  The characteristics of the cosmic microwave background provide circumstantial
evidence that the hot radiation-dominated epoch in the early universe was
preceded by a period of inflationary expansion. Here, we show how a measurement
of the stochastic gravitational wave background can reveal the cosmic history
and the physical conditions during inflation, subsequent pre- and re-heating,
and the beginning of the hot big bang era. This is exemplified with a
particularly well-motivated and predictive minimal extension of the Standard
Model which is known to provide a complete model for particle physics -- up to
the Planck scale, and for cosmology -- back to inflation.
