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 nonvanishing 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 ghostfree around the Minkowski background for a range of parameters. A key feature of these theories is that there exist a nonghost massive spin-2 particle and a nonghost 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. Ghostfreedom therefore sets, besides other constraints, an upper bound on the mass of the torsion. In addition to the above mentioned particle species (a massive spin-2 particle, a massive spin-0 particle and the massless spin-2 graviton), the ghostfree 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.

Highlights

  • Einstein’s general relativity (GR) is one of the most successful gravitational theories, it has been believed that GR is incomplete in the ultraviolet (UV) regime and is merely a low energy effective field theory (EFT)

  • In the limit of the infinite mass of the torsion, the Riemann-Cartan geometry reduces to the Riemannian geometry and 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

  • Imposing some conditions on the coupling constants of the theory, we find a new classes of theories in which the massless spin-2 graviton, the massive spin-2 particle and the massive spin-0 particle, which appear in the graviton propagator as in the usual quadratic curvature theory, can coexist without any ghost instability at least around the Minkowski background

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Summary

INTRODUCTION

Einstein’s general relativity (GR) is one of the most successful gravitational theories, it has been believed that GR is incomplete in the ultraviolet (UV) regime and is merely a low energy effective field theory (EFT). In the limit where the ghosts due to generic higher curvature terms are infinitely heavy, a higher curvature theory reduces to one of fðRÞ theories, which can be recast to the form of scalartensor theories [4] For this reason, it appears that phenomenologically interesting signatures of higher derivative corrections to the Einstein gravity come only from the spin0 particle, at least in the context of the standard Riemannian geometry.

ACTION
Quadratic Lagrangian
Matter scattering via gravitational interaction
STABILITY CONDITIONS
Tensor perturbations
Scalar and pseudoscalar perturbations
Pseudoscalar perturbations
Scalar perturbations
Vector perturbations
Summary of the stability conditions
CONCLUDING REMARKS
Full Text
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