https://doi.org/10.1140/epjc/s10052-021-09559-x
Regular Article - Theoretical Physics
Cosmological dynamics and bifurcation analysis of the general non-minimal coupled scalar field models
1
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
Received:
12
February
2021
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
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3
