| Abstract: | Observations of the cosmic microwave background (CMB) furnish to date the tightest constraints on the nature of the primordial fluctuations and, therefore, the physics of inflation. These measurements exploit the fact that different inflationary mechanisms imprint distinct signatures in the non-Gaussianity of the primeval curvature perturbations. Interestingly, independent and competitive constraints can be obtained by measuring the statistical properties of large scale density fluctuations in the low redshift Universe. I will discuss recent theoretical and observational developments, and argue that upcoming galaxy redshift surveys can achieve limits (at least) an order of magnitude better than the CMB Planck mission. |