Ghosts in pure and hybrid formalisms of gravity theories: a unified analysis

TL;DR

This paper develops a method to analyze the field content of pure and hybrid gravity theories, identifying ghost and tachyon degrees of freedom, and highlights f(X) theories as promising hybrid extensions of General Relativity.

Contribution

It introduces a unified analysis framework for pure and hybrid gravity formalisms, focusing on their propagating degrees of freedom and stability properties.

Findings

Identifies conditions for ghost-free hybrid gravity theories.

Classifies new higher-order derivative gravity models.

Highlights f(X) theories as viable hybrid gravity extensions.

Abstract

In the first order formalism of gravitational theories, the spacetime connection is considered as an independent variable to vary together with the metric. However, the metric still generates its Levi-Civita connection that turns out to determine the geodesics of matter. Recently, "hybrid" gravity theories have been introduced by constructing actions involving both the independent Palatini connection and the metric Levi-Civita connection. In this study a method is developed to analyse the field content of such theories, in particular to determine whether the propagating degrees of freedom are ghosts or tachyons. New types of second, fourth and sixth order derivative gravity theories are investigated and the so called f(X) theories are singled out as a viable class of "hybrid" extensions of General Relativity.