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