Title: Hawking-like radiation as tunnelling from the apparent horizon in a FRW Universe Authors: Tao Zhu, Ji-Rong Ren, Douglas Singleton

We study Hawking-like radiation in a Friedmann-Robertson-Walker (FRW) universe using the quasi-classical WKB/tunnelling method which pictures this process as a "tunnelling" of particles from behind the apparent horizon. The correct temperature of the Hawking-like radiation from the FRW spacetime is obtained using a canonical invariant tunnelling amplitude. In contrast to the usual quantum mechanical WKB/tunnelling problem where the tunnelling amplitude has only a spatial contribution, we find that the tunnelling amplitude for FRW spacetime (i.e. the imaginary part of the action) has both spatial and temporal contributions. In addition we study back reaction and energy conservation of the radiated particles and find that the tunnelling probability and change in entropy, {\cal S} are related by the relationship: \Gamma\propto\exp[-\Delta {\cal S}] which differs from the standard result \Gamma\propto\exp[\Delta {\cal S}]. By regarding the whole FRW universe as an isolated adiabatic system the change in the total entropy is zero. Then splitting the entropy between interior and exterior parts of the horizon (\Delta {\cal S}_{total} =\Delta {\cal S}_{int} + \Delta {\cal S}_{ext}=0), we can explain the origin of the minus sign difference with the usual result: our \Delta {\cal S} is for the interior region while the standard result from black hole physics is for the exterior region.