Primordial 'fNL' non-Gaussianity and perturbations beyond the present horizon

We show a primordial nonlinear ('fNL') term may produce unphysically large CMB anisotropy for a red-tilted primordial power spectrum (n<1) because of coupling to primordial fluctuation on the largest scale. We consider a primordial power spectrum models of a running spectral index, and a transition at very low wave numbers. We find that only negative running spectral index models are allowed, provided that there is no transition at a low wave numbers (i.e. k<<1). For models of a constant spectral index, we find log(kc/k0) > or approx. -184, at 1σ level, on the transition scale of sharp cutoff models, using recent CMB and SDSS data.