Constraints on Supersymmetric Grand Unified Theories from Cosmology

Abstract

Within the context of SUSY GUTs, cosmic strings are generically formed at the end of hybrid inflation. However, the WMAP CMB measurements strongly constrain the possible cosmic strings contribution to the angular power spectrum of anisotropies. We investigate the parameter space of SUSY hybrid (F- and D- term) inflation, to get the conditions under which theoretical predictions are in agreement with data. The predictions of F-term inflation are in agreement with data, only if the superpotential coupling $\kappa$ is small. In particular, for SUSY SO(10), the upper bound is $\kappa\lsim 7\times 10^{-7}$. This fine tuning problem can be lifted if we employ the curvaton mechanism, in which case $\kappa\lsim 8\times 10^{-3}$; higher values are not allowed by the gravitino constraint. The constraint on $\kappa$ is equivalent to a constraint on the SSB mass scale $M$, namely $M \lsim 2\times 10^{15}$ GeV. The study of D-term inflation shows that the inflaton field is of the order of the Planck scale; one should therefore consider SUGRA. We find that the cosmic strings contribution to the CMB anisotropies is not constant, but it is strongly dependent on the gauge coupling $g$ and on the superpotential coupling $\lambda$. We obtain $g\lsim 2\times 10^{-2}$ and $\lambda \lsim 3\times 10^{-5}$. SUGRA corrections induce also a lower limit for $\lambda$. Equivalently, the Fayet-Iliopoulos term $\xi$ must satisfy $\sqrt\xi \lsim 2\times 10^{15}$ GeV. This constraint holds for all allowed values of $g$.