  Thermal history of the Universe between inflation and big-bang
nucleosynthesis has not yet been revealed observationally. It will be probed by
the detection of primordial gravitational waves generated during inflation,
which contain information on the reheating temperature as well as the equation
of state of the Universe after inflation. Based on Fisher information
formalism, we examine how accurately the tensor-to-scalar ratio and reheating
temperature after inflation can be simultaneously determined with space-based
gravitational wave detectors such as the DECI-hertz Interferometer
Gravitational-wave Observatory (DECIGO) and the Big-Bang Observer (BBO). We
show that the reheating temperature is best determined if it is around 10^7 GeV
for tensor-to-scalar ratio of around 0.1, and explore the detectable parameter
space. We also find that equation of state of the early Universe can be also
determined accurately enough to distinguish different equation-of-state
parameters if the inflationary gravitational waves are successfully detected.
Thus future gravitational wave detectors provide a unique and promising
opportunity to reveal the thermal history of the Universe around 10^7 GeV.
