Greybody factor and power spectra of the Hawking radiation in the 4D Einstein-Gauss-Bonnet de-Sitter gravity

A novel 4D Einstein-Gauss-Bonnet gravity was recently formulated by Glavan and Lin [Phys. Rev. Lett. 124, 081301 (2020)]. Although this theory may run into trouble at the level of action or equations of motion, the spherically symmetric black hole solution, which can be successfully reproduced in those consistent theories of 4D EGB gravity, is still meaningful and worthy of study. In this paper, we investigate Hawking radiation in the spacetime containing such a de Sitter black hole. Both the greybody factor and the power spectra of the Hawking radiation of the massless scalar are studied numerically for the full range of various parameters, including the GB coupling constant alpha, the cosmological constant Lambda and the coupling constant related to the scalar filed xi. In particular, we find a negative alpha leads to a larger greybody factor than that of a alpha >= 0. While, for the power spectra of the Hawking radiation the situation is quite the opposite. The reason is that the temperature of the black hole would be very high when alpha <0. Actually, we observe that the temperature would be arbitrarily high when <alpha> approaches to the lower bound.