Second-Order Cosmological Perturbations from Inflation
Abstract
We present the first computation of the cosmological perturbations generated during inflation up to second-order in deviations from the homogeneous background solution. Our results, which fully account for the inflaton self-interactions as well as for the second-order fluctuations of the background metric, provide the exact expression for the gauge-invariant curvature perturbation bispectrum produced during inflation in terms of the slow-roll parameters or, alternatively, in terms of the scalar spectral n_S and and the tensor to adiabatic scalar amplitude ratio r. The bispectrum represents a specific non-Gaussian signature of fluctuations generated by quantum oscillations during slow-roll inflation. Our findings indicate that -- for a broad class of single-field models of inflation -- the level of non-Gaussianity in the cosmic microwave background anisotropies is large enough to be detectable by present and forthcoming satellite missions such as MAP and Planck.Keywords
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