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In this work, we study the propagation of scalar fields in the gravitationalbackground of a higher-dimensional Schwarzschild-de-Sitter black hole as wellas on the projected-on-the-brane 4-dimensional background. The scalar fieldshave also a non-minimal coupling to the corresponding, bulk or brane, scalarcurvature. We perform a comprehensive study by deriving exact numerical resultsfor the greybody factors, and study their profile in terms of particle andspacetime properties. We then proceed to derive the Hawking radiation spectrafor a higher-dimensional Schwarzschild-de-Sitter black hole, and we study bothbulk and brane channels. We demonstrate that the non-minimal field coupling,that creates an effective mass term for the fields, suppresses the energyemission rates while the cosmological constant assumes a dual role. Bycomputing the relative energy rates and the total emissivity ratio for bulk andbrane emission, we demonstrate that the combined effect of a large number ofextra dimensions and value of the field coupling gives to the bulk channel theclear domination in the bulk-brane energy balance.

Hawking Radiation Spectra for Scalar Fields by a Higher-Dimensional Schwarzschild-de-Sitter Black Hole