Quintessence for the Steep Potential | Center Manifold Theorem in Cosmology

✍️ About: In this video, we have presented a review of the Quintessence field minimally coupled with Dark matter in the context of the Dynamical System Analysis. For the Quintessence Field, we have considered the potential to be an exponential type having different steeper constants. The study gives both accelerating and non-accelerating critical points for which the Eigenvalues become non-hyperbolic.
🤯The non-hyperbolic term used for the case where any real part of the eigenvalues of the Jacobian Matrix is zero and the rest have either positive or negative values. In that case, the stability of the critical points can not be determined by using the standard Linearization Technique. Hence, I have discussed the "Center Manifold Theorem" to discuss stability. I have not given a greater depth regarding this technique, although I present a rough idea to understand this technique.
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📚 Research Articles :
My Research Papers and Other Important Research Articles:
[1] Dynamical stability of K-essence field interacting non-minimally with a perfect fluid -- arxiv.org/abs/...
[2] Dynamics of dark energy -- arxiv.org/abs/...
[3] Dynamics of purely kinetic k-essence in presence of a perfect fluid -- arxiv.org/abs/...
[5] Dynamical Systems and Cosmology -- www.google.co....
[6] Dynamical System Analysis for Steep Potentials -- arxiv.org/abs/...
[7] Dynamics of purely kinetic k-essence in presence of a perfect fluid --
arxiv.org/abs/...
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🎥 Playlist:
Dynamics of Dark Energy REVIEW -- • Dynamics of Dark Energ...
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👽 Tags :
#Quintessence #Steep_potential #Divergent_Dynamical_System #Quintessence_Dynamics
#Quintessence #center_manifold_theorem #Stability_analysis_cosmology #dark_energy #dark_matter #Physics_research #kessence #dynamical_stability #Dynamical_System_Analysis

[@cosmickap]

Hey guys join your hands to share my videos.

[@quinncept2]

nice

[@ratulmandal9046]

Can u pls tell me how to plot x vs N ,y vs N for a dynamical system ..?

[@cosmickap]

Solve the differential equation in Mathematica or python, and plot the solutions of these parameters against N.

[@ratulmandal9046]

But for solve we need initial conditions.can I contact you for some query ?

[@cosmickap]

yeah sure. you can email me [e-mail]