Prospects for determination of thermal history after inflation with future gravitational wave detectors

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 the 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 and the Big-Bang Observer. 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.