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Quantum Corrections in Massive Gravity

Claudia de Rham, Lavinia Heisenberg, Raquel H. Ribeiro

TL;DR

This work investigates the quantum stability of ghost-free massive gravity at one loop. By separating matter- and graviton-loop contributions, the authors show that covariantly coupled matter loops induce only a running of the cosmological constant, leaving the ghost-free potential structure intact as in GR. In contrast, graviton loops can detune the potential away from the FP form, but the induced ghost mass remains at or above the Planck scale due to a quantum-level Vainshtein mechanism, even for large backgrounds. Overall, the special mass structure of ghost-free massive gravity is technically natural at one-loop, with matter loops benign and graviton-loop detuning controlled by background redressing, reinforcing the viability of the theory within its EFT regime.

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.

Quantum Corrections in Massive Gravity

TL;DR

This work investigates the quantum stability of ghost-free massive gravity at one loop. By separating matter- and graviton-loop contributions, the authors show that covariantly coupled matter loops induce only a running of the cosmological constant, leaving the ghost-free potential structure intact as in GR. In contrast, graviton loops can detune the potential away from the FP form, but the induced ghost mass remains at or above the Planck scale due to a quantum-level Vainshtein mechanism, even for large backgrounds. Overall, the special mass structure of ghost-free massive gravity is technically natural at one-loop, with matter loops benign and graviton-loop detuning controlled by background redressing, reinforcing the viability of the theory within its EFT regime.

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.

Paper Structure

This paper contains 19 sections, 70 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Ghost-free massive gravity
  3. Ghost-free potential
  4. Quantum corrections in the decoupling limit
  5. Propagator in unitary gauge
  6. Matter loops
  7. Framework
  8. One-loop effective action
  9. Perturbative approach
  10. Graviton loops
  11. Renormalization of the interactions
  12. Detuning of the potential structure
  13. One-loop effective action
  14. Form of the potential at one-loop
  15. Mass of the ghost
  16. ...and 4 more sections

Figures (7)

  • Figure 1: Contribution to the graviton tadpole from a matter loop. Dashes denote the matter field propagator, whereas solid lines denote the graviton. This convention will be adopted throughout the paper.
  • Figure 2: One-loop contributions to the 5-point function.
  • Figure 3: One-loop contribution to the 2-point correlation function from a graviton internal line.
  • Figure 4: Contribution to the scalar field two-point function from graviton/matter loops.
  • Figure 5: Contribution to the graviton 2-point function from matter loops.
  • ...and 2 more figures