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

TL;DR

This paper investigates whether a quantized free scalar field on flat FRW spacetimes can produce a Chaplygin gas equation of state, finding significant restrictions and suggesting incompatibility with semi-classical Einstein equations.

Contribution

It characterizes homogeneous and isotropic Hadamard states for the scalar field and demonstrates the incompatibility of Chaplygin gas equations with these states in certain cosmological settings.

Findings

No Chaplygin gas equation of state compatible with HIH states on certain FRW spacetimes.

Explicit construction of a simple HIH state for the scalar field.

Indications that the semi-classical Einstein equation cannot be consistently solved with a Chaplygin gas.

Abstract

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. Finally, we argue that the semi-classical Einstein equation and the Chaplygin gas equation of state can presumably not be consistently solved for the quantized free scalar field.