Constraints on supersymmetric hybrid inflation models

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 , 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 logκ = −2.34 ± 0.38 and M = (0.518 ± 0.059) × 10¹⁶ GeV. The inclusion of non-minimal supergravity corrections can modify these values somewhat. In the corresponding analysis for D-term inflation, we find logκ = −4.24 ± 0.19 and m_FI = (0.245 ± 0.031) × 10¹⁶ 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 ≈0.3 μK rms peaking at . This is of comparable amplitude to the expected signal due to gravitational lensing of the adiabatic E-mode signal on these scales.