General Relativity Package for Friedman Eqns: MATLAB, Mathematica

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Discussion Overview

The discussion revolves around the simulation of the Friedmann equations in the context of cosmology, specifically focusing on their numerical integration using MATLAB or Mathematica. Participants explore the nature of the equations and the implications of varying parameters within the models.

Discussion Character

  • Exploratory, Technical explanation, Homework-related

Main Points Raised

  • One participant seeks recommendations for packages in MATLAB or Mathematica to simulate the Friedmann equations under different conditions of flat space.
  • Another participant questions the necessity of a package, suggesting that the Friedmann equations are simple and can be numerically integrated without specialized tools.
  • A participant expresses curiosity about the nature of the Friedmann equations, asking if they are simple ordinary differential equations and whether MATLAB can handle coupled ODEs.
  • A later reply indicates that if only one type of energy component is considered, the Friedmann equations can potentially be solved analytically.

Areas of Agreement / Disagreement

There is no consensus on the necessity of a package for simulating the Friedmann equations, with differing views on their complexity and the methods of integration. Some participants believe they can be handled simply, while others seek more structured approaches.

Contextual Notes

Participants express varying assumptions about the energy components involved and the specific goals of their simulations, which may affect the applicability of different methods.

David DCruz
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I need to simulate the Friedman equations under different conditions of flat space. Can someone please tell me a good package in MATLAB, Mathematica or stand alone. I am most well versed in MATLAB but have coded in Mathematica before.
 
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Why do you need a package? The Friedmann equations are rather simple and easily numerically integrated for various energy contents of the Universe.
 
I am just about to study the Friedman equations. Are they just simple ordinary differential equations? Can inbuilt functions in MATLAB handle coupled ODE's? I primarily want to vary the 'w' parameter to see how the scale factor changes as the universe evolves.
 
David DCruz said:
I am just about to study the Friedman equations. Are they just simple ordinary differential equations?
Yes and yes.

Can inbuilt functions in MATLAB handle coupled ODE's? I primarily want to vary the 'w' parameter to see how the scale factor changes as the universe evolves.

This to me is somewhat suggests that you are going to consider one type of energy component only. If that is all you want to do the Friedmann equations can be solved analytically.
 

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