Testing Primordial Non-Gaussianity in CMB Anisotropies

Recent second-order perturbation computations have provided an accurate prediction for the primordial gravitational potential, Φ(x), in scenarios in which cosmological perturbations are generated either during or after inflation. This enables us to make realistic predictions for a non-Gaussian part of Φ(x), which is generically written in momentum space as a double convolution of its Gaussian part with a suitable kernel, fNL(k1,k2). This kernel defines the amplitude and angular structure of the non-Gaussian signals and originates from the evolution of second-order perturbations after the generation of the curvature perturbation. We derive a generic formula for the cosmic microwave background angular bispectrum with arbitrary fNL(k1,k2), and examine the detectability of the primordial non-Gaussian signals from various scenarios such as single-field inflation, inhomogeneous reheating, and curvaton scenarios. Our results show that in the standard slow-roll inflation scenario the signal actually comes from the momentum-dependent part of fNL(k1,k2), and thus it is important to include the momentum dependence in the data analysis. In the other scenarios the primordial non-Gaussianity is comparable to or larger than these post-inflationary effects. We find that the Wilkinson Microwave Anisotropy Probe cannot detect non-Gaussian signals generated by these models. Numerical calculations for l>500 are still computationally expensive, and we are not yet able to extend our calculations to Planck’s angular resolution; however, there is an encouraging trend which shows that Planck may be able to detect these non-Gaussian signals.