Polarization states of gravitational waves with a massive graviton

Abstract

Using the Newman−Penrose formalism, we obtain the explicit expressions for the polarization modes of weak, plane gravitational waves with a massive graviton. Our analysis is restricted for a specific bimetric theory whose term of mass, for the graviton, appears as an effective extra contribution to the stress-energy tensor. We obtain for such kind of theory that the extra states of polarization have amplitude several orders of magnitude smaller than the polarizations purely general relativity (GR), h + and h × , in the VIRGO−LIGO frequency band. This result appears using the best limit to the graviton mass inferred from solar system observations and if we consider that all the components of the metric perturbation have the same amplitude h. However, if we consider low frequency gravitational waves (e.g., f GW ∼ 10 −7 Hz), the extra polarization states produce similar Newman−Penrose amplitudes that the polarization states purely GR. This particular characteristic of the bimetric theory studied here could be used, for example, to directly impose limits on the mass of the graviton from future experiments that study the cosmic microwave background (CMB).

On the longitudinal response function of interferometers for massive gravitational waves from a bimetric theory of gravity

“…An extension of linearized general relativity which takes into account massive gravitons gives a weak-field stress-energy tensor [14,15] …”

“…where m g is the mass of the graviton, and (g 0 ) µν the non-dynamical background metric (note: differently from [15] in this paper we work with G = 1, c = 1 and = 1, exactly like in [14]). In this way the field equations can be obtained in an einstenian form like…”

“…Detectors for GWs will be important for a better knowledge of the Universe and also to confirm or ruling out the physical consistency of General Relativity or of any other theory of gravitation [9,10,11,12,13,14,15]. This is because, in the context of Extended Theories of Gravity, some differences between General Relativity and the others theories can be pointed out starting by the linearized theory of gravity [9,10,12,14,15].…”

“…This is because, in the context of Extended Theories of Gravity, some differences between General Relativity and the others theories can be pointed out starting by the linearized theory of gravity [9,10,12,14,15]. In this picture, recently, some papers in the literature have shown that, from a bimetric theory of gravity, it is possible to produce massive gravitational waves which generate a longitudinal component in a particular polarization of the wave [14,15]. After a review of previous works (i.e.…”

“…After a review of previous works (i.e. the work of de Paula, Miranda and Marinho [15] and my previous research [14]) on this topic, which is due to provide a context to bring out the relevance of the results, in this paper the longitudinal response function of interferometers for this particular polarization of the wave is computed in its full frequency dependence and in two different gauges, showing the gauge invariance, with specific application to the Virgo and LIGO interferometers.…”