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

Understand

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.