Ricci Semi-Symmetric Robertson–Walker Spacetime in f ( R )-Gravity

H. Aruna Kumara, Abdul Haseeb (), V. Venkatesha and Mohd Bilal
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H. Aruna Kumara: Department of Mathematics, BMS Institute of Technology and Management, Yelahanka, Bangalore 5600664, Karnataka, India
Abdul Haseeb: Department of Mathematics, College of Science, Jazan University, Jazan 45142, Saudi Arabia
V. Venkatesha: Department of Mathematics, Kuvempu University, Shivamogga 577451, India
Mohd Bilal: Department of Mathematical Sciences, Faculty of Applied Sciences, Umm Al-Qura University, Makkah 21955, Saudi Arabia

Mathematics, 2025, vol. 13, issue 6, 1-13

Abstract: We investigated the properties of Ricci semi-symmetric Robertson–Walker spacetimes within the framework of f ( R ) -gravity theory. Initially, we established that Ricci semi-symmetric Robertson–Walker spacetimes are locally isometric to either Minkowski or de Sitter spacetimes. We then focused on the 4-dimensional formulation of these spacetimes in f ( R ) -gravity, deriving expressions for the isotropic pressure p and energy density σ . To further develop our understanding, we explored various energy conditions to constrain the functional form of f ( R ) . We analyzed several models, namely f ( R ) = R − α ( 1 − e − R α ) , f ( R ) = R − β tanh R , and f ( R ) = R − log ( m R ) , where α , β , and m are constants. Our findings suggest that the equations of state parameters for these models are compatible with the universe’s accelerating expansion, indicating an equation of state parameter ω = − 1 . Moreover, while these models satisfy the null, weak, and dominant energy conditions reflective of the observed accelerated expansion, our analysis reveals that they violate the strong energy condition.

Keywords: Ricci semi-symmetric spacetime; Robertson–Walker spacetime; f ( R )-gravity theory; energy conditions in modified gravity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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