A solution to the initial condition problems of inflation : NATON

The recent astonishing realization of the negative absolute temperature (NAT) for motional degrees of freedom \cite{Braun_ea13} inspires its possible application to the early universe. The existence of the upper bound on the energy of the system is the sufficient requirement for a NAT and this might correspond to the Planck scale at the Big Bang model. It has been argued that standard inflation requires an initial patch that is smooth over distance scales a bit larger than the causal horizon at the onset of inflation. We show that this initial condition problem can be solved if the NAT fermion, dubbed ``NATON'', occupies the Universe before the standard inflation is ignited by providing mini inflation prior to the standard one. As long as NATON dominated era lasts until at least ten times older than the Planck time, it makes the Universe homogeneous enough to derive the successful standard inflation.