Phase-space structure of cosmological thermogravity

Abstract

An emergent gravity model was shown to contain an associated emergent breaking of Lorentz invariance and violations of stress-energy conservation. Its simplest flat dust solution accelerates at late times without vacuum energy and has already been used as an analytic benchmark for observational tests. We study the wider homogeneous dynamics and solutions of this theory. For a single non-conserved dust fluid, the variables $Ω_m=ρ/(3H^2)$ and $u=(HL_2)^{-1}$ form a two-dimensional autonomous system with an exact first integral. The complete expanding solution space separates into three classes: trajectories ending on an asymptotically de Sitter fixed line, a critical trajectory corresponding to the analytic solution of Isichei and Magueijo, and trajectories that turn around and recollapse. We then consider the phenomenologically cleaner model in which only cold dark matter violates energy conservation (while the baryons and photons behave as normal). The phase space becomes three-dimensional, with a line of matter repellers and a line of vacuum fixed points. Each normally attracting vacuum point with $0<u_0<3$ possesses a two-dimensional stable sheet. The limit in which the CDM abundance tends to zero is singular: finite-$u_0$ sheets meet the exactly baryonic plane on trajectories containing a cosmological-constant-like integration constant, whereas the zero-integration-constant baryonic solution remains at $Ω_b=1$ and runs to $u\to\infty$. The critical endpoint $u_0=3$ separates these late-time behaviours and generalizes the special single-fluid solution.