Regular Article - Theoretical Physics
Cosmological dynamics and bifurcation analysis of the general non-minimal coupled scalar field models
Department of Mathematics, North-Eastern Hill University, 793022, Shillong, Meghalaya, India
2 Department of Mathematics, St. Anthony’s College, 793001, Shillong, Meghalaya, India
3 Mathematics Division, Department of Basic Sciences and Social Sciences, North-Eastern Hill University, 793022, Shillong, Meghalaya, India
4 Inter-University Centre for Astronomy and Astrophysics, 411007, Pune, India
Accepted: 18 August 2021
Published online: 29 August 2021
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 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.
© The Author(s) 2021
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