The Chaplygin Gas Equation of State for the Quantized Free Scalar Field on Cosmological Spacetimes

Understand

We try to answer the question whether the quantized free scalar field on a spatially flat Friedmann-Robertson-Walker (FRW) spacetime is a matter model that can induce a Chaplygin gas equation of state.

• For this purpose we first describe how one can obtain every possible homogeneous and isotropic Hadamard (HIH) state once any such state is given.
• We also identify a condition on the scale factor sufficient to entail the existence of a simple HIH state $-$ this state is constructed explicitly and can thence be used as a starting point for constructing all HIH states.
• Furthermore, we employ these results to show that on an FRW spacetime with non-positive constant scalar curvature there is, with one exception, no Chaplygin gas equation of state compatible with any HIH state.