The Equal-time Wigner formalism from quantum kinetic theory has been successfully used within the field of plasma physics to describe both classical and quantum plasmas, and it has also been used to describe relativistic ones. Recently this formalism has also been applied to the problem of particles in a curved spacetime; by transforming a real, massive scalar field that propagates on this curved spacetime we can derive a set of phase-space functions and evolution equations for these that can describe the phenomenon of cosmological particle production, giving results that can be interpreted in terms of the energy momentum tensor. These phase-space functions can also be interpreted similarly to the distribution function of classical kinetic theory, making physical interpretations of the results easier. In the case of homogeneously curved spacetime, the quantum kinetic results have been shown to agree with more commonly used methods, but they give evolution equations that differ from the ones derived for the homogeneous case. In this thesis we thus use the equal-time Wigner formalism for the case of a real and massive scalar field propagating on a weakly inhomogeneously curved spacetime, without backreactions on the gravitational field, to derive a set of phase-space functions and evolution equations that describe this system. We also simplify these evolution equations for some specific types of inhomogeneities, and show that they agree with the equations derived by others for the homogeneous case.
Björn Eriksson (Thu,) studied this question.