# A note on the cosmological constant in f(R) gravity

## TL;DR

This paper examines the constraints on f(R) modified gravity models in cosmology, concluding that either Einstein's cosmological constant is necessary or dark energy's equation of state is more complex than a simple perfect fluid.

## Contribution

It highlights the limitations of f(R) gravity in explaining late-time acceleration without reverting to Einstein's cosmological constant or complex dark energy models.

## Key findings

- Einstein's cosmological constant remains the simplest explanation.
- f(R) models must closely mimic Einstein gravity to fit observations.
- Dark energy may not be well-described by a constant equation of state.

## Abstract

The starting point in this note is $f(R)$ modified gravity in a cosmological setting. We assume a spatially flat Universe to describe late-time cosmology and the perfect-fluid equation of state $p=\omega\rho$ to model the hypothesized dark energy. Given that on a cosmological scale, $f(R)$ modified gravity must remain close to Einstein gravity to be consistent with observation, it was concluded that either (1) Einstein's cosmological constant is the only acceptable model for the accelerated expansion or (2) that the equation of state for dark energy is far more complicated than the perfect-fluid model and may even exclude a constant $\omega$.