Indirect imprints of primordial non-Gaussianity on cosmic microwave background

Primordial non-Gaussianity arising from inflationary models is a unique probe of non-trivial dynamics of the inflaton field and its interactions with other fields. Often when examining and constraining the scalar non-Gaussianity arising from inflation, certain templates are adopted for the scalar non-Gaussianity parameter $f_{_{\rm NL}}$, in classifying their behaviors in terms of wavenumbers. The current constraints from cosmic microwave background (CMB) on such templates of $f_{_{\rm NL}}$ are weak and provide rather large bounds on their amplitudes. In this work, we explore a different method of constraining $f_{_{\rm NL}}$ through their effect on the scalar power. We compute the correction to the scalar power due to $f_{_{\rm NL}}$ while accounting for its generic scale dependence. We then compute the angular power spectrum of CMB arising from such non-Gaussian corrections to explore possible imprints. We initially illustrate this method using the conventional templates of $f_{_{\rm NL}}$ such as local, equilateral and orthogonal types, with and without the running of the parameter. We further employ this method to an oscillatory form of $f_{_{\rm NL}}$ and lastly on a realistic model of inflation proposed by Starobinsky. Though this method does not improve much on the constraints on the first three templates of $f_{_{\rm NL}}$, it provides interesting insights on models that do not conform to these templates. We infer that the non-Gaussian correction to the spectrum can be sensitive to model parameters that are degenerate at the level of the original power spectrum. Hence, this method of computing indirect imprints of $f_{_{\rm NL}}$ on angular power spectrum of CMB provides a new avenue to explore primordial scalar non-Gaussianity and possibly constrain them effectively.