Abstract
Non-minimal coupled scalar field models are well-known for providing interesting cosmological features. These include a late-time dark energy behavior, a phantom dark energy evolution without singularity, an early-time inflationary Universe, scaling solutions, convergence to the standard Lambda CDM, etc. While the usual stability analysis helps us determine the evolution of a model geometrically, bifurcation theory allows us to precisely locate the parameters’ values describing the global dynamics without a fine-tuning of initial conditions. Using the center manifold theory and bifurcation analysis, we show that the general model undergoes a transcritical bifurcation, predicting us to tune our models to have certain desired dynamics. We obtained a class of models and a range of parameters capable of describing a cosmic evolution from an early radiation era towards a late time dark energy era over a wide range of initial conditions. There is also a possible scenario of crossing the phantom divide line. We also find a class of models where the late time attractor mechanism is indistinguishable from a structurally stable general relativity-based model; thus, we can elude the big rip singularity generically. Therefore, bifurcation theory allows us to select models that are viable with cosmological observations.
Highlights
Models provide a natural solution to the problem associated with the energy scale difference between inflation and the Universe’s dark energy (DE) era [2]
We found that only class of models where the parameters λV∗, λF∗ belong to the common region of region I of Fig. 1b and region VII of Fig. 1e; and in the common region of region II of Fig. 1c and region VIII of Fig. 1e can possibly lead to physically interesting generic evolutionary scenarios
We focused on the bifurcation analysis to investigate the effect of varying the model parameters on the global dynamics
Summary
Most of the cosmological model’s governing equations are nonlinear and pose a severe impediment to extract exact analytical solutions. Bifurcation theory can help extract a class of models describing the observed dynamical evolution irrespective of initial conditions for a wide range of parameters. The analysis for a general non-minimal coupled scalar field model will certainly help us to identify classes of viable models. Bifurcation scenarios and chaos were discussed in the context of Horava–Lifshitz gravity [37], non-minimal coupled scalar field with Ratra–Peebles potential [21], interacting f (T ) gravity [38] and bulk viscous cosmology [39]. Humieja et al in [21] extract the conditions of model parameters under which a specific non-minimal coupling with Ratra–Peebles potential generically evolve from an early de Sitter to a late time de Sitter state.
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