In this paper, the theory of gravity of a (2+1)-sized bodyallel is considered and the effect of a minimally bound fermionic field on a theory with additional mass is investigated. The Friedman equations and the equations of motion of a fermionic field are generalized and their interrelation is determined.. The Noether gauge symmetry method was used to find cosmological solutions. In addition, the influence of the obtained solutions and theoretical results on the alternative interpretation of gravity was discussed. The role of torsion in teleparallel gravity with mass, its effect on the dynamics of space and interaction with fermionic fields is considered in detail. This approach allows us to present an extended model of gravity theories. 
The comparative advantages of teleparallel gravity with traditional theories of gravity are considered, its cosmological application and its possibilities are studied. In particular, using the solutions we obtained, the properties of the space-time under consideration and its relationship to the distribution of energy-momentum were determined. The influence of torsion fields in theory was studied and their gravitational influence and compatibility with the general theory of relativity were analyzed. This teleparallel study can become the basis for the development of advanced gravity options and consideration of alternative cosmological models. The results showed that there are solutions that characterize the progressive expansion of the universe.

NASSIPBEKOVA S.A.

master student, L.N. Gumilyov Eurasian Netional University, Astana, Kazakhstan

Е-mail: nassipbekovasaule@gmail.com, https://orcid.org/0009-0002-6862-8569

MYRZAKULOV N.А.

PhD, Acting Associate Professor, L.N. Gumilyov Eurasian Netional University, Astana, Kazakhstan

Е-mail: nmyrzakulov@gmail.com, https://orcid.org/0000-0001-8691-9939

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