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.
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