Visualization of cosmological density fluctuations with phase space analysis: case study: Brans–Dicke theory

Cosmological perturbation theory is a powerful tool to understanding the large-scale structure of the Universe. However, the set of field equations describes the general linear perturbations for the cosmological models is highly nonlinear and coupled where no analytical solution can be found. It is only after some simplification and numerical computation that we obtain limited solutions. On way around is to employ the phase space analysis and investigate the asymptotic stability of the model. The advantage of using this approach is that the system of field equations become simpler to solve numerically. The algorithm also determines the stability of the system. Here, we apply this approach in Brans–Dicke cosmology and study the attractor solutions after fitting the model with the SNeIa observational data. As a result, the model confirms small fluctuations of energy density. The model also predicts current universe acceleration confirmed by observation and benefits from phase space analysis that the new dynamical variables are independent of the model initial conditions.