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

TL;DR

This paper uses bifurcation theory to analyze non-minimally coupled scalar field cosmological models, identifying parameter ranges that produce realistic cosmic evolution and avoid singularities, thus aiding model viability assessment.

Contribution

It applies bifurcation analysis and center manifold theory to classify and select scalar field models with desirable cosmological behaviors without fine-tuning initial conditions.

Findings

Models exhibit transcritical bifurcation, enabling desired dynamics.

Range of parameters produce evolution from radiation to dark energy.

Some models mimic stable general relativity late-time behavior.

Abstract

Non-minimally 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, which predicts 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 that of 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.