Calculating the redshift at which radiation energy density equaled mass density

In summary: Keep it up.In summary, to calculate the redshift at which the universe shifted from radiation dominated to mass dominated, one must assume a flat universe with H0 = 70 and use the formula density rad = aT^4 to determine the energy densities of both the CMB and matter. The redshift for "matter-radiation equality" is approximately z = 3600, while the redshift for "recombination" (origin of CMB) is about z = 1100. However, there is a subtlety in including neutrinos as radiation, which could lead to a higher estimate for z.
  • #1
yijiao
1
0
how do you calculate the redshift at which the universe shifted from radiation dominated to mass dominated

i was told to assume a flat universe with H0 = 70

also the temperature, to which i was given the formula density rad = aT^4

for the first part, i tried using density is propotional to scale factor ^3 and ^4

but it's not working too hot :(

help please, i need it done by tonight :(
 
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  • #2
yijiao said:
how do you calculate the redshift at which the universe shifted from radiation dominated to mass dominated

i was told to assume a flat universe with H0 = 70

also the temperature, to which i was given the formula density rad = aT^4

for the first part, i tried using density is propotional to scale factor ^3 and ^4

but it's not working too hot :(

help please, i need it done by tonight :(

Gee you have to get it done by tonight. There are some other guys who are really good, but they are not around right now. I will try to help a little in case they don't show up before you have to finish.

I think the answer is z= 3200, or so.

You know that for the CMB the redshift is z = 1100, so this is longer ago than the recombination.

I guess you take the energy density of the CMB, and multiply by 32004
and you take the energy-equivalent of matter density and multiply by 32003

and the two energy densities are supposed to be equal at the transition

I think there is a lot of cancelation, and that what it comes down to is this equation

3200 x CMB energy density = matter energy density

And what that boils down to is an equation for z (which I suspect is around 3200). Here is the equation

z = (CMB energy density)/(equivalent energy density of matter)
============

if 3200 is the right z, then the temperature at the time would have been

3200 x 2.725 kelvin.

Im answering quick without really remembering the material but if you need quick help you can try to get some good out of this. Dont rely on it or trust it too much tho. Good luck
 
  • #4
Chronos said:
If it's of any use, the gruesome details can be found here:
http://www.astro.uu.se/~nisse/courses/kos2006/lnotes/ln6.pdf

that does indeed have it
equations 134 thru 137 on page 3 (so you won't have to hunt thru the whole thing), and the answer they get is approximately z = 3600

this is the redshift for "matter-radiation equality"

the redshift for "recombination" (origin of CMB) is about z = 1100 and they also derive an estimate of that.

good find! some Swedish professor's course material apparently. could be useful for other things as well.

(there is a subtlety---this guy includes NEUTRINOS as radiation because back in those days they would be so hot they would be relativistic. so he treats the neutrino background as radiation, and that is what leads him to say 3600. If he didnt he'd get a higher estimate for z---so that was a flaw in my quick sloppy response a few days ago)
 
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  • #5
Your post was not flawed, it was rigorously correct. Using the neutrino correction is speculative. Your z~3200 result is within the error bars and well reasoned. Your cold, logical explanations are simply amazing.
 
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1. What is the significance of calculating the redshift at which radiation energy density equaled mass density?

The redshift at which radiation energy density equaled mass density is an important parameter in understanding the early universe. It marks the transition from a radiation-dominated universe to a matter-dominated universe, and provides insight into the expansion and evolution of the universe.

2. How is the redshift at which radiation energy density equaled mass density calculated?

The redshift at which radiation energy density equaled mass density can be calculated using the Friedmann equations, which describe the evolution of the universe based on its energy density and expansion rate. By equating the energy density of radiation and matter, the redshift can be solved for.

3. What is the relationship between redshift and the expansion of the universe?

Redshift is a measure of how much the light from a distant object has been stretched due to the expansion of the universe. The higher the redshift, the farther away the object is and the faster it is moving away from us.

4. How does the redshift at which radiation energy density equaled mass density change over time?

As the universe continues to expand, the redshift at which radiation energy density equaled mass density increases. This is because the energy density of radiation decreases at a faster rate compared to the energy density of matter.

5. What does the calculation of the redshift at which radiation energy density equaled mass density tell us about the age of the universe?

By determining the redshift at which radiation energy density equaled mass density, scientists can estimate the age of the universe. This is because the transition from a radiation-dominated universe to a matter-dominated universe occurred at a specific time in the past, which can be calculated using the redshift value.

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