On the Response of Gravitational Antennas to Dilatonic Waves Typeset Using Revt E X

It is pointed out that the coupling of macroscopic test masses to the gravi-dilaton background of string theory is non geodesic, in general, and cannot be parametrized by a Brans-Dicke model of scalar-tensor gravity. The response of gravitational antennas to dilatonic waves should be analyzed through a generalized equation of geodesic deviation, taking into account the possible direct coupling of the background to the (composition-dependent) dilatonic charge of the antenna. 1 A number of papers has recently explored the interesting possibility of detecting scalar waves, with coupling strength to matter of gravitational order, exploiting both resonant mass 1]-3] and interferometric 4,5] gravity wave detectors. Indeed, gravitational antennas conceived to respond to the tensor part of metric uctuations can also respond to the scalar oscillations of the metric background, induced by the coupling to some fundamental scalar component of the gravitational multiplet. Such papers are basically motivated by the possible emission of scalar waves in astro-physical process, like the spherically symmetric collapse of a star, or of a cloud of dust 2,6]. Another motivation is the possible presence or a relic cosmic background of (light enough) scalar particles. Such particles could be produced copiously in the early Universe (see for instance 7,8]), and could survive until today in the form of a stochastic background of scalar waves, representing a possible signiicant fraction of the present large scale density of dark matter. Given the extreme weakness of their couplings, gravitational antennas are probably (at present) the only plausible candidates for their direct detection 9]. In all the quoted papers 1]-5], the analysis of the possible response of the detector was performed assuming a geodesic coupling of the test masses (representing the detector) to the scalar component of the metric uctuations. The standard equation of geodesic deviation was subsequently applied to estimate the detector sensitivity. This is certainly justiied when the gravitational scalar-tensor interactions are parametrized by a strictly \Brans-Dicke type" model of gravity, as always assumed in 1]-5]. In that case, a \Jordan frame" exists in which there are no couplings to the scalar eld in the matter part of the action, and the scalar interactions are totally absorbed in the rescaled metric. This is not the most general case, however, and one of the purposes of this paper is to point out that this is not the case, in particular, for the coupling of macroscopic test masses to the scalar dilaton …