f(R) Gravity: From the Pioneer Anomaly to the Cosmic Acceleration

TL;DR

This paper explores a modified gravity model using $f(R)$ theory to explain phenomena from the Pioneer anomaly to cosmic acceleration, proposing a specific functional form that fits multiple astrophysical observations.

Contribution

It introduces a new $f(R)$ functional form that accounts for solar system anomalies, galaxy rotation curves, and late-time cosmic acceleration within a unified framework.

Findings

The proposed $f(R)$ model explains the Pioneer anomaly.

It reproduces flat galaxy rotation curves.

It predicts positive late-time cosmic acceleration.

Abstract

We use metric formalism in $f(R)$ modified gravity to study the dynamics of various systems from the solar system to the cosmological scale. we assume an ansatz for the derivative of action as a function of distance and describe the Pioneer anomaly and the flat rotation curve of the spiral galaxies. Having the asymptotic behavior of action, we propose the action of $f(R) = (R + \Lambda)(1 + \ln(R/R_c)/(R/R_0 + 2/\alpha))$ where in galactic and solar system scales it can recover our desired form. The vacuum solution of this action also results in a positive late time acceleration for the universe. We fix the parameters of this model, comparing with the Pioneer anomaly, rotation curve of spiral galaxies and Supernova Type Ia gold sample data.