Detecting a stochastic background of scalar gravitational waves with LIGO

With the “bouncing photon” treatment, the gauge invariance of the response function of interferometers to scalar gravitational waves (SGWs) has been recently demonstrated in its full frequency dependence in three different gauges well known in literature, while in previous works such invariance was only proved in the low frequencies approximation. After a review of scalar tensor theories of gravity, in this paper the analysis of the response function to SGWs is generalized in the full angular and frequency dependences and directly in the gauge of the local observer, which is the gauge of a laboratory environment on Earth. The result is used to analyse the cross-correlation between the two LIGO interferometers in their advanced configuration for a potential detection of a stochastic background of SGWs and to release a lower bound for the integration time of such detection. A comparison between the response function introduced in this paper and previous low-frequency approximated ones is also performed. Because the lower bounds result very long, we hope in the LISA interferometer and in a further growth in the sensitivity of advanced projects. PACS numbers: 04.80.Nn, 04.30.Nk, 04.50.+h