Eur. Phys. J. C (2017) 77: 589
https://doi.org/10.1140/epjc/s10052-017-5172-3

Regular Article - Theoretical Physics

Gravitational effective action at second order in curvature and gravitational waves

¹ Department of Physics and Astronomy, University of Sussex, Brighton, BN1 9QH, UK
² Dipartimento di Fisica “E. Pancini”, Università di Napoli “Federico II”, Via Cinthia, 80126, Naples, Italy
³ Istituto Nazionale di Fisica Nucleare (INFN), Sez. di Napoli, Via Cinthia 9, 80126, Naples, Italy
⁴ Gran Sasso Science Institute, Via F. Crispi 7, 67100, L’Aquila, Italy

^* e-mail: x.calmet@sussex.ac.uk

Received: 18 August 2017
Accepted: 28 August 2017
Published online: 7 September 2017

Abstract

We consider the full effective theory for quantum gravity at second order in curvature including non-local terms. We show that the theory contains two new degrees of freedom beyond the massless graviton: namely a massive spin-2 ghost and a massive scalar field. Furthermore, we show that it is impossible to fine-tune the parameters of the effective action to eliminate completely the classical spin-2 ghost because of the non-local terms in the effective action. Being a classical field, it is not clear anyway that this ghost is problematic. It simply implies a repulsive contribution to Newton’s potential. We then consider how to extract the parameters of the effective action and show that it is possible to measure, at least in principle, the parameters of the local terms independently of each other using a combination of observations of gravitational waves and measurements performed by pendulum type experiments searching for deviations of Newton’s potential.