  We consider the primordial gravitational wave (GW) background in a class of
spatially-flat inflationary cosmological models with cold dark matter (CDM), a
cosmological constant, and a broken-scale-invariant (BSI) steplike primordial
(initial) spectrum of adiabatic perturbations produced in an exactly solvable
inflationary model where the inflaton potential has a rapid change of its first
derivative at some point. In contrast to inflationary models with a scale-free
initial spectrum, these models may have a GW power spectrum whose amplitude
(though not its shape) is arbitrary for fixed amplitude and shape of the
adiabatic perturbations power spectrum. In the presence of a positive
cosmological constant, the models investigated here possess the striking
property that a significant part of the large-angle CMB temperature anisotropy
observed in the COBE experiment is due to primordial GW. Confronting them with
existing observational data on CMB angular temperature fluctuations, galaxy
clustering and peculiar velocities of galaxies, we find that for the best
parameter values Omega_Lambda=0.7 and h=0.7, the GW contribution to the CMB
anisotropy can be as large as that of the scalar fluctuations.
