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

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SUMMARY

The discussion focuses on calculating the scale factor for a universe beginning at the Big Bang using the Friedmann equation. The scale factor, denoted as r(t), represents the distance from Earth to a galaxy at a given time t, with r0 being the current distance. The user initially struggled with isolating the scale factor and determining the unknown values but later resolved the issue independently. This highlights the importance of understanding the Friedmann equation in cosmology.

PREREQUISITES
  • Understanding of the Friedmann equation in cosmology
  • Knowledge of scale factors in the context of the universe's expansion
  • Familiarity with basic astrophysical concepts related to distance measurements
  • Ability to manipulate algebraic equations for problem-solving
NEXT STEPS
  • Study the Friedmann equations in detail to understand their implications for cosmic evolution
  • Explore the concept of scale factors and their role in cosmological models
  • Learn about distance measures in cosmology, including luminosity and angular diameter distances
  • Investigate the implications of different cosmological parameters on the scale factor
USEFUL FOR

Astronomy students, cosmologists, and researchers interested in the early universe and the mathematical modeling of cosmic expansion.

Hangst
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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!
 
Last edited:
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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.
 
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.
 

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