Cosmological Application in Kaluza-Klein Theory: Generalized Sudden Singularity

doi:10.1080/1726037X.2019.1668147

Open Access Article

Cosmological Application in Kaluza-Klein Theory: Generalized Sudden Singularity

pp. 205–220Vol. 17Issue 2July 2019DOI: 10.1080/1726037X.2019.1668147XML

Received:: 15 Feb 2019
Accepted:: 25 Mar 2019
Published Online:: 18 Nov 2019
Article type:: Article
Language:: EN
Article no.:: 1726037X.2019.1668147
Pages:: 205–220

Abstract

In this paper, we considered the cosmological application by taking G and Λ to be a function of t in Kaluza-Klein cosmology. We use the Taylor’s expansion of cosmological function Λ(t), up to the first order of time t and evaluated the cosmological parameters by using the modified equation of state of the form p = −ρ − f (ρ), where f (ρ) = αρ. The analytical properties of R(t), ρ(t) and H(t) are investigated and it is observed that from the solutions of the field equations, the generalized sudden singularity occurs at a finite time in the framework of Kaluza-Klein theory of gravitation.

Keywords

Kaluza-Klein TheoryTaylor’s Expansion of cosmological functionGeneralized Sudden Singularity

Subject Classifications

54H20

References

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OverduinJ. M. and WessonP. S., Kaluza-Klein Gravity , , 303 - 378 ( 1997 ). doi: 10.1016/S0370-1573(96)00046-4
OverduinJ. M. and CooperstockF. I., Evolution of the Scale Factor with a Variable Cosmological Term , , 43506 ( 1998 ). doi: 10.1103/PhysRevD.58.043506
PadmanabhanT., Cosmological Constantthe Weight of the Vacuum , . , 235 - 320 ( 2003 ). doi: 10.1016/S0370-1573(03)00120-0
PeeblesP. J. E. and RatraB., The Cosmological Constant and Dark Energy , , 559 ( 2003 ). doi: 10.1103/RevModPhys.75.559
PollackM. D., On the connection between the cosmological constant and the gravitational constant in a theory of induced gravity , , 287 - 290 ( 1984 ). doi: 10.1016/0370-2693(84)90089-3
PolyakovA. M., Phase Transitions and the Universe , , 187 - 187 ( 1982 ). doi: 10.1070/PU1982v025n03ABEH004529
SahniV. and StarobinskyA., The Case for a Positive Cosmological Λ-term , . ( 4 ), 373 - 443 ( 2000 ). doi: 10.1142/S0218271800000542
SharifM. and FaridaK., Kaluza-Klein Cosmology with Varying G and Λ , . , 209 - 214 ( 2011 ). doi: 10.1007/s10509-011-0711-0
SteinhardtP. J. and TurokN., Why the Cosmological Constant is Small and Positive , , 1180 - 1183 ( 2006 ). doi: 10.1126/science.1126231
WanasM. T., NashedG. L. and NowayaA. A., Cosmological Applications in Kaluza-Klein Theory , , ( 2012 ). doi: 10.1088/1674-1056/21/4/049801

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[1] Al-RawafA. S., A Cosmological Model with a Generalized Cosmological Constant , , ( 1998 ) ( 1998 ). doi: 10.1142/S0217732398000498

[2] AppelquistT., ChodosA. and FreundP. G. O., Modern Kaluza-Klein Theories, (1987) .

[3] AzriH. and BoinamesA., Cosmological Consequences of a Variable Cosmological Constant Model , . , 1750060 ( 2017 ). doi: 10.1142/S0218271817500602

[4] BermanM. S., Cosmological Models with a Variable Cosmological Term , , 1075 ( 1991 ). doi: 10.1103/PhysRevD.43.1075

[5] BermanM. S., Cosmological Models with a Variable Gravitational and Cosmological constants , . , 465 - 469 (1991) . doi: 10.1007/BF00756609

[6] CanutoV., HsiehS. H., AdamsP. J., Mach’s principle, the cosmological constant, and the scale-covariant theory of gravity . Phys. Rev. Lett. D . ( 10 ), 3577 ( 1978 ).

[7] ChenW., and WuY. S., Implications of a Cosmological Constant Varying as R 2 , , 695 ( 1990 ). doi: 10.1103/PhysRevD.41.695

[8] DolgovA. D., Higher Spin Fields and the Problem of the Cosmological Constant , , 5881 ( 1997 ). doi: 10.1103/PhysRevD.55.5881

[9] HenkeC., Quantum Vacuum energy in General Relativity , . , 126 - 129 ( 2018 ). doi: 10.1140/epjc/s10052-018-5621-7

[10] KaluzaT., Zum unittsproblem der physik. Sitzungsberichte der Kniglich Preuischen Akademie der Wissenschaften (Berlin) , . , 966 - 972 ( 1921 ).

[11] KazanasD., Dynamics of the Universe and Spontaneous Symmetry Bbreaking , . , L59 - L63 ( 1980 ). doi: 10.1086/183361

[12] KleinO., Quantum Theory and Five-Dimensional Theory of Relativity, . . , 895 - 906 ( 1926 ). doi: 10.1007/BF01397481

[13] KleinO., The Atomicity of Electricity as a Quantum Theory Law , .) , 516 ( 1926 ). doi: 10.1038/118516a0

[14] LeeH. C., An Introduction to Kaluza-Klein Theories , . ( 1984 ).

[15] LimaJ. A. S. and MaiaJ. M. F., Some Cosmological Consequences of a Λ-term Varying as H2+ R-n , , 591 - 599 ( 1993 ). doi: 10.1142/S0217732393000611

[16] OverduinJ. M. and WessonP. S., Kaluza-Klein Gravity , , 303 - 378 ( 1997 ). doi: 10.1016/S0370-1573(96)00046-4

[17] OverduinJ. M. and CooperstockF. I., Evolution of the Scale Factor with a Variable Cosmological Term , , 43506 ( 1998 ). doi: 10.1103/PhysRevD.58.043506

[18] PadmanabhanT., Cosmological Constantthe Weight of the Vacuum , . , 235 - 320 ( 2003 ). doi: 10.1016/S0370-1573(03)00120-0

[19] PeeblesP. J. E. and RatraB., The Cosmological Constant and Dark Energy , , 559 ( 2003 ). doi: 10.1103/RevModPhys.75.559

[20] PollackM. D., On the connection between the cosmological constant and the gravitational constant in a theory of induced gravity , , 287 - 290 ( 1984 ). doi: 10.1016/0370-2693(84)90089-3

[21] PolyakovA. M., Phase Transitions and the Universe , , 187 - 187 ( 1982 ). doi: 10.1070/PU1982v025n03ABEH004529

[22] SahniV. and StarobinskyA., The Case for a Positive Cosmological Λ-term , . ( 4 ), 373 - 443 ( 2000 ). doi: 10.1142/S0218271800000542

[23] SharifM. and FaridaK., Kaluza-Klein Cosmology with Varying G and Λ , . , 209 - 214 ( 2011 ). doi: 10.1007/s10509-011-0711-0

[24] SteinhardtP. J. and TurokN., Why the Cosmological Constant is Small and Positive , , 1180 - 1183 ( 2006 ). doi: 10.1126/science.1126231

[25] WanasM. T., NashedG. L. and NowayaA. A., Cosmological Applications in Kaluza-Klein Theory , , ( 2012 ). doi: 10.1088/1674-1056/21/4/049801

Journal of Dynamical Systems and Geometric Theories

WoS JIF 2026 : 0.5 (Q3)

Cosmological Application in Kaluza-Klein Theory: Generalized Sudden Singularity

Abstract

Keywords

Subject Classifications

References