# Ghostfree quadratic curvature theories with massive spin-2 and spin-0 particles

## TL;DR

This paper develops new ghost-free quadratic curvature gravity theories within Riemann-Cartan geometry, featuring massive spin-2 and spin-0 particles, and explores their particle spectrum, ghost elimination conditions, and physical implications.

## Contribution

It introduces novel ghost-free quadratic curvature theories with torsion, identifying conditions for ghost elimination and analyzing the resulting particle spectrum.

## Key findings

- Existence of ghost-free theories with massive spin-2 and spin-0 particles.
- Conditions on coupling constants to remove ghosts.
- Additional massive spin-1 particles mediating spin-dependent gravity.

## Abstract

We consider generic derivative corrections to the Einstein gravity and find new classes of theories without ghost around the Minkowski background by means of an extension of the spacetime geometry. We assume the Riemann-Cartan geometry, i.e. a geometry with a non-vanishing torsion, and consider all possible terms in the Lagrangian up to scaling dimension four. We first clarify the number, spins, and parities of all particle species around the Minkowski background and find that some of those particle species are ghosts for generic choices of parameters. For special choices of the parameters, on the other hand, those would-be ghosts become infinitely heavy and thus can be removed from the physical content of particle species. Imposing the conditions on the coupling constants to eliminate the ghosts, we find new quadratic curvature theories which are ghost-free around the Minkowski background for a range of parameters. A key feature of these theories is that there exist a non-ghost massive spin-2 particle and a non-ghost massive spin-0 particle in the graviton propagator, as well as the massless spin-2 graviton. In the limit of the infinite mass of the torsion, the Riemann-Cartan geometry reduces to the Riemannian geometry and thus the physical content of particle species coincides with that of the well-known quadratic curvature theory in the metric formalism, i.e. a massive spin-2 ghost, a massive spin-0 particle and the massless spin-2 graviton. Ghost-freedom therefore sets, besides other constraints, an upper bound on the mass of the torsion. In addition to the above mentioned particle species, the ghost-free theory contains either the set of a massive spin-1 and a massive spin-0 (Class I) or a couple of spin-1 (Class II). These additional particle species mediate gravity sourced by the spin of matter fields.