NONEXISTENCE SOLUTIONS OF BIANCHI TYPE IV UNIVERSE IN PRESENCE OF SCALAR FIELD


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Çağlar H., Taşer D., Aygün S.

BILTEK-VII INTERNATIONAL SYMPOSIUM ON CURRENT DEVELOPMENTS IN SCIENCE, TECHNOLOGY AND SOCIAL SCIENCES, Ankara, Turkey, 26 - 27 May 2023, pp.1017-1024

  • Publication Type: Conference Paper / Full Text
  • City: Ankara
  • Country: Turkey
  • Page Numbers: pp.1017-1024
  • Çanakkale Onsekiz Mart University Affiliated: Yes

Abstract

This study was carried out to examine the effect on the geometric structure of the universe and the distribution of matter, based on the foundations of Einstein's General Relativity (GR) theory. In the study, the Bianchi Type – IV spacetime line element, which mathematically models the homogeneous and anisotropic second phase of the universe, was used. The matter distribution of the constructed model is expressed with the mass scalar field energy momentum tensor. This matter distribution and the Bianchi IV space-time have been studied within the framework of the Lyra theory suggested as an alternative to Einstein's General Relativity theory. Lyra theory is one of the alternative gravitational theories to solve the cosmological constant problem in GR theory. In Lyra theory, there is the displacement vector , expressed by the vector field  and . It is suggested that the displacement vector can be used in the Lyra theory instead of Einstein's suggestion of the cosmological constant Λ in the GR theory. Many studies on Lyra theory have agree with that this suggestion. In Lyra theory, in the presence of massive scalar field matter for the Bianchi IV universe, six field equations were obtained. It was put out that one of the field equations reduced the solutions of model to nonexistence solutions. This equation comes from the cross terms of the line element of Bianchi IV spacetime. Thus, it was concluded that the scale factors of Bianchi spacetime could be ,  or . One or more of these values provide the corresponding field equation. However, even none of these results provide the expression of Bianchi type IV spacetime. In addition, these results reduce the field equations to physically and mathematically meaningless expressions. It has been determined that some universe models created with the Bianchi IV space-time metric have also reached nonexistence solutions. Related studies and constructed universe model solutions are discussed in detail in the conclusion and evaluation section.