Measuring the expansion of the universe
  We draw a figure from where it is possible to measure the number of e-folds
of expansion of the universe with a ruler. We find model independent bounds for
the number of e-folds during inflation, reheating and radiation. We also give a
lower bound to the size of the universe at the beginning of observable
inflation. Finally, we show that consistency with a relevant diagram requires
the existence of a new form of energy to drive the present expansion of the
universe.
