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Statistical nature of non-Gaussianity from cubic order primordial perturbations: CMB map simulations and genus statistic

We simulate CMB maps including non-Gaussianity arising from cubic order perturbations of the primordial gravitational potential, characterized by the non-linearity parameter $g_{NL}$. The maps are used to study the characteristic nature of the resulting non-Gaussian temperature fluctuations. We measure the genus and investigate how it deviates from Gaussian shape as a function of $g_{NL}$ and smoothing scale. We find that the deviation of the non-Gaussian genus curve from the Gaussian one has an antisymmetric, sine function like shape, implying more hot and more cold spots for $g_{NL}>0$ and less of both for $g_{NL}<0$. The deviation increases linearly with $g_{NL}$ and also exhibits mild increase as the smoothing scale increases. We further study other statistics derived from the genus, namely, the number of hot spots, the number of cold spots, combined number of hot and cold spots and the slope of the genus curve at mean temperature fluctuation. We find that these observables carry signatures of $g_{NL}$ that are clearly distinct from the quadratic order perturbations, encoded in the parameter $f_{NL}$. Hence they can be very useful tools for distinguishing not only between non-Gaussian temperature fluctuations and Gaussian ones but also between $g_{NL}$ and $f_{NL}$ type non-Gaussianities.