Gibbons and Hawking [Phys. Rev. D 15, 2738 (1977)] have shown that the
horizon of de Sitter space emits radiation in the same way as the event horizon
of the black hole. But actual cosmological horizons are not event horizons,
except in de Sitter space. Nevertheless, this paper proves Gibbon's and
Hawking's radiation formula as an exact result for any flat space expanding
with strictly positive Hubble parameter. The paper gives visual and intuitive
insight into why this is the case. The paper also indicates how cosmological
horizons are related to the dynamical Casimir effect, which makes experimental
tests with laboratory analogues possible.