Unified f (R) gravity at local scales

We explore the shifted f (R)(proportional to R1+delta) model with delta as a distinguishing physical parameter for the study of constraints at local scales. The corresponding dynamics confronted with different geodesics (null and non-null) along with their conformal analog are investigated. For null geodesics, we discuss the light deflection angle, whereas, for non-null geodesics under the weak field limit, we investigate the perihelion advance of the Mercury orbit in f(R) Schwarzschild background, respectively. The extent of an additional force, appearing for non-null geodesics, depends on delta. Such phenomenological investigations allow us to strictly constrain delta to be approximately O(10(-6)) with a difference of unity in orders at galactic and planetary scales and seem to provide a unique f (R) at local scales. Our results suggest that the present form of the model is suitable for the alternative explanation of dark matter-like effects at local scales.

Automated summary

We explore the shifted f (R) model with delta as a distinguishing physical parameter for the study of constraints at local scales. This model seems to provide a unique f (R) at local scales and is suitable for the alternative explanation of dark matter-like effects.