We point out that the inclusion of a string component contributing around 5%
to the CMB power spectrum amplitude on large scales can increase the preferred
value of the spectral index n_s of density fluctuations measured by CMB
experiments. While this finding applies to any cosmological scenario involving
strings, we consider in particular models of supersymmetric hybrid inflation,
which predict n_s >= 0.98, in tension with the CMB data when strings are not
included. Using MCMC analysis we constrain the parameter space allowed for F-
and D-term inflation. For the F-term model, using minimal supergravity
corrections, we find that \log\kappa= -2.34\pm 0.38 and M= (0.518\pm 0.059) *
10^16 GeV. The inclusion of non-minimal supergravity corrections can modify
these values somewhat. In the corresponding analysis for D-term inflation, we
find \log\kappa= -4.24\pm 0.19 and m_FI= (0.245\pm 0.031) * 10^16 GeV. Under
the assumption that these models are correct, these results represent precision
measurements of important parameters of a Grand Unified Theory. We consider the
possible uncertainties in our measurements and additional constraints on the
scenario from the stochastic background of gravitational waves produced by the
strings. The best-fitting model predicts a B-mode polarization signal \approx
0.3 \mu K rms peaking at l \approx 1000. This is of comparable amplitude to the
expected signal due to gravitational lensing of the adiabatic E-mode signal on
these scales.Comment: 21 pages, 16 figure
