No absorption in de Sitter space

We study the wave equation for a minimally coupled massive scalar in D-dimensional de Sitter space. We compute the absorption cross section to investigate its cosmological horizon in the southern diamond. By analogy of the quantum mechanics, it is found that there is no absorption in de Sitter space. This means that de Sitter space is usually in thermal equilibrium, like the black hole in anti de Sitter space. It confirms that the cosmological horizon not only emits radiation but also absorbs that previously emitted by itself at the same rate, keeping the curvature radius of de Sitter space fixed.