Negative pressure as a quantum effect in free-streaming in the cosmological background

We present a study of energy density and pressure of a free real scalar quantum field after its decoupling from a thermal bath in the spatially flat Friedman-Lemaître-Robertson-Walker spacetime by solving the Klein-Gordon equation both analytically and numerically for different predetermined scale factor functions 𝑎⁡(𝑡). The energy density and pressure, defined by subtracting the vacuum expectation values at the decoupling time, feature corrections with respect to the classical free-streaming solution of the relativistic Boltzmann equation. We show that if the expansion rate is comparable or larger than 𝑚⁢𝑐2/ℏ or 𝐾⁢𝑇0/ℏ where 𝑚 is the mass and 𝑇0 the decoupling temperature, both energy density and pressure gets strong quantum corrections which substantially modify their classical dependence on the scale factor 𝑎⁡(𝑡) and drive pressure to large negative values. For a minimally coupled field with a very low mass in an expanding de Sitter universe quantum corrections are dominant driving pressure and energy density to become asymptotically constant with an equation of state 𝑝/𝜖 ≃−1, thereby mimicking a cosmological constant. For a minimally coupled massless field, quantum corrections are asymptotically dominant for any accelerated expansion.