Evolution of gauge-invariant scalar perturbations from inflation to reheating

We assume that at a late stage of inflation, a scalar inflaton field, a thermal plasma, and a spacetime metric coexisted and interacted with each other. We expand them to the linear order around a homogeneous background and combine the perturbations into a set of gauge invariant variables. For the latter we derive evolution equations in the framework of smooth reheating. Having resolved some numerical challenges, we provide solutions for a set of benchmarks, from inflation all the way until radiation domination. In particular, our solution exhibits some key features of the inflationary paradigm, for example: gauge invariant 'curvature perturbations' obtain the same constant value when they are outside of the Hubble horizon and experience acoustic oscillations upon re-entry.