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The term primordial gravitational waves indicates the first gravitational waves, formed in the early universe. The term generally is used to refer to gravitational waves presumed to have left an imprint in CMB anisotropies, a reason for studying the anisotropies. Imprints being searched for consist of B-mode polarization, because of all the effects of the waves on the CMB, the B-modes are expected stand out to the largest degree. As of 6/2020, B-modes clearly attributable to primordial gravitational waves have not been detected, though observers found a candidate signal in 2014, which was then determined to be consistent with known effects of Milky Way dust on the CMB. (One type of effort to assist in detecting the CMB B-modes consists of surveys aimed at discovering all possible sources of such B-modes within the galaxy, for foreground subtraction.)
Theories have proposed a number of sources for such primordial gravitational waves: inflation itself is probably the one of most intense interest: such waves could be the most direct evidence to date. Other proposed sources would have occurred soon after inflation, among them, reheating and topological defects. Early black hole mergers of primordial black holes are another possible source. Efforts to detect the resulting CMB B-modes include: