Nongaussian and nonscale-invariant perturbations from tachyonic   preheating in hybrid inflation
  We show that in hybrid inflation it is possible to generate large second-order perturbations in the cosmic microwave background due to the instability of the tachyonic field during preheating. We carefully calculate this effect from the tachyon contribution to the gauge-invariant curvature perturbation, clarifying some confusion in the literature concerning nonlocal terms in the tachyon curvature perturbation; we show explicitly that such terms are absent. We quantitatively compute the nongaussianity generated by the tachyon field during the preheating phase and translate the experimental constraints on the nonlinearity parameter f_{NL} into constraints on the parameters of the model. We also show that nonscale-invariant second-order perturbations from the tachyon field can become larger than the inflaton-generated first-order perturbations, leading to stronger constraints than those coming from nongaussianity. The width of the excluded region in terms of the logarithm of the dimensionless coupling g, grows linearly with the log of the ratio of the Planck mass to the tachyon VEV, \log(M_p/v); hence very large regions are ruled out if the inflationary scale v is small. We apply these results to string-theoretic brane-antibrane inflation, and find a stringent upper bound on the string coupling, g_s < 10^{-4.5}. 
Neil Barnaby, James M. Cline