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We show a primordial non-linear "f_NL" term may produce unphysically largeCMB anisotropy for a red-tilted primordial power spectrum (n<1), because ofcoupling to primordial fluctuation on the largest scale. We consider aprimordial power spectrum models of a running spectral index, and a transitionat very low wavenumbers. We find that only negative running spectral indexmodels are allowed, provided that there is no transition at a low wavenumbers(i.e. k<<1). For models of a constant spectral index, we find log(k_c/k_0)>-184, at 1 sigma level, on the transition scale of sharp cut-off models, usingrecent CMB and SDSS data.

The primordial "f_NL" non-Gaussianity, and perturbations beyond the present horizon