Weakly model-independent determination of total expansion during inflation

We study systematically the total expansion experienced by a certain perturbation mode during single-field inflation, not resorting to explicit models of inflation or reheating. By assuming that during the reheating stage the equation of state w{rh} can be written as a function of e-folds, the unknown dynamics during reheating parametrized by w{rh} is confined within a time integral so that any dependence on the models of inflation and reheating is isolated from model-independent contributions. Especially, the dependence on the reheating dynamics via w{rh} and the reheating temperature T{rh} is dominating. We give two illustrative examples of w{rh} to discuss its impacts on the total expansion, which can be different as much as 10 even for the same reheating temperature, depending on the shape of w{rh}. We also discuss the profile degeneracy of w{rh}, and argue when the degeneracy is lifted.