We provide the gauge-invariant expression for large-scale cosmic microwave background temperature fluctuations at second-order perturbation theory. This enables us to define unambiguously the nonlinearity parameter f(NL), which is used by experimental collaborations to pin down the level of non-Gaussianity in the temperature fluctuations. Furthermore, it contains a primordial term encoding all the information about the non-Gaussianity generated at primordial epochs and about the mechanism which gave rise to cosmological perturbations, thus neatly disentangling the primordial contribution to non-Gaussianity from the one caused by the postinflationary evolution.
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Bartolo et al. (2004) studied this question.
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