Inflation—a period of accelerated expansion is currently considered the most promising paradigm for describing the early stages of the universe. The success of the inflationary scenario rests on its ability to explain not only the homogeneity of the background, but also the characteristics of the in homogeneities superimposed upon it. The inflationary epoch magnifies the tiny fluctuations in the quantum fields present at the beginning of the epoch into classical perturbations that leave their imprints as anisotropies in the cosmic microwave background (CMB). These anisotropies in turn act as seeds for the formation of the large-scale structure that we observe at the present time as galaxies and clusters of galaxies. With anisotropies in the CMB being measured with higher and higher precision, we are currently able to test the predictions of inflation better and better. In this talk, after introducing the motivations and essential features of inflation, I provide a brief overview of cosmological perturbation theory, and discuss the constraints from the most recent WMAP data on the inflationary parameters.

After an elementary introduction, we focus on the density dependence of the interaction energy of the gas at Feshbach resonance. A naive perturbative approach cannot explain universality, but gives the unexpected cancellation of the first order exchange energy withthe perturbative correlation energy at resonance for short range interactions. A curious, almost shape-independent property of the attractive two-bodypotential is found at Feshbach resonance.