Detailed analysis of the dependence of the one-loop counterterms on the gauge and parametrization in the Einstein gravity with the cosmological constant

TL;DR

This paper investigates how gauge choices and parametrizations affect one-loop counterterms in Einstein gravity with a cosmological constant, providing explicit calculations and discussing renormalization group functions.

Contribution

It provides explicit off-shell one-loop counterterm calculations in arbitrary gauges and parametrizations for Einstein gravity with a cosmological constant, using REDUCE.

Findings

Counterterms depend on gauge and parametrization choices

Explicit calculations of off-shell counterterms are presented

A method for off-shell renormalization group functions is discussed

Abstract

In this paper, the dependence of the Einstein gravity with the cosmological constant as well as of this theory in the first-order formalism on the gauge and parametrization is been analyzed. The one-loop counterterms off the mass shell have been plainly calculated in arbitrary gauge and parametrization. The tensor package of analytic calculations, written in REDUCE, allowed all the calculations to be carried out. A method of renormalization group functions calculations off shell is discussed.