Space laser interferometers can determine the thermal history of the   early Universe
  It is shown that space-based gravitational wave detectors such as DECIGO and/or Big Bang Observer (BBO) will provide us with invaluable information on the cosmic thermal history after inflation and they will be able to determine the reheat temperature $T_R$ provided that it lies in the range preferred by the cosmological gravitino problem, $T_R\sim 10^{5-9}$ GeV. Therefore it is strongly desired that they will be put into practice as soon as possible. 
Kazunori Nakayama, Shun Saito, Yudai Suwa, and Jun'ichi Yokoyama