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

AI Thread Summary
The discussion revolves around using the Friedmann equation to calculate the scale factor of the universe from the Big Bang. The user initially expresses confusion about how to isolate the scale factor and determine the unknown values needed for the calculation. After some contemplation, the user resolves their issue independently and indicates that further assistance is no longer required. The thread highlights the importance of the Friedmann equation in cosmological studies. The conversation concludes with the user requesting to lock the thread as they have found a solution.
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.
 

Thread 'Errors and significant figures'

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Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
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