# Numerically solving Scalar field coupled to Friedman equation

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• Soony143
In summary, the speaker is a research student of MS Physics who is struggling to numerically solve the Friedman equation coupled to a scalar field in a research paper by Sean Carroll, Mark Trodden, and Hoffman titled "Can the dark energy equation of state parameter w be less than-1?" They have received a reply from one of the authors who suggests rescaling parameters and solving equations 5 and 14 together, as well as providing a resource for approaching the problem.
Soony143
TL;DR Summary
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.

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.

Soony143
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.
""""

berkeman

## 1. What is a Scalar field coupled to Friedman equation?

A Scalar field coupled to Friedman equation is a mathematical model used in cosmology to describe the dynamics of the universe. It combines the Friedman equation, which describes the expansion of the universe, with a scalar field, which represents a hypothetical energy field that permeates all of space.

## 2. How is a Scalar field coupled to Friedman equation solved numerically?

To numerically solve a Scalar field coupled to Friedman equation, a computer program is used to solve a set of differential equations that describe the evolution of the scalar field and the expansion of the universe. This involves using numerical methods, such as the Runge-Kutta method, to approximate the solutions to these equations at different points in time.

## 3. What is the significance of solving a Scalar field coupled to Friedman equation?

Solving a Scalar field coupled to Friedman equation allows scientists to better understand the behavior of the universe and how it has evolved over time. It can also help to test different theories and models of the universe, and provide insights into the nature of dark energy and the ultimate fate of the universe.

## 4. What challenges are associated with numerically solving a Scalar field coupled to Friedman equation?

One of the main challenges in numerically solving a Scalar field coupled to Friedman equation is accurately modeling the complex interactions between the scalar field and the expansion of the universe. This requires sophisticated numerical methods and computational power, as well as careful consideration of the initial conditions and parameters used in the calculations.

## 5. How does the accuracy of the numerical solutions compare to observational data?

The accuracy of the numerical solutions for a Scalar field coupled to Friedman equation can vary depending on the specific model and assumptions used. However, in general, these solutions have been found to be consistent with observational data, such as measurements of the cosmic microwave background and the expansion rate of the universe. Ongoing research and improvements in numerical methods continue to improve the accuracy of these solutions.

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