Hawking radiation from the cosmological horizon in a FRW universe

It is well known that there is a Hawking radiation from the cosmological horizon of the de-sitter spacetime, and the de-sitter spacetime can be a special case of a FRW universe. Therefore, there may be a corresponding Hawking radiation in a FRW universe. Indeed, there have been several clues showing that there is a Hawking radiation from the apparent horizon of a FRW universe. In our paper, however, we find that the Hawking radiation may come from the cosmological horizon. Moreover, we also find that the Hawking radiation from the apparent horizon of a FRW universe in some previous works can be a special case in our result, and the condition is that the variation rate of cosmological horizon $\overset{.}{r}_{H}$ is zero. Note that, this condition is also consistent with the underlying integrable condition in these works from the apparent horizon.Comment: V3: 12 pages, no figure, typos corrected, new references added, version shorted and accepted by PL