Entropy generation, particle creation, and quantum field theory in a cosmological spacetime: When do number and entropy increase?

This paper reexamines the statistical quantum field theory of a free, minimally coupled, real scalar field Φ in a statically bounded, classical Friedmann cosmology, where the time-dependent scale factor Ω(t) tends to constant values ${\Omega }_1$ and ${\Omega }_2$ for t<$t_1$ and t>$t_2$. The principal objective is to investigate the intuition that ‘‘entropy’’ S correlates with average particle number 〈N〉, so that increases in 〈N〉 induced by parametric amplification manifest a one-to-one connection with increases in S. The definition of particle number $N_k$ becomes unambiguous for t>$t_2$ and t<$t_1$, where the spacetime is static, the spatial modes ±k for early and late times being coupled by Bogoliubov coefficients ${\alpha }_k$ and ${\beta }_k$.