Acoustic signatures in the primary microwave background bispectrum - art. no. 063002

If the primordial fluctuations are non-Gaussian, then this non-Gaussianity will be apparent in the cosmic microwave background (CMB) sky. With their s ensitive all-sky observation, MAP and Planck satellites should be able to d etect weak non-Gaussianity in the CMB sky. On a large angular scale, there is a simple relationship between the CMB temperature and the primordial cur vature perturbation: DeltaT/T = - Phi /3. On smaller scales. however, the r adiation transfer function becomes more complex. In this paper, we present the angular bispectrum of the primary CMB anisotropy that uses the full tra nsfer function. We find that the bispectrum has a series of acoustic peaks that change a sign and a period of acoustic oscillations is twice as long a s that of the angular power spectrum. Using a single non-linear coupling pa rameter to characterize the amplitude of the bispectrum. we estimate the ex pected signal-to-noise ratio for COPE, MAP, and Planck experiments. In orde r to detect the primary CMB bispectrum by each experiment, we find that the coupling parameter should be larger than 600, 20, and 5 for COBE, MAP, and Planck experiments, respectively. Even for the ideal noise-free and infini tesimal thin-beam experiment, the parameter should be larger than 3. We hav e included effects from the cosmic variance, detector noise, and foreground sources in the signal-to-noise estimation. Since the simple inflationary s cenarios predict that the parameter is an order of 0.01, the detection of t he primary bispectrum by any kind of experiments should be problematic for those scenarios. We compare the sensitivity of the primary bispectrum to th e primary skewness and conclude that, when we can compute the predicted for m of the bispectrum, it becomes a "matched filter" for detecting the non-Ga ussianity in the data and a much more powerful tool than the skewness. For example, we need the coupling parameter of larger than 800, 80, 70, and 60 for each relevant experiment in order to detect the primary skewness. We al so show that MAP and Planck can separate the primary bispectrum from variou s secondary bispectra on the basis of the shape difference. The primary CMB bispectrum is a test of the inflationary scenario and also a probe of the non-linear physics in the very early universe.