Deceleration versus Acceleration Universe in Different Frames of $F(R)$ Gravity

Understand

In this paper we study the occurrence of accelerating universe versus decelerating universe between the F(R) gravity frame (Jordan frame) and non-minimally coupled scalar field theory frame, and the minimally coupled scalar field theory frame (Einstein frame) for various models.

• As we show, if acceleration is imposed in one frame, it will not necessarily correspond to an accelerating metric when transformed in another frame.
• As we will demonstrate, this issue is model and frame-dependent but it seems there is no general scheme which permits to classify such cases.