Ju l 2 01 6 Gravitational Waves in Effective Quantum Gravity

In this short paper we investigate quantum gravitational effects on Einstein’s equations using effective field theory techniques. We consider the leading order quantum gravitational correction to the wave equation. Besides the usual massless mode, we find a pair of modes with complex masses. These massive particles have a width and could thus lead to a damping of gravitational waves if excited in violent astrophysical processes producing gravitational waves such as e.g. black hole mergers. We discuss the consequences for gravitational wave events such as GW 150914 recently observed by the Advanced LIGO collaboration. x.calmet@sussex.ac. uk ibere.kuntz@sussex.ac. uk s.mohapatra@sussex.ac. uk The recent discovery of gravitational waves by the Advanced LIGO collaboration [1] marks the beginning of a new era in astronomy which could shed some new light on our universe revealing its darkest elements that do not interact with electromagnetic radiations. This discovery could also lead to some new insights in theoretical physics. In this short paper we study the leading effect of quantum gravity on gravitational waves using effective field theory techniques. While the discovery of a theory of quantum gravity might still be far away, it is possible to use effective field theory techniques to make actual predictions in quantum gravity. Assuming that diffeomorphism invariance is the correct symmetry of quantum gravity at the Planck scale and assuming that we know the field content below the Planck scale, we can write down an effective action for any theory of quantum gravity. This effective theory, dubbed Effective Quantum Gravity, is valid up to energies close to the Planck mass. It is obtained by linearizing general relativity around a chosen background. The massless graviton is described by a massless spin 2 tensor which is quantized using the standard quantum field theoretical procedure. It is well known that this theory is non-renormalizable, but divergences can be absorbed into the Wilson coefficients of higher dimensional operators compatible with diffeomorphism invariance. The difference with a standard renormalizable theory resides in the fact that an infinite number of measurements are necessary to determine the action to all orders. Nevertheless, Effective Quantum Gravity enables some predictions which are model independent and which therefore represent true tests of quantum gravity, whatever the underlying theory might be. We will first investigate quantum gravitational corrections to linearized Einstein’s equations. Solving these equations, we show that besides the usual solution that corresponds to the propagation of the massless graviton, there are solutions corresponding to massive degrees of freedom. If these massive degrees of freedom are excited during violent astrophysical processes a sizable fraction of the energy released by such processes could be emitted into this modes. We shall show that the corresponding gravitational wave is damped and that the energy of the wave could thus dissipate. We then study whether the recent discovery of gravitational waves by the Advanced LIGO collaboration [1] could lead to a test of quantum gravity. Given a matter Lagrangian coupled to general relativity with Ns scalar degrees of freedom, Nf fermions and NV vectors one can calculate the graviton vacuum polarization in the large N = Ns + 3Nf + 12NV limit with keeping NGN , where GN is Newton’s constant, small. Since we are interested in energies below M⋆ which is the energy scale at which the effective theory breaks down, we do not need to consider the graviton self-interactions which are suppressed by powers of 1/N in comparison to the matter loops. Note that M⋆ is a dynamical quantity and does not necessarily corresponds to the usual reduced Planck mass of order 10 GeV (see e.g. [2]). The divergence in this diagram can be isolated using dimen-