Abstract
We simulate CMB maps including non-Gaussianity arising from cubic orderperturbations of the primordial gravitational potential, characterizedby the non-linearity parameter gNL. The maps are used to study the characteristic nature of the resulting non-Gaussian temperaturefluctuations. We measure the genus and investigate how it deviatesfrom Gaussian shape as a function of gNL and smoothing scale. We find that the deviation of the non-Gaussian genus curve from the Gaussian one has anantisymmetric, sine functionlike shape, implying more hot and more cold spots for gNL > 0 andless of both for gNL < 0. The deviation increases linearly withgNL and also exhibits mild increase as the smoothing scale increases. We further study other statistics derived from thegenus, namely, the number of hot spots,the number of cold spots, combined number of hot and cold spots and theslope of the genus curve at mean temperature fluctuation. We findthat these observables carry signatures of gNL that are clearlydistinct from the quadratic order perturbations, encoded in theparameter fNL. Hence they can be very useful tools for distinguishing notonly between non-Gaussian temperature fluctuations and Gaussian onesbut also between gNL and fNL type non-Gaussianities.
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