Frontiers of inflationary cosmology

After a brief review the theory of cosmological perturbations, I highlight some recent progress in the area of reheating in inflationary cosmology, fo cusing in particular on parametric amplification of super-Hubble cosmologic al fluctuations, and on the role of noise in the resonance dynamics (yieldi ng a new proof of Anderson localization). I then discuss several important conceptual problems for the current realizations of inflation based on fund amental scalar matter fields, and review some new approaches at solving the se problems.