Numerically solving Scalar field coupled to Friedman equation

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Discussion Overview

The discussion revolves around the numerical solution of the Friedman equation coupled to a scalar field, specifically in the context of a research paper by Sean Carroll, Mark Trodden, and Hoffman. The focus is on the challenges faced by a research student in implementing these equations for their thesis work.

Discussion Character

  • Homework-related
  • Technical explanation
  • Exploratory

Main Points Raised

  • A research student expresses urgency in needing help to numerically solve the Friedman equation coupled to a scalar field, referencing specific equations from a research paper.
  • One participant suggests starting by listing boundary conditions and symmetries to simplify the differential equations involved.
  • A reply from one of the authors of the referenced paper indicates that the problem is standard and has been solved by many, suggesting the use of Mathematica and the rescaling of parameters to avoid large values like the Planck mass.
  • The author notes that not all equations need to be solved, as some are redundant, and emphasizes the importance of solving equations 5 and 14 together.
  • The author also mentions that the Friedman equation is typically the more challenging part and provides a resource for approaching the solution.

Areas of Agreement / Disagreement

Participants generally agree on the standard nature of the problem and the approach to solving it, but there is no consensus on the specific methods or boundary conditions to be used.

Contextual Notes

The discussion does not clarify the specific boundary conditions or symmetries that may be relevant to the problem, and the complexity of the numerical solution remains unresolved.

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.
 
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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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