Non-Gaussian and nonscale-invariant perturbations from tachyonic preheating in hybrid inflation

Abstract

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 non-Gaussianity 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 with spectral index $n=4$ can become larger than the inflaton-generated first-order perturbations, leading to stronger constraints than those coming from non-Gaussianity. 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, $\mathrm{log}({M}_{p}/v)$; 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, ${g}_{s}<{10}^{\ensuremath{-}4.5}$.