Gravitational wave observations may inform us about cosmology in at least two ways: by studies of individual sources at cosmological distances that give information about cosmography (the structure and kinematics of the universe) and about early structure formation, and by direct observation of a stochastic background of gravitational waves of cosmological origin. In turn, a stochastic background could either be astrophysical in origin (generated by any of a myriad of astrophysical systems that have arisen since cosmological structure formation began, as described in Section 8.2.2), or it could come from the Big Bang itself (generated by quantum processes associated with inflation or with spontaneous symmetry breaking in the extremely early universe, as described in Section 8.2.1). The observation of a cosmic gravitational wave background (CGWB) is probably the most fundamentally important observation that gravitational wave detectors can make. But the astrophysical gravitational wave background (AGWB) also contains important information and may mask the CGWB over much of the accessible spectrum.
The detection of discrete sources at cosmological distances will require high sensitivity. Advanced ground-based detectors should be able to see a few individual sources (mainly stellar-mass black hole binaries) at redshifts approaching 1, with which they may be able to make a good determination of the Hubble constant. But LISA’s observations of the coalescences of massive black hole binaries at all redshifts should make LISA a significant tool for cosmography. We examine cosmography measurements in Section 8.3. These high- observations may also contain interesting information about early structure formation, such as the relationship between SMBH formation and galaxy formation. We have mentioned this already in Section 7.2.4.
Both kinds of detectors will search for a stochastic background in their own wave band. As we have seen earlier, LISA will almost certainly detect an AGWB from binary systems in our galaxy, and both LISA and advanced ground-based detectors may see a CGWB, if the more optimistic estimates of its strength are correct. But scientists are already sketching designs for a mission to follow LISA with much higher sensitivity, dedicated to observing the CGWB from inflation. Stochastic searches are described in Section 8.1.2.
Other detection methods are also being used to probe the spectrum of the background radiation at longer wavelengths. Pulsar timing observations (Section 8.1.3) are already being used to set limits on the background at periods of a few years, and they will reach much greater sensitivity when coherent antenna arrays (like the Square Kilometer Array [225, 108]) are available. And observations of the temperature fluctuations of the cosmic microwave background (Section 8.1.4) have the potential to reveal the gravitational wave content of the universe at the redshift of decoupling, which means at wavelength scales comparable to the size of the universe [302, 215].
Before examining the details of detection, we begin by examining the statistics of a random gravitational wave background. A good introduction to the theory of the CGWB is the set of lectures by Bruce Allen at the 1996 Les Houches summer school . The first paper of the LSC on searches for a stochastic background  also contains a brief introduction.
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