F_R_Gravity

This repository contains part of the implemented code for my master thesis titled Non-linear analysis of solar system tests in $f(R)$ gravity which can be found in http://132.248.9.195/ptd2023/febrero/0835817/Index.html

The main objective of the code is to solve numerically the $f(R)$ gravity field equations for a for a spherically symmetric and static (SSS) matter distribution.

$$ ds^2 =-n(r)dt^2+m(r)dr^2+ r^2 d\Omega^2 $$

F_R_Tools.py

This file contains the main classes used for solving the RHS of the $f(R)$ field equations.

The main class is

class ModelFR

which contains the general expressions for the RHS of the field equations and other important quantities.

class STBS

Corresponds to the Staronbinsky $f(R)$ model (Starobinsky, A. A. “Disappearing Cosmological Constant in f(R) Gravity”. JETP Letters, 86, (2007))

$$ f(R)^\text{STBS}= R + \lambda R_S\left[\left(1+\frac{R^2}{R_S^2}\right)^{-q}-1\right] $$

class MJW

Corresponds to the Miranda $f(R)$ model (Miranda, V. et al. “Viable Singularity-Free f(R) Gravity Without a Cosmological Constant”. Physical Review Letters, 102, (2009), 221101.)

$$ f(R)^{\text{MJWQ}} = R -\alpha_{\text{M}} R_*\ln{\left(1+ \frac{R}{R_*}\right)} $$

 class HUSAW

Corresponds to the Hu-Sawicki $f(R)$ model (Hu, W. and Sawicki, I. “Models of f(R) Cosmic Acceleration That Evade Solar-System Tests”. Physical Review D, 76, (2007), 064004.)

$$ f(R)^{\text{HS}} = R - \frac{c_{1} m^{2} \left(\frac{R}{m^{2}}\right)^{n}}{c_{2} \left(\frac{R}{m^{2}}\right)^{n} + 1} $$

Notebooks

• The notebook F_R_Plots shows how to use the $f(R)$ classes to obtain plots of the $f(R)$ functions and its derivatives.
• The notebook F_R_Solver shows how to implement the numerical solution for the Starobinsky $f(R)$ model

Additional Notes

The shooting method is not within these files. However, you can request the code by emailing me.