quantum effects in curved spacetime.

Contribution

It introduces a new third tensor contribution to the graviton self-energy on de Sitter background, extending previous flat space and general background formulations.

Findings

Derived the third tensor contribution for graviton self-energy in de Sitter space.

Connected tensor operators to linearized curvature tensors in cosmology.

Enhanced the theoretical framework for quantum gravity in curved spacetime.

Abstract

We re-consider the graviton self-energy induced by a loop of massless, minimally coupled scalars on de Sitter background. On flat space background it can be represented as a sum of two tensor differential operators acting on scalar structure functions. On a general background these tensor differential operators can be constructed from the linearized Ricci scalar and the linearized Weyl tensor. However, in cosmology one requires a third contribution which we derive here.