Quantum Corrections in Massive Gravity

TL;DR

This paper calculates one-loop quantum corrections in ghost-free massive gravity, showing how matter fields affect the cosmological constant and how the potential's structure remains stable against ghost instabilities at this order.

Contribution

It provides the first detailed one-loop analysis of ghost-free massive gravity, demonstrating the quantum stability of its special mass structure.

Findings

Matter fields influence the cosmological constant's running.

Graviton loops destabilize the potential but avoid low-scale ghosts.

The ghost-free structure is technically natural at one-loop.

Abstract

We compute the one-loop quantum corrections to the potential of ghost-free massive gravity. We show how the mass of external matter fields contribute to the running of the cosmological constant, but do not change the ghost-free structure of the massive gravity potential at one-loop. When considering gravitons running in the loops, we show how the structure of the potential gets destabilized at the quantum level, but in a way which would never involve a ghost with a mass smaller than the Planck scale. This is done by explicitly computing the one-loop effective action and supplementing it with the Vainshtein mechanism. We conclude that to one-loop order the special mass structure of ghost-free massive gravity is technically natural.