  There are at least three cosmic backgrounds of primordial gravitational waves
coming from inflation: those produced during inflation and associated with the
stretching of quantum 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 background has its own characteristic spectrum with specific
features. We describe in detail the origin of extra peaks in the PGW background
from preheating in the case in which inflation ends with the formation of
cosmic strings due to an Abelian Higgs model after hybrid inflation. We then
discuss the prospects for detecting each gravitational wave background, and
distinguishing between them with a very sensitive probe, the local B-mode of
the cosmic microwave background polarization.
