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Homework Statement
Expansion of the universe is described by the scale factor R(t), where t is the time after the Big Bang. For a flat universe the scale factor is today
R(t)=C_{1}\cdot t^{\frac{2}{3}}
When the Universe was radiation dominated, for t <200,000 years, the scale factor was
R(t)=C_{2}\cdot \sqrt{t}
Today, about 12 billion years after the Big Bang, we measure the distance to another superhop to 1 billion light years. How big would the distance between these sites one year after the Big Bang, if we assume that we live in a flat universe.
The attempt at a solution
I express the distance in meters
R(t)=9.461\cdot 10^{24}\, m
Then I express the time in seconds
t=3.787\cdot 10^{17}\, s
I found that the constant is
C_{1}=1.8075\cdot 10^{13}
I need to know the constant C_{2}, but I'm not sure how I'll be able to calculate it.
I have tested just to put C_{1}=C_{2}, but the result for the distance was wrong. I then realized that the two constants have different units.
Does anyone have a suggestion how I may proceed?
Expansion of the universe is described by the scale factor R(t), where t is the time after the Big Bang. For a flat universe the scale factor is today
R(t)=C_{1}\cdot t^{\frac{2}{3}}
When the Universe was radiation dominated, for t <200,000 years, the scale factor was
R(t)=C_{2}\cdot \sqrt{t}
Today, about 12 billion years after the Big Bang, we measure the distance to another superhop to 1 billion light years. How big would the distance between these sites one year after the Big Bang, if we assume that we live in a flat universe.
The attempt at a solution
I express the distance in meters
R(t)=9.461\cdot 10^{24}\, m
Then I express the time in seconds
t=3.787\cdot 10^{17}\, s
I found that the constant is
C_{1}=1.8075\cdot 10^{13}
I need to know the constant C_{2}, but I'm not sure how I'll be able to calculate it.
I have tested just to put C_{1}=C_{2}, but the result for the distance was wrong. I then realized that the two constants have different units.
Does anyone have a suggestion how I may proceed?