Gravitational waves (g.w.) are a unique source of information on the very early Universe. The detection of a background of g.w. would in fact have a big impact on early Universe cosmology and on high energy physics, as relic g.w. decoupled from the primordial plasma below the Plank scale, when the Universe had a temperature . The reason why they are so interesting is the same reason why they are so difficult to detect: due to their small cross section, g.w. produced in the very early Universe still retain in their spectrum the information of the Universe at the time they have been decoupled.

The cosmological stochastic g.w. background is expected to be isotropic, stationary and unpolarized. It is characterized by its frequency spectrum, both in terms of energy density per unit logarithmic interval of frequency, (where is the Hubble constant) or in terms of the spectral density of the signal .

The dimensionless function of the frequency
and the spectral density of the signal
are related by the formula:

Then:

Gravitational wave experiments with interferometers and with resonant mass detectors can do searches for stochastic gravitational waves. The detector's sensitivity to the stochastic background is obtained using the previous Equation, where is the detector's strain noise spectral density (expressed in units of 1/Hz).

Using one detector the measurement of the noise spectrum only provides an upper limit for the g.w. stochastic background spectrum. This limit can be considerably improved, or even an estimation of the spectrum can be attempted by cross-correlating the output signals of two (or more) antennas.

M. Maggiore[1] has done a very interesting and complete review of both theoretical and experimental aspects of the search for stochastic GW backgrounds of cosmological origins. In his report an extended bibliography on the subject may also be found.