Tests for primordial non-Gaussianity

We investigate the relative sensitivities of several tests for deviations f rom Gaussianity in the primordial distribution of density perturbations. We consider models for non-Gaussianity that mimic that which comes from infla tion as well as that which comes from topological defects. The tests we con sider involve the cosmic microwave background (CMB), large-scale structure, high-redshift galaxies, and the abundances and properties of clusters. We find that the CMB is superior at finding non-Gaussianity in the primordial gravitational potential (as inflation would produce), while observations of high-redshift galaxies are much better suited to find non-Gaussianity that resembles that expected from topological defects. We derive a simple expre ssion that relates the abundance of high-redshift objects in non-Gaussian m odels to the primordial skewness.