Multitracer technique for galaxy bispectrum: An application to constraints on nonlocal primordial non-Gaussianities

If the primordial fluctuations are non-Gaussian, then this non-Gaussianity will be apparent in the cosmic microwave background (CMB) sky. With their sensitive all-sky observation, MAP and Planck satellites should be able to detect weak non-Gaussianity in the CMB sky. On large angular scale, there is a simple relationship between the CMB temperature and the primordial curvature perturbation. On smaller scales; however, the radiation transfer function becomes more complex. In this paper, we present the angular bispectrum of the primary CMB anisotropy that uses the full transfer 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 as that of the angular power spectrum. Using a single non-linear coupling parameter to characterize the amplitude of the bispectrum, we estimate the expected signal-to-noise ratio for COBE, MAP, and Planck experiments. We find that the detection of the primary bispectrum by any kind of experiments should be problematic for the simple slow-roll inflationary scenarios. We compare the sensitivity of the primary bispectrum to the primary skewness and conclude that when we can compute the predicted form of the bispectrum, it becomes a ``matched filter'' for detecting the non-Gaussianity in the data, and much more powerful tool than the skewness. We also show that MAP and Planck can separate the primary bispectrum from various 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.

We study the effect of primordial nongaussianity on large-scale structure, focusing upon the most massive virialized objects. Using analytic arguments and N-body simulations, we calculate the mass function and clustering of dark matter halos across a range of redshifts and levels of nongaussianity. We propose a simple fitting function for the mass function valid across the entire range of our simulations. We find pronounced effects of nongaussianity on the clustering of dark matter halos, leading to strongly scale-dependent bias. This suggests that the large-scale clustering of rare objects may provide a sensitive probe of primordial nongaussianity. We very roughly estimate that upcoming surveys can constrain nongaussianity at the level |fNL| <~ 10, competitive with forecasted constraints from the microwave background.

Dark matter haloes are biased tracers of the underlying dark matter distribution. We use a simple model to provide a relation between the abundance of dark matter haloes and their spatial distribution on large scales. Our model shows that knowledge of the unconditional mass function alone is sufficient to provide an accurate estimate of the large scale bias factor. Then we use the mass function measured in numerical simulations of SCDM, OCDM and LCDM to compute this bias. Comparison with these simulations shows that this simple way of estimating the bias relation and its evolution is accurate for less massive haloes as well as massive ones. In particular, we show that haloes which are less/more massive than typical M* haloes at the time they form are more/less strongly clustered than formulae based on the standard Press-Schechter mass function predict.