# An Inverse $f(R)$ Gravitation for Cosmic Speed up, and Dark Energy Equivalent

## TL;DR

This paper introduces an inverse $f(R)$ gravity approach to explain cosmic acceleration by reconstructing the gravity function from observationally motivated scale factors, comparing it with standard dark energy models.

## Contribution

It proposes a novel inverse $f(R)$ method to derive gravity functions from empirical scale factors, offering an alternative to dark energy explanations for cosmic acceleration.

## Key findings

- Reconstructed $f(R)$ functions consistent with observed cosmic acceleration.
- Identified dark energy parameters needed to match modified gravity models.
- Compared modified gravity and dark energy scenarios to explain cosmic speed up.

## Abstract

To explain the cosmic speed up, brought to light by the recent SNIa and CMB observations, we propose the following: a) In a spacetime endowed with a FRW metric, we choose an empirical scale factor that best explains the observations. b) We assume a modified gravity, generated by an unspecified field lagrangian, $f(R)$. c) We use the adopted empirical scale factor to work back retroactively to obtain $f(R)$, hence the term `Inverse $f(R)$'. d) Next we consider the classic GR and a conventional FRW universe that, in addition to its known baryonic content, possesses a hypothetical `Dark Energy' component. We compare the two scenarios, and find the density, the pressure, and the equation of the state of the Dark Energy required to make up for the differences between the conventional and the modified GR models.