Inconsistency with de Sitter spacetime in a new approach to gravitational particle production

We study a claimed new mechanism for particle production and black hole evaporation through a spatially dependent temperature. This new temperature is comparable to the Hawking result near the black hole, but is very small far away, and therefore could be a small correction. Here we apply the proposed reasoning to the case of de Sitter space, finding that it over predicts the de Sitter temperature of a minimally coupled scalar by factor of $\approx 4.3$ and over predicts the particle production rate by a factor of $\approx 52$. For non-minimally coupled scalars, it has other various problems; it predicts a negative particle production for conformal, or nearly conformal, coupled scalars; it predicts unsuppressed productions of heavy scalars. This all demonstrates an inconsistency in the proposed formalism.