= Local-type primordial non-Gaussianity
{title2=$f_{\rm NL}$}
A local quadratic departure from a <Gaussian random field> is
$$
\varphi(\mathbf x)=\varphi_G(\mathbf x)+f_{\rm NL}\bigl(\varphi_G(\mathbf x)^2-\langle\varphi_G^2\rangle\bigr).
$$
The subtraction removes the homogeneous mean. At leading order, <Wick theorem> gives the <primordial bispectrum> $B_\varphi=2f_{\rm NL}[P_\varphi(k_1)P_\varphi(k_2)+\text{cyclic terms}]$. The numerical convention depends on which potential or <comoving curvature perturbation> is used.
Back to article page