  A stochastic background of primordial gravitational waves could be detected
soon in the polarization of the CMB and/or with laser interferometers. There
are at least three GWB coming from inflation: those produced during inflation
and associated with the stretching of space-time modes; those produced at the
violent stage of preheating after inflation; and those associated with the
self-ordering of Goldstone modes if inflation ends via a global symmetry
breaking scenario, like in hybrid inflation. Each GW background has its own
characteristic spectrum with specific features. We discuss the prospects for
detecting each GWB and distinguishing between them with a very sensitive probe,
the local B-mode of CMB polarization.

Cosmology and Nongalactic Astrophysics;General Relativity and Quantum Cosmology;High Energy Physics - Phenomenology