Calculating the scale factor (cosmology) for a universe starting at the Big Bang

In summary, the Friedmann-equation can be used to determine the scale factor for a Universe in its early stages, starting with the Big Bang. This is done by isolating the scale factor and finding values for the two unknown components, r(t) and r0, using the equation for the scale factor and the Friedmann equation.
  • #1
Hangst
12
0

Homework Statement



Show that by using the Friedmann-equation you can determine the scale factor for a Universe in it's early stages (starting with the Big Bang) to:

2pt1084.png


Homework Equations



The equation for the scale factor:

2le2l2c.png


Where r(t) is the distance from us to a given galaxy to the time t and r0 is the galaxies current distance from us.And the Friedmann equation:

zyfqf9.png


The Attempt at a Solution



I'm dumbfounded and I have no idea of what to do. This is for a major paper and any help is much appreciated. If you don't understand the problem, please do say so and I'll try and clear it up. Thanks a lot!
 
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  • #2
Here is my thinking so far: isolate the scale factor so that you have:

15qrud3.png


and then find values for the two unknowns somehow.
 
  • #3
Hangst said:
Here is my thinking so far: isolate the scale factor so that you have:

15qrud3.png


and then find values for the two unknowns somehow.

Doesn't matter anymore, figured it out. You can lock this now.
 

Related to Calculating the scale factor (cosmology) for a universe starting at the Big Bang

1. What is the scale factor in cosmology?

The scale factor is a dimensionless quantity that describes the relative expansion or contraction of the universe over time. It is used in cosmology to measure the change in size of the universe since the Big Bang.

2. How is the scale factor calculated?

The scale factor is calculated using the Friedmann equations, which are mathematical equations that describe the evolution of the universe. These equations take into account the energy and matter content of the universe and the curvature of space.

3. What is the relationship between the scale factor and the age of the universe?

The scale factor is directly related to the age of the universe. As the scale factor increases, the age of the universe also increases. This means that the universe has been expanding since the Big Bang and continues to do so at an increasing rate.

4. How does the scale factor change over time?

The scale factor changes over time based on the energy and matter content of the universe. In the early universe, the scale factor was very small and the universe was rapidly expanding. As the universe aged and matter and energy interacted, the scale factor began to increase at a slower rate.

5. What is the significance of the scale factor in understanding the history of the universe?

The scale factor is a crucial factor in understanding the history of the universe. It allows scientists to track the evolution of the universe since the Big Bang and make predictions about its future. It also provides insights into the expansion rate of the universe and the influence of different forms of energy and matter on its evolution.

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