We present the results of research into inflationary cosmology. This consists firstly of a basic overview of the inflationary scenario, including the currently accepted model of inflation as being driven by a weakly interacting scalar field with a slowly varying effective potential energy function. We then consider the theory of density perturbations, their quantum origins in the inflaton scalar field, and evolution in a rapidly expanding universe. This all acts as background material for the research carried out, which involves the generation of density perturbations by a non-standard effective potential for the inflaton field, and how their evolution is effected by features in the potential. The potentials are motivated by phase transitions in fields weakly coupled to the inflaton. These potentials violate the normally assumed slow roll conditions and the resulting power spectra do not have the scale independence characteristic of slow roll. Instead they exhibit scale dependent oscillations, whose nature depend on the details of the potential being considered. We finally consider the effect such power spectra would have on the Cosmic Microwave Background and compare this to the current observational data.