Structure Topology and Symplectic Geometry

Shah, Kamal; Lei, M.

doi:10.5772/intechopen.80177

2021

DOI: 10.5772/intechopen.80177

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Structure Topology and Symplectic Geometry

Kamal Shah¹,

M. Lei²

Abstract: He obtained an MSc from Government Post Graduate Jehanzeb College Swat in 2005. He joined the University of Malakand as a lecturer in 2007. Dr. Shah obtained a Ph.D. in Fractional Calculus in 2016 from the University of Malakand. He has published numerous articles in scientific journals and has supervised many MPhil and Ph.D. students. Dr. Min Lei has worked at Shanghai Jiaotong University as an associate professor since 2004.

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Dynamical Reason for a Cyclic Universe

2021

Symmetry

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By analyzing the energy-momentum tensor and equations of state of ideal gas, scalar, spinor and vector potential in detail, we find that the total mass density of all matter is always positive, and the initial total pressure is negative. Under these conditions, by qualitatively analyzing the global behavior of the dynamical equation of cosmological model, we get the following results: (i) K=1, namely, the global spatial structure of the universe should be a three-dimensional sphere S3; (ii) 0≤Λ<10−24ly−2, the cosmological constant should be zero or an infinitesimal; (iii) a(t)>0, the initial singularity of the universe is unreachable, and the evolution of the universe should be cyclic in time. Since the matter components considered are quite complete and the proof is very elementary and strict, these conclusions are quite reliable in logic and compatible with all observational data. Obviously, these conclusions will be very helpful to correct some popular misconceptions and bring great convenience to further research other problems in cosmology such as the properties of dark matter and dark energy. In addition, the macroscopic Lagrangian of fluid model is derived.

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Dynamical Reason for a Cyclic Universe

2021

Symmetry

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Structure Topology and Symplectic Geometry

Cited by 1 publication

References 48 publications

Dynamical Reason for a Cyclic Universe

Dynamical Reason for a Cyclic Universe

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