Tackling Higher Derivative Ghosts with the Euclidean Path Integral

TL;DR

This paper explores using the Euclidean path integral to handle ghost degrees of freedom in higher derivative gravity theories, including sixth-order derivatives, and assesses its effectiveness in Minkowski and de Sitter backgrounds.

Contribution

It extends the Euclidean path integral approach to sixth-derivative terms and analyzes its viability in different cosmological backgrounds.

Findings

Euclidean path integral works in Minkowski background

Probability distribution can be defined in de Sitter background

Method faces some difficulties in de Sitter space

Abstract

An alternative to the effective field theory approach to treat ghosts in higher derivative theories is to attempt to integrate them out via the Euclidean path integral formalism. It has been suggested that this method could provide a consistent framework within which we might tolerate the ghost degrees of freedom that plague, among other theories, the higher derivative gravity models that have been proposed to explain cosmic acceleration. We consider the extension of this idea to treating a class of terms with order six derivatives, and find that for a general term the Euclidean path integral approach works in the most trivial background, Minkowski. Moreover we see that even in de Sitter background, despite some difficulties, it is possible to define a probability distribution for tensorial perturbations of the metric.