Cosmological dynamics and bifurcation analysis of the general non-minimal coupled scalar field models

• Main Authors: Wompherdeiki Khyllep, Jibitesh Dutta
• Format: Article
• Language: English
• Published: SpringerOpen 2021-08-01
• Series: European Physical Journal C: Particles and Fields
• Online Access: https://doi.org/10.1140/epjc/s10052-021-09559-x
• ISSN: 1434-6044; 1434-6052

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 $$\Lambda $$ Λ 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.