Some Models of Cyclic and Knot Universes

Yesmakhanova, Kuralay; Myrzakulov, N.; Yerzhanov, Koblandy; Nugmanova, Gulgassyl; Serikbayaev, N.S.; Myrzakulov, Ratbay

doi:10.48550/arxiv.1201.4360

Cited by 4 publications

(6 citation statements)

References 27 publications

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“…For this solution the corresponding universe we call the figure-eight knot universe as the solution (10.9)-(10.11) is nothing but the parametric equation of the figure-eight knot (see also Refs. [46]- [47]).…”

Section: The Figure-eight Knot Universementioning

confidence: 99%

$$F(T)$$ gravity and k-essence

Myrzakulov

2012

Gen Relativ Gravit

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Modified teleparallel gravity theory with the torsion scalar have recently gained a lot of attention as a possible explanation of dark energy. We perform a thorough reconstruction analysis on the so-called F (T ) models, where F (T ) is some general function of the torsion term, and derive conditions for the equivalence between of F (T ) models with purely kinetic k-essence. We present a new class models of F (T )-gravity and k-essence. We also proposed some new models of generalized gases and knot universes as well as some generalizations of F (T ) gravity. *

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Section: The Figure-eight Knot Universementioning

confidence: 99%

$$F(T)$$ gravity and k-essence

Myrzakulov

2012

Gen Relativ Gravit

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“…Next, we present one of the two periodical generalizations of the MCG. Its EoS reads [102][103][104][105]…”

Section: Mg -Xxiii Modelmentioning

confidence: 99%

“…Furthermore, related to the cyclic universe, the (trefoil and figure-eight) knot universe has been investigated in Ref. [102][103][104][105]. In addition, motivated by the studies on the role of applying the Weierstrass ℘(t), ζ(t) and σ(t)-functions and the Jacobian elliptic functions to astrophysics and cosmology [106][107][108][109][110], the equation of state (EoS) for the cyclic universes in the homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime has been reconstructed by using the Weierstrass and Jacobian elliptic functions in Ref.…”

Section: Introductionmentioning

confidence: 99%

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Periodic Cosmological Evolutions of Equation of State for Dark Energy

Bamba

Debnath

Yesmakhanova

et al. 2012

Entropy

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We demonstrate two periodic or quasi-periodic generalizations of the Chaplygin gas (CG) type models to explain the origins of dark energy as well as dark matter by using the Weierstrass ℘(t), σ(t) and ζ(t) functions with two periods being infinite. If the universe can evolve periodically, a non-singular universe can be realized. Furthermore, we examine the cosmological evolution and nature of the equation of state (EoS) of dark energy in the Friedmann-Lemaître-Robertson-Walker cosmology. It is explicitly illustrated that there exist three type models in which the universe always stays in the non-phantom (quintessence) phase, whereas it always evolves in the phantom phase, or the crossing of the phantom divide can be realized. The scalar fields and the corresponding potentials are also analyzed for different types of models.

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“…Myrzakulov [8] constructed several concrete models describing the trefoil and figure-eight knot universes from Bianchi-type I cosmology and examined the cosmological features and properties in detail. Yesmakhanova et al [9] constructed a cosmological model by assuming the periodic forms for pressure and energy density as a functions of time, there exists a coordinate set, in which the time evolutions of the space is knot like. Very recent, the concept of viscosity is introduced into dark energy study.…”

Section: Introductionmentioning

confidence: 99%

Kaluza–Klein Bulk Viscous Fluid Cosmological Models and the Validity of the Second Law of Thermodynamics in f(R, T) Gravity

Samanta

Myrzakulov

Shah

2017

Zeitschrift Für Naturforschung A

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The authors considered the bulk viscous fluid in f (R, T ) gravity within the framework of Kaluza-Klein space time. The bulk viscous coefficient (ξ) expressed as ξ = ξ 0 + ξ 1ȧ a + ξ 2ä a , where ξ 0 , ξ 1 and ξ 2 are positive constants. We take p = (γ − 1)ρ, where 0 ≤ γ ≤ 2 as an equation of state for perfect fluid. The exact solutions to the corresponding field equations are given by assuming a particular model of the form of f (R, T ) = R + 2f (T ), where f (T ) = λT , λ is constant. We studied the cosmological model in two stages, in first stage: we studied the model with no viscosity, and in second stage: we studied the model involve with viscosity. The cosmological model involve with viscosity is studied by five possible scenarios for bulk viscous fluid coefficient (ξ). The total bulk viscous coefficient seems to be negative, when the bulk viscous coefficient is proportional to ξ 2ä a , hence the second law of thermodynamics is not valid, however, it is valid with the generalized second law of thermodynamics. The total bulk viscous coefficient seems to be positive, when, the bulk viscous coefficient is proportional to ξ = ξ 1ȧ a , ξ = ξ 1ȧ a + ξ 2ä a and ξ = ξ 0 + ξ 1ȧ a + ξ 2ä a , so the second law of thermodynamics and the generalized second law of thermodynamics is satisfied throughout the evolution. We calculate statefinder parameters of the model and observed that, it is different from the ∧CDM model. Finally, some physical and geometrical properties of the models are discussed.where h.c. means Hermitian conjugate, S E is the Einstein action describing gravity, E = det(−g µν ) 1 2 , α is the gravitational coupling constant and R is the Ricci scalar.The original Kaluza-Klein theory derive with one extra spatial dimension. The appropriate metric tensor for five dimensional space time iŝThe fifth dimension is postulated to be comfactified, rolled-up in a small circle, which provides us the explanation for the un-observability of the extra dimension. Hence the topology of the five dimensional space time is M 4 × S 1 , where M 4 is the standard four-dimensional Minkowski spacetime and S 1 is a circle with very small radius. The simplest way to imagine space with one extra dimension is to imagine a small circle at every point of 3-dimensional space.Inflation is an important idea in cosmology. There are two scenarios proposed in Kaluza-Klein cosmology. The first scenario [3] is: the scale of standard 3-dimensional space expands when the scale of internal space changes slowly with time. The second scenario ([4], [5]) is: inflation occurs near the singularity a(t) → ∞, b(t) → 0 (t → t 0 ).Expansion of our universe is in an accelerating way which is suggested by type Ia supernova observational data ([6], [7]). Myrzakulov [8] constructed several concrete models describing the trefoil and figure-eight knot universes from Bianchi-type I cosmology and examined the cosmological features and properties in detail. Yesmakhanova et al [9] constructed a cosmological model by assuming the periodic forms for pressure and en...

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Some Models of Cyclic and Knot Universes

Cited by 4 publications

References 27 publications

$$F(T)$$ gravity and k-essence

$$F(T)$$ gravity and k-essence

Periodic Cosmological Evolutions of Equation of State for Dark Energy

Kaluza–Klein Bulk Viscous Fluid Cosmological Models and the Validity of the Second Law of Thermodynamics in f(R, T) Gravity

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