  We assess the relative contribution to the COBE - measured microwave
anisotropy arising both from relic gravity waves as well as primordial density
perturbations originating during inflation. We show that the gravity wave
contribution to the CMBR anisotropy depends sensitively upon $n$ -- the
primordial spectral index ($\dk^2 \propto k^n$), increasing as $n$ deviates
from a Harrison - Zeldovich spectrum (n = 1). As a result, for $n < 0.84$ the
contribution from gravity waves towards $\delta T/ T $ is greater than the
corresponding contribution from density perturbations, whereas for $n > 0.84$
the reverse is true. ($ n = 0.84$ corresponds to an expansion index $p = 13.5$
in models with power-law inflation $a \propto t^p$. ) Our results show that for
a scale-invariant Harrison-Zeldovich spectrum generated by chaotic inflation,
gravity waves contribute approximately $24\%$ to the CMBR anisotropy measured
by COBE. Applying our results to the cold dark matter scenario for galaxy
formation, we find that in general CDM models with tilted power spectra ($n <
1$), require the biasing parameter to be greater than unity, on scales of
$16h_{50}^{-1} Mpc$. We also obtain an expression for the COBE - normalised
amplitude and spectrum of the stochastic gravity wave background and compare it
with the sensitivity of planned laser-interferometer gravity wave detectors.
