Research Article
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An Investigation into LRS Bianchi I Universe in Brans-Dicke Theory

Year 2023, Issue: 44, 87 - 96, 30.09.2023

Halife Çağlar

https://doi.org/10.53570/jnt.1352470

Abstract

In this study, the homogenous and anisotropic locally rotationally symmetric (LRS) Bianchi type-I universe filled with the bulk viscous and the string cloud matter has been investigated in the Brans-Dicke (BD) scalar-tensor theory. The modified Einstein field equations of the constructed model have been solved by using the relation of the scale factors $A=B^m$ and considering the deceleration parameter to be $q=m-1$. It is found that the string does not survive for the model due to the obtained zero string energy density ($\rho_s=0$) and agrees with some studies in recent years. Moreover, it is possible to say that string matter may be turned into phantom energy over time, depending on the obtained negative rest energy density of the matter. When BD scalar field $\Phi$ is assumed constant, the attained solutions are reduced to General Relativity (GR) solutions for the static vacuum. Thus, the constructed model has not allowed the reduction of the BD solutions to GR solutions, including the matter distributions. In addition, some expansion models for choosing a value of constant $m$ have been obtained and provided. All the results have been analyzed in detail.

Keywords

LRS Bianchi I universe Brans-Dicke theory bulk viscous string cloud deceleration parameter

References

  • A. Einstein, The Foundation of the General Theory of Relativity, Annalen der Physik 49 (7) (1916) 769--822.
  • A. Friedman, Über die Krümmung des Raumes, Zeitschrift für Physik 10 (1922) 377--386.
  • G. Lemaitre, Un Univers Homogène de Masse Constante et de Rayon Croissant Rendant Compte de la Vitesse Radiale des Nébuleuses Extra-galactiques, Annales de la Société Scientifique de Bruxelles A47 (1927) 49--59.
  • E. Hubble, A Relation Between Distance and Radial Velocity Among Extra-Galaktik Nebulae, Proceedings of the National Academy of Sciences of the USA 15 (3) (1929) 168--173.
  • S. Perlmutter, G. Aldering, G. Goldhaber, R. Knop, P. Nugent, P. G. Castro, S. Deustua, S. Fabbro, A. Goobar, D. E. Groom, I. M. Hook, A. G. Kim, M. Y. Kim, J. C. Lee, N. J. Nunes, R. Pain, C. R. Pennypacker, R. Quimby, C. Lidman, R. S. Ellis, M. Irwin, R. G. McMahon, P. Ruiz-Lapuente, N. Walton, B. Schaefer, B. J. Boyle, A. V. Filippenko, T. Matheson, A. S. Fruchter, N. Panagia, H. J. M. Newberg, W. J. Couch, The Supernova Cosmology Project, Measurements of $\Omega$ and $\Lambda$ from $42$ High-Redshift Supernovae, The Astrophysical Journal 517 (2) (1999) 565--586.
  • D. N. Spergel, L. Verde, H. V. Peiris, E. Komatsu, M. Nolta, C. L. Bennett, M. Halpern, G. Hinshaw, N. Jarosik, A. Kogut, M. Limon, S. S. Meyer, L. Page, G. S. Tucker, J. L. Weiland, E. Wollack, E. L. Wright, First-Year Wilkinson Microwave Anisotropy Probe (WMAP)* Observations: Determination of Cosmological Parameters, The Astrophysical Journal Supplement Series 148 (1) (2003) 175--194.
  • R. A. Knop, G. Aldering, R. Amanullah, P. Astier, G. Blanc, M. S. Burns, A. Conley, S. E. Deustua, M. Doi, R. Ellis, S. Fabbro, G. Folatelli, A. S. Fruchter, G. Garavini, S. Garmond, K. Garton, R. Gibbons, G. Goldhaber, A. Goobar, D. E. Groom, D. Hardin, I. Hook, D. A. Howell, A. G. Kim, B. C. Lee, C. Lidman, J. Mendez, S. Nobili, P. E. Nugent, R. Pain, N. Panagia, C. R. Pennypacker, S. Perlmutter, R. Quimby, J. Raux, N. Regnault, P. Ruiz-Lapuente, G. Sainton, B. Schaefer, K. Schahmaneche, E. Smith, A. L. Spadafora, V. Stanishev, M. Sullivan, N. A. Walton, L. Wang, W. M. Wood-Vasey, N. Yasuda, The Supernova Cosmology Project, New Constraints on $\Omega_M$, $\Omega_\Lambda$, and $w$ from an Independent Set of 11 High-Redshift Supernovae Observed with the Hubble Space Telescope, Astrophysical Journal 598 (2003) 102--137.
  • G. Lyra, Uber eine Modifikation der Riemannschen Geometrie, Mathematische Zeitschrift 54 (1) (1951) 52--64.
  • G. A. Barber, On Two ``Self-Creation'' Cosmologies, General Relativity and Gravitation 14 (1982) 117--136.
  • F. Hoyle, J. V. Narlikar, A Radical Departure from the `Steady-State' Concept in Cosmology, Proceedings of the Royal Society of London Series A, Mathematical and Physical Sciences 290 (1421) (1966) 162--176.
  • H. Y{\i}lmaz, New Approach to General Relativity, Physical Review 111 (1958) 1417--1426.
  • C. Brans, R. H. Dicke, Mach’s Principle and a Relativistic Theory of Gravitation, Physical Review 124 (1961) 925--935.
  • Ya. B. Zel’dovich, Cosmological Fluctuations Produced Near a Singularity, Monthly Notices of the Royal Astronomical Society 192 (4) (1980) 663--667.
  • T. W. B. Kibble, Topology of Cosmic Domains and Strings, Journal of Physics A: Mathematical and General 9 (8) (1976) 1387--1398.
  • {\"{O}. Delice}, Local Cosmic Strings in Brans-Dicke Theory with a Cosmological Constant, Physical Review D 74 (6) (2006) 067703 1--4.
  • D. R. K. Reddy, S. M. V. Rao, Axially Symmetric String Cosmological Model in Brans-Dicke Theory of Gravitation, Astrophysics and Space Science 305 (2) (2006) 183--186
  • V. U. M. Rao, D. Neelima, Axially Symmetric Bulk Viscous String Cosmological Models in GR and Brans-Dicke Theory of Gravitation, ISRN Astronomy and Astrophysics 2013 (2013) Article ID 543483 6 pages.
  • T. S. Vidya, C. P. Rao, R. B. Vijaya, D. R. K. Reddy, Bianchi Type-III Bulk Viscous String Cosmological Model in Brans-Dicke Theory of Gravitation, Astrophysics and Space Science 349 (1) (2014) 479--483.
  • N. K. Sharma, J. K. Singh, Some Exact Solutions of Bianchi Type-II String Cosmological Models with Magnetic Field in Brans-Dicke Theory of Gravitation, International Journal of Theoretical Physics 54 (5) (2015) 1633--1643.
  • D. Trivedi, A. K. Bhabor, Higher Dimensional Bianchi Type-III String Cosmological Models with Dark Energy in Brans-Dicke Scalar-Tensor Theory of Gravitation, New Astronomy 89 (2021) Article ID 101658 9 pages.
  • K. L. Mahanta, A. K. Biswal, P. K. Sahoo, Bulk Viscous String Cloud with Strange Quark Matter in Brans-Dicke Theory, European Physical Journal-Plus 129 (2014) 141--146.
  • N. C. Chakraborty, S. Chakraborty, A. Dolgov, Brans-Dicke Theory in Bianchi III Model and Inflationary Scenario, International Journal of Modern Physics D 11 (3) (2002) 391--404.
  • K. S. Adhav, M. R. Ugale, C. B. Kale, M. P. Bhende, Plane Symmetric Vacuum Bianchi Type-III Cosmological Model in Brans-Dicke Theory, International Journal of Theoretical Physics 48 (1) (2009) 178--182
  • H. \c{C}ağlar, S.Ayg\"un, C. Akta\c{s}, D. Ta\c{s}er, LRS Binachi I Model with Strange Quark Matter Attached to String Cloud in Brans-Dicke Theory, International Physics Conference of the Balkan Physical Union 22 (2014) 221014 129--137.
  • H. \c{C}a\u{g}lar, S.Ayg{\"u}n, Exact Solutions of Bulk Viscous with String Cloud Attached to Strange Quark Matter for Higher Dimensional FRW Universe in Lyra Geometry, AIP Conference Proceedings 1722 (2016) 050001 1--5.
  • H. \c{C}a\u{g}lar, S. Ayg{\"u}n, Bulk Viscous String Cloud with Strange Quark Matter in Self Creation Cosmology, IOSR Journal of Mathematics 11 (6) (2015) 53--59.
  • H. \c{C}a\u{g}lar, S. Ayg\"un, Non-existence of Brans-Dicke Theory in Higher Dimensional FRW Universe, Astrophysics and Space Science 361 (2016) 1--6.
  • S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, John Wiley \& Sons, New York, 1972.
  • V. U. M. Rao, D. Neelima, Cosmological Models with Strange Quark Matter Attached to String Cloud in GR and Brans-Dicke Theory of Gravitation, The European Physical Journal-Plus 129 (2014) 122--136.
  • A. Dixit, R. Zia, A. Pradhan, Anisotropic Bulk Viscous String Cosmological Models of the Universe under a Time-Dependent Deceleration Parameter, Pramana 94 (1) (2020) Article Number 25 11 pages.
  • G. Mohanty, S. K. Sahu, P. K. Saho, Massive Scalar Field in the Bianchi Type I Space Time, Astrophysics and Space Science 288 (2003) 421–427.
  • K. S. Adhav, LRS Bianchi Type-I Cosmological Model in $f(R,T)$ Theory of Gravity, Astrophysics and Space Science 339 (2012) 365–369.
  • O. \"{O}zdemir, C. Akta\c{s}, Anisotropic Universe Models with Magnetized Strange Quark Matter in $f(R)$ Gravity Theory, Modern Phys. Lett. A 35 (14) (2020) 2050111 9 pages.
  • D. Ta\c{s}er, M. U. Do\u{g}ru, Scalar Fields in $f(G)$ Gravity, International Journal of Geometric Methods in Modern Physics 17 (09) (2020) 2050132 17 pages.
  • R. Bali, Magnetized Cosmological Model, International Journal of Theoretical Physics A 25 (1986) 755--761.
  • K. S. Adhav, LRS Bianchi Type-I Cosmological Model with Linearly Varying Deceleration Parameter, The European Physical Journal-Plus 126 (2011) 122--128.
  • P. K. Sahoo, B. Mishra, String Cloud and Domain Walls with Quark Matter for Plane Symmetric Cosmological Model in Bimetric Theory, Journal of Theoretical and Applied Physics 7 (2013) 12--16.
  • M. Kiran, D. R. K. Reddy, Non-existence of Bianchi Type-III Bulk Viscous String Cosmological Model in $f(R,T)$ Gravity, Astrophysics and Space Science 346 (2013) 521--524.
  • S. M. Carroll, M. Hoffman, Can the Dark Energy Equation-of-State Parameter $w$ be Less than A1?, Physical Review D 68 (2003) 023509 1--11.

Year 2023, Issue: 44, 87 - 96, 30.09.2023

Halife Çağlar

https://doi.org/10.53570/jnt.1352470

Abstract

References

  • A. Einstein, The Foundation of the General Theory of Relativity, Annalen der Physik 49 (7) (1916) 769--822.
  • A. Friedman, Über die Krümmung des Raumes, Zeitschrift für Physik 10 (1922) 377--386.
  • G. Lemaitre, Un Univers Homogène de Masse Constante et de Rayon Croissant Rendant Compte de la Vitesse Radiale des Nébuleuses Extra-galactiques, Annales de la Société Scientifique de Bruxelles A47 (1927) 49--59.
  • E. Hubble, A Relation Between Distance and Radial Velocity Among Extra-Galaktik Nebulae, Proceedings of the National Academy of Sciences of the USA 15 (3) (1929) 168--173.
  • S. Perlmutter, G. Aldering, G. Goldhaber, R. Knop, P. Nugent, P. G. Castro, S. Deustua, S. Fabbro, A. Goobar, D. E. Groom, I. M. Hook, A. G. Kim, M. Y. Kim, J. C. Lee, N. J. Nunes, R. Pain, C. R. Pennypacker, R. Quimby, C. Lidman, R. S. Ellis, M. Irwin, R. G. McMahon, P. Ruiz-Lapuente, N. Walton, B. Schaefer, B. J. Boyle, A. V. Filippenko, T. Matheson, A. S. Fruchter, N. Panagia, H. J. M. Newberg, W. J. Couch, The Supernova Cosmology Project, Measurements of $\Omega$ and $\Lambda$ from $42$ High-Redshift Supernovae, The Astrophysical Journal 517 (2) (1999) 565--586.
  • D. N. Spergel, L. Verde, H. V. Peiris, E. Komatsu, M. Nolta, C. L. Bennett, M. Halpern, G. Hinshaw, N. Jarosik, A. Kogut, M. Limon, S. S. Meyer, L. Page, G. S. Tucker, J. L. Weiland, E. Wollack, E. L. Wright, First-Year Wilkinson Microwave Anisotropy Probe (WMAP)* Observations: Determination of Cosmological Parameters, The Astrophysical Journal Supplement Series 148 (1) (2003) 175--194.
  • R. A. Knop, G. Aldering, R. Amanullah, P. Astier, G. Blanc, M. S. Burns, A. Conley, S. E. Deustua, M. Doi, R. Ellis, S. Fabbro, G. Folatelli, A. S. Fruchter, G. Garavini, S. Garmond, K. Garton, R. Gibbons, G. Goldhaber, A. Goobar, D. E. Groom, D. Hardin, I. Hook, D. A. Howell, A. G. Kim, B. C. Lee, C. Lidman, J. Mendez, S. Nobili, P. E. Nugent, R. Pain, N. Panagia, C. R. Pennypacker, S. Perlmutter, R. Quimby, J. Raux, N. Regnault, P. Ruiz-Lapuente, G. Sainton, B. Schaefer, K. Schahmaneche, E. Smith, A. L. Spadafora, V. Stanishev, M. Sullivan, N. A. Walton, L. Wang, W. M. Wood-Vasey, N. Yasuda, The Supernova Cosmology Project, New Constraints on $\Omega_M$, $\Omega_\Lambda$, and $w$ from an Independent Set of 11 High-Redshift Supernovae Observed with the Hubble Space Telescope, Astrophysical Journal 598 (2003) 102--137.
  • G. Lyra, Uber eine Modifikation der Riemannschen Geometrie, Mathematische Zeitschrift 54 (1) (1951) 52--64.
  • G. A. Barber, On Two ``Self-Creation'' Cosmologies, General Relativity and Gravitation 14 (1982) 117--136.
  • F. Hoyle, J. V. Narlikar, A Radical Departure from the `Steady-State' Concept in Cosmology, Proceedings of the Royal Society of London Series A, Mathematical and Physical Sciences 290 (1421) (1966) 162--176.
  • H. Y{\i}lmaz, New Approach to General Relativity, Physical Review 111 (1958) 1417--1426.
  • C. Brans, R. H. Dicke, Mach’s Principle and a Relativistic Theory of Gravitation, Physical Review 124 (1961) 925--935.
  • Ya. B. Zel’dovich, Cosmological Fluctuations Produced Near a Singularity, Monthly Notices of the Royal Astronomical Society 192 (4) (1980) 663--667.
  • T. W. B. Kibble, Topology of Cosmic Domains and Strings, Journal of Physics A: Mathematical and General 9 (8) (1976) 1387--1398.
  • {\"{O}. Delice}, Local Cosmic Strings in Brans-Dicke Theory with a Cosmological Constant, Physical Review D 74 (6) (2006) 067703 1--4.
  • D. R. K. Reddy, S. M. V. Rao, Axially Symmetric String Cosmological Model in Brans-Dicke Theory of Gravitation, Astrophysics and Space Science 305 (2) (2006) 183--186
  • V. U. M. Rao, D. Neelima, Axially Symmetric Bulk Viscous String Cosmological Models in GR and Brans-Dicke Theory of Gravitation, ISRN Astronomy and Astrophysics 2013 (2013) Article ID 543483 6 pages.
  • T. S. Vidya, C. P. Rao, R. B. Vijaya, D. R. K. Reddy, Bianchi Type-III Bulk Viscous String Cosmological Model in Brans-Dicke Theory of Gravitation, Astrophysics and Space Science 349 (1) (2014) 479--483.
  • N. K. Sharma, J. K. Singh, Some Exact Solutions of Bianchi Type-II String Cosmological Models with Magnetic Field in Brans-Dicke Theory of Gravitation, International Journal of Theoretical Physics 54 (5) (2015) 1633--1643.
  • D. Trivedi, A. K. Bhabor, Higher Dimensional Bianchi Type-III String Cosmological Models with Dark Energy in Brans-Dicke Scalar-Tensor Theory of Gravitation, New Astronomy 89 (2021) Article ID 101658 9 pages.
  • K. L. Mahanta, A. K. Biswal, P. K. Sahoo, Bulk Viscous String Cloud with Strange Quark Matter in Brans-Dicke Theory, European Physical Journal-Plus 129 (2014) 141--146.
  • N. C. Chakraborty, S. Chakraborty, A. Dolgov, Brans-Dicke Theory in Bianchi III Model and Inflationary Scenario, International Journal of Modern Physics D 11 (3) (2002) 391--404.
  • K. S. Adhav, M. R. Ugale, C. B. Kale, M. P. Bhende, Plane Symmetric Vacuum Bianchi Type-III Cosmological Model in Brans-Dicke Theory, International Journal of Theoretical Physics 48 (1) (2009) 178--182
  • H. \c{C}ağlar, S.Ayg\"un, C. Akta\c{s}, D. Ta\c{s}er, LRS Binachi I Model with Strange Quark Matter Attached to String Cloud in Brans-Dicke Theory, International Physics Conference of the Balkan Physical Union 22 (2014) 221014 129--137.
  • H. \c{C}a\u{g}lar, S.Ayg{\"u}n, Exact Solutions of Bulk Viscous with String Cloud Attached to Strange Quark Matter for Higher Dimensional FRW Universe in Lyra Geometry, AIP Conference Proceedings 1722 (2016) 050001 1--5.
  • H. \c{C}a\u{g}lar, S. Ayg{\"u}n, Bulk Viscous String Cloud with Strange Quark Matter in Self Creation Cosmology, IOSR Journal of Mathematics 11 (6) (2015) 53--59.
  • H. \c{C}a\u{g}lar, S. Ayg\"un, Non-existence of Brans-Dicke Theory in Higher Dimensional FRW Universe, Astrophysics and Space Science 361 (2016) 1--6.
  • S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, John Wiley \& Sons, New York, 1972.
  • V. U. M. Rao, D. Neelima, Cosmological Models with Strange Quark Matter Attached to String Cloud in GR and Brans-Dicke Theory of Gravitation, The European Physical Journal-Plus 129 (2014) 122--136.
  • A. Dixit, R. Zia, A. Pradhan, Anisotropic Bulk Viscous String Cosmological Models of the Universe under a Time-Dependent Deceleration Parameter, Pramana 94 (1) (2020) Article Number 25 11 pages.
  • G. Mohanty, S. K. Sahu, P. K. Saho, Massive Scalar Field in the Bianchi Type I Space Time, Astrophysics and Space Science 288 (2003) 421–427.
  • K. S. Adhav, LRS Bianchi Type-I Cosmological Model in $f(R,T)$ Theory of Gravity, Astrophysics and Space Science 339 (2012) 365–369.
  • O. \"{O}zdemir, C. Akta\c{s}, Anisotropic Universe Models with Magnetized Strange Quark Matter in $f(R)$ Gravity Theory, Modern Phys. Lett. A 35 (14) (2020) 2050111 9 pages.
  • D. Ta\c{s}er, M. U. Do\u{g}ru, Scalar Fields in $f(G)$ Gravity, International Journal of Geometric Methods in Modern Physics 17 (09) (2020) 2050132 17 pages.
  • R. Bali, Magnetized Cosmological Model, International Journal of Theoretical Physics A 25 (1986) 755--761.
  • K. S. Adhav, LRS Bianchi Type-I Cosmological Model with Linearly Varying Deceleration Parameter, The European Physical Journal-Plus 126 (2011) 122--128.
  • P. K. Sahoo, B. Mishra, String Cloud and Domain Walls with Quark Matter for Plane Symmetric Cosmological Model in Bimetric Theory, Journal of Theoretical and Applied Physics 7 (2013) 12--16.
  • M. Kiran, D. R. K. Reddy, Non-existence of Bianchi Type-III Bulk Viscous String Cosmological Model in $f(R,T)$ Gravity, Astrophysics and Space Science 346 (2013) 521--524.
  • S. M. Carroll, M. Hoffman, Can the Dark Energy Equation-of-State Parameter $w$ be Less than A1?, Physical Review D 68 (2003) 023509 1--11.
There are 39 citations in total.

Details

Primary Language English
Subjects Topology, Pure Mathematics (Other)
Journal Section Research Article
Authors

Halife Çağlar 0000-0003-2877-1221

Publication Date September 30, 2023
Submission Date August 30, 2023
Published in Issue Year 2023 Issue: 44

Cite

APA Çağlar, H. (2023). An Investigation into LRS Bianchi I Universe in Brans-Dicke Theory. Journal of New Theory(44), 87-96. https://doi.org/10.53570/jnt.1352470
AMA Çağlar H. An Investigation into LRS Bianchi I Universe in Brans-Dicke Theory. JNT. September 2023;(44):87-96. doi:10.53570/jnt.1352470
Chicago Çağlar, Halife. “An Investigation into LRS Bianchi I Universe in Brans-Dicke Theory”. Journal of New Theory, no. 44 (September 2023): 87-96. https://doi.org/10.53570/jnt.1352470.
EndNote Çağlar H (September 1, 2023) An Investigation into LRS Bianchi I Universe in Brans-Dicke Theory. Journal of New Theory 44 87–96.
IEEE H. Çağlar, “An Investigation into LRS Bianchi I Universe in Brans-Dicke Theory”, JNT, no. 44, pp. 87–96, September 2023, doi: 10.53570/jnt.1352470.
ISNAD Çağlar, Halife. “An Investigation into LRS Bianchi I Universe in Brans-Dicke Theory”. Journal of New Theory 44 (September 2023), 87-96. https://doi.org/10.53570/jnt.1352470.
JAMA Çağlar H. An Investigation into LRS Bianchi I Universe in Brans-Dicke Theory. JNT. 2023;:87–96.
MLA Çağlar, Halife. “An Investigation into LRS Bianchi I Universe in Brans-Dicke Theory”. Journal of New Theory, no. 44, 2023, pp. 87-96, doi:10.53570/jnt.1352470.
Vancouver Çağlar H. An Investigation into LRS Bianchi I Universe in Brans-Dicke Theory. JNT. 2023(44):87-96.
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