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

## TL;DR

This paper investigates how the acceleration or deceleration of the universe varies across different frames in F(R) gravity and scalar field theories, revealing that acceleration properties are frame-dependent and lack a universal classification scheme.

## Contribution

It analyzes the frame dependence of cosmic acceleration in various F(R) and scalar field models, highlighting the non-equivalence of acceleration behavior across frames.

## Key findings

- Acceleration in one frame does not imply acceleration in another
- Frame and model dependence of acceleration behavior
- No universal classification scheme for acceleration across frames

## Abstract

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.