Covariant derivative expansion for the renormalization of gravity

TL;DR

This paper computes one-loop UV divergences in gravity with matter using a covariant derivative expansion, extending the method to include dynamical metrics and non-linear effects.

Contribution

It introduces a covariant derivative expansion method for gravity's renormalization, accounting for dynamical metrics and non-linearities in the effective action.

Findings

Calculated one-loop UV divergences in gravity with matter fields.

Extended covariant derivative expansion to include dynamical metrics.

Provided a framework for analyzing gravity's renormalization with non-linear effects.

Abstract

The one loop UV divergences of Hilbert-Einstein gravity with a cosmological constant and spin 0, 1/2 and 1 matter are computed making use of a covariant derivative expansion and functional methods. For this purpose the transformation that yields the covariant derivative is extended to include a dynamical metric and the expansion in the fields themselves is made covariant which is relevant for the effective action due to the non-linear character of gravity