Graduate Numerically solving Scalar field coupled to Friedman equation

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SUMMARY

This discussion centers on numerically solving the Friedman equation coupled to a scalar field, specifically referencing the research paper by Sean Carroll, Mark Trodden, and Hoffman. The relevant equations for this task are equations 5 and 14 from the paper. A key recommendation is to rescale parameters to avoid using large dimensionful constants like the Planck mass and to solve the equations simultaneously, as the Friedman equation is first order. The discussion highlights the importance of identifying boundary conditions and symmetries to simplify the problem.

PREREQUISITES
  • Understanding of the Friedman equation and its implications in cosmology.
  • Familiarity with scalar fields in theoretical physics.
  • Proficiency in Mathematica for numerical solutions.
  • Knowledge of boundary conditions and symmetries in differential equations.
NEXT STEPS
  • Research how to rescale parameters in numerical simulations of the Friedman equation.
  • Learn about solving first-order differential equations in Mathematica.
  • Study examples of numerical solutions for scalar field equations in cosmology.
  • Explore techniques for identifying and applying symmetries to reduce equation complexity.
USEFUL FOR

This discussion is beneficial for graduate students in physics, researchers working on cosmological models, and anyone interested in numerical methods for solving differential equations in theoretical physics.

Soony143
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TL;DR
I am a research student of MS PHYSICS. I have to numerically solve Friedman equation coupled to scalar field(phi). It is given in research paper of Sean Carroll, Mark Trodden and Hoffman entitled as ""can the dark energy equation of state parameter w be less than-1?"" http://dx.doi.org/10.1103/PhysRevD.68.023509
The equations, that can be used are equation 5 and 14.
Plz someone help me, since it took me two extra semesters and I am on a verge of losing my degree, as per university policy.
I am a research student of MS PHYSICS. I have to numerically solve Friedman equation coupled to scalar field(phi). It is given in research paper of Sean Carroll, Mark Trodden and Hoffman entitled as ""can the dark energy equation of state parameter w be less than-1?"" http://dx.doi.org/10.1103/PhysRevD.68.023509
The equations, that can be used are equation 5 and 14.
Plz someone help me, since it took me two extra semesters and I am on a verge of losing my degree, as per university policy.
 
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I know 0 about this topic, however, I’d start by listing all boundary conditions and all symmetries the problem is expected to have. Every symmetry should allow you to reduce the complexity of the resulting differential equation. Hopefully this will greatly improve your chances for a numerical solution.
 
Will be a kind act.. thanks
 
Following is the reply i received from one of the author of the paper, when I requested him to help me
""""
Hi,
I won’t be able to spend a lot of time on this but your question is not really about our paper. You’re asking about solving the Friedman equation coupled to a scalar field. This is a standard system that many authors have solved numerically It can be done in Mathematica, but one should rescale parameters so that one need not use large dimensionaful parameters like the Planck mass. Furthermore, you need not solve equation all three equations since they are redundant. Solving 5 and 14 together is sufficient.

Typically, the more difficult part of this is the Friedman equation, which is first order. You can find an example of how to approach solving it here
https://web.physics.ucsb.edu/~gravitybook/mathematica.html

You would need to include the scalar equation and solve them simultaneously.
""""
 

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