  Two-dimensional Schwarzschild-de Sitter is a convenient spacetime in which to
study the effects of horizons on quantum fields since the spacetime contains
two horizons, and the wave equation for a massless minimally coupled scalar
field can be solved exactly. The two-point correlation function of a massless
scalar is computed in the Unruh state. It is found that the field correlations
grow linearly in terms of a particular time coordinate that is good in the
future development of the past horizons, and that the rate of growth is equal
to the sum of the black hole plus cosmological surface gravities. This time
dependence results from additive contributions of each horizon component of the
past Cauchy surface that is used to define the state. The state becomes the
Bunch-Davies vacuum in the cosmological far field limit. The two point function
for the field velocities is also analyzed and a peak is found when one point is
between the black hole and cosmological horizons and one point is outside the
future cosmological horizon.
