How a projectively flat geometry regulates F(R)-gravity theory?. (6th December 2021)

• Record Type: Journal Article
• Authors: Loo, Tee-How; De, Avik; Mandal, Sanjay; Sahoo, P K
• Is Part Of: Physica scripta. Volume 96:Number 12(2021)
• Publication Date: 2021-12-06
• Subjects: f(R) gravity -- flat geometry -- energy conditions -- FRW metric; Physics -- Periodicals; 530.05
• DOI: 10.1088/1402-4896/ac3a51
• Languages: English
• ISSNs: 0031-8949

Abstract

Abstract: In the present paper we examine a projectively flat spacetime solution of F ( R )-gravity theory. It is seen that once we deploy projective flatness in the geometry of the spacetime, the matter field has constant energy density and isotropic pressure. We then make the condition weaker and discuss the effects of projectively harmonic spacetime geometry in F ( R )-gravity theory and show that the spacetime in this case reduces to a generalised Robertson-Walker spacetime with a shear, vorticity, acceleration free perfect fluid with a specific form of expansion scalar presented in terms of the scale factor. Role of conharmonic curvature tensor in the spacetime geometry is also briefly discussed. Some analysis of the obtained results are conducted in terms of couple of F ( R )-gravity models.