Quantum Scalar Field in D-dimensional de Sitter Spacetimes
  In this work we investigate the quantum theory of scalar fields propagating in a $D-$dimensional de Sitter spacetime. The method of dynamic invariants is used to obtain the solution of the time-dependent Schr\"odinger equation. The quantum behavior of the scalar field in this background is analyzed, and the results generalize previous ones found in the literature. We point that the Bunch-Davies thermal bath depends on the choice of $D$ and the conformal parameter $\xi$. This is important in extra dimension physics, as in the Randall-Sundrum model. 
G. Alencar, I. Guedes, R. R. Landim and R.N. Costa Filho
hep-th gr-qc