Einstein’s field equations as a fold bifurcation

Kohli, Ikjyot Singh; Haslam, Michael C.

doi:10.1016/j.geomphys.2017.10.001

Cited by 6 publications

(9 citation statements)

References 30 publications

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“…The dynamical analysis can be enriched further with using the biffurcation theory methods. Recently, the problem of bifurcations in the FRW cosmology with perfect fluid and the cosmological constant was investigated in the work of Kohli and Haslam [14]. They demonstrated that as the cosmological constant parameter is varied, expanding de Sitter and contracting de Sitter universes emerge via fold bifurcation.…”

Section: Introductionmentioning

confidence: 99%

Bifurcations in Ratra–Peebles quintessence models and their extensions

Humieja

Szydłowski

2019

Eur. Phys. J. C

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We have used the dynamical system approach in order to investigate the dynamics of cosmological models of the flat Universe with a non-minimally coupled canonical and phantom scalar field and the Ratra-Peebles potential. Applying methods of the bifurcation theory we have found three cases for which the Universe undergoes a generic evolution emerging from either the de Sitter or the static Universe state and finishing at the de Sitter state, without the presence of the initial singularity. This generic class of solutions explains both the inflation and the late-time acceleration of the Universe. In this class inflation is an endogenous effect of dynamics itself.

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Section: Introductionmentioning

confidence: 99%

Bifurcations in Ratra–Peebles quintessence models and their extensions

Humieja

Szydłowski

2019

Eur. Phys. J. C

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“…Bogdanov-Takens bifurcations have been shown to occur in Bianchi IX cosmological models in the frame work of Gauss-Bonnet gravity [11]. A more recent study [12] has also demonstrated the occurrence of such a bifurcation in Friedmann-Roberston-Walker (FRW) cosmology in the presence of cosmological constant without considering viscosity. The latter study is of limited scope due to neglecting viscosity which is a real physical dissipative effect which is essential for getting certain desirable properties of Bogdanov-Takens system such as the finiteness of the number of fixed points.…”

Section: Introductionmentioning

confidence: 96%

“…The latter study is of limited scope due to neglecting viscosity which is a real physical dissipative effect which is essential for getting certain desirable properties of Bogdanov-Takens system such as the finiteness of the number of fixed points. Up to the best of our knowledge, the works in [11,12] are the only two instances in cosmological studies where the Bogdanov-Takens bifurcations occurred. In fact, investigating and classifying all possible solutions and their stability properties in cosmological models enhances our understanding of the models.…”

Section: Introductionmentioning

confidence: 99%

Degenerate Bogdanov–Takens bifurcations in a bulk viscous cosmology

2020

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Using the dynamical system theory we show that the Friedmann–Robertson–Walker (FRW) cosmological model with bulk viscous fluid in the presence of cosmological constant is equivalent to a degenerate two dimensional Bogdanov–Takens normal form. The equation of state parameter, $$\omega $$ ω , the bulk viscosity coefficient, $$\xi $$ ξ , and the cosmological constant, $$\Lambda $$ Λ , define the necessary parameters for unfolding the degenerate Bogdanov-Takens system. The fixed points of the system are discussed together with the variation of their stability properties upon changing the relevant parameters $$\omega , \Lambda $$ ω , Λ and $$\xi $$ ξ . The variation of the stability properties are visualized by the appropriate bifurcation diagrams. Phase portrait for finite domain and global phase portrait are displayed and the issue of the structural stability is discussed. Typical issues such as late acceleration or inflation that can be induced by viscosity and could have relevance to observational cosmology are also discussed.

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“…For instance, Ref. [32] shows that in FRW-models with perfect fluids and the cosmological constant, the expanding and contracting deSitter Universe arise as bifurcation. It is worth mentioning that interesting bifurcation scenarios were reported in the Randall-Sundrum braneworld model [33], interacting Veneziano ghost DE [34], Brans-Dicke model [35], nonminimal coupled scalar field model [31,36] etc.…”

Section: Introductionmentioning

confidence: 99%

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

Khyllep

Dutta

2021

Eur. Phys. J. C

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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.

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Einstein’s field equations as a fold bifurcation

Cited by 6 publications

References 30 publications

Bifurcations in Ratra–Peebles quintessence models and their extensions

Bifurcations in Ratra–Peebles quintessence models and their extensions

Degenerate Bogdanov–Takens bifurcations in a bulk viscous cosmology

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

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