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 .