General Friedmann equation - how to solve this differential equation?

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Homework Statement
Solve the differential equation
Relevant Equations
(adot / a)^2 = k / a^q
friedman.png


Hello fellow physicists, I am taking a course "Introduction to Cosmology" and I am asked to solve this equation called the Friedmann equation. I understand what it represents (scale factor of cosmic time) but I have no idea how to solve this differential equation, even though I took a whole course on solving those (Euler-Lagrange etc.)

Please give me a small pointer :)
 
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Take the square root (which sign is the right one?) and then separate variables.
 
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vanhees71 said:
Take the square root (which sign is the right one?) and then separate variables.
Thanks! That was way more obvious than I thought. Summer break always breaks me up.
 
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1. What is the General Friedmann equation?

The General Friedmann equation is a mathematical equation used in cosmology to describe the evolution of the universe. It is based on Einstein's theory of general relativity and takes into account the expansion of the universe, the energy density of matter and radiation, and the curvature of space.

2. How do you solve the General Friedmann equation?

The General Friedmann equation is a second-order differential equation that can be solved using various mathematical techniques such as separation of variables, substitution, or numerical methods. The specific method used will depend on the initial conditions and assumptions of the problem.

3. What are the main assumptions of the General Friedmann equation?

The General Friedmann equation assumes that the universe is homogeneous and isotropic, meaning that it is the same in all directions and at all points in time. It also assumes that the universe is filled with a perfect fluid, which means that it has a constant energy density and pressure.

4. How does the General Friedmann equation relate to the expansion of the universe?

The General Friedmann equation includes a term known as the Hubble parameter, which describes the rate at which the universe is expanding. As the universe expands, the Hubble parameter increases, leading to changes in the other variables in the equation and ultimately affecting the evolution of the universe.

5. What are the implications of solving the General Friedmann equation?

Solving the General Friedmann equation allows us to understand the evolution of the universe and make predictions about its future. It also helps us to test and refine our understanding of the laws of physics, including Einstein's theory of general relativity. Additionally, the solutions to the equation can provide insights into the nature of dark matter and dark energy, which are still poorly understood components of the universe.

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