The Ligo-Ligo cross correlation for the detection of relic scalar gravitational waves

Abstract

In the earlier work arXiv:0706.3782 we studied the cross correlation between the Virgo interferometer and the MiniGRAIL resonant sphere for the detection of relic scalar gravitational waves (SGWs). We have shown that the overlap reduction function for the cross correlation between Virgo and the monopole mode of MiniGRAIL is very small, but a maximum was also found in the correlation at about 2710Hz, in the range of the MiniGRAIL sensitivity. In this paper the analysis is improved. After carefully reviewing the response function of interferometers to SGWs directly in the gauge of the local observer, the result is used to analyze the cross correlation between the two LIGO interferometers in their advanced configuration for a potential detection of relic SGWs and to release a lower bound for the integration time of such a detection. By using a new, frequency-dependent, overlap reduction function, a comparison with previous low-frequency approximations is therefore discussed. This is the first time that such a cross-correlation is computed in all the frequency spectrum of relic SGWs. The computation of a better signal to noise ratio is very important to understand if a scalar component of GWs is present at high frequency. With the new overlap reduction function, an order of magnitude is gained concerning the integration time for detecting the relic SGWs' signal. This could be very important for a potential detection if advanced projects further improve their sensitivity. .