Quantum corrections in massive gravity

We compute the one-loop quantum corrections to the potential of ghost-free massive gravity. We show how the mass of external matter fields contributes to the running of the cosmological constant, but does 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.

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 five-point function.

Figure 3

One-loop contribution to the two-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 two-point function from matter loops.

Figure 6

One-loop contributions to the three-point function.

Figure 7

One-loop contributions to the four-point function.