Studying Astronomy: Struggling with Cosmology Maths

[mrjaffa]

Hi everyone. Loving the forum, don't know how I haven't stmble upon it already.

I'm studying Astronomy at the OU and finding a lot of the maths tough. Especially finding the chapters on Cosmology very difficult.

I've seen another post regarding Scale Factor, so hope it's ok posting this too.

There's a question in the textbook, asking to determine the scale factor at the time when energy density for matter and radiation was the same using Rt / Rt(0)

So Rt(0) is now, which is just 1. And I believe Rt is stated as being 10^-4.

So 10^-4 / 1 is just going to be 10^-4. This seems odd. Am I missing something?

Thanks :-)

 

[marcus]

Hi Mr. Jaffa, and welcome!
We have a "homework help" section for helping with textbook problems that are part of coursework and the moderators may want to move this thread over to that section.
I just want to say hello and compare notation, someone else may be able to help you with the actual problem.

I am used to the notation z_eq for "redshift at matter-radiation equality"

In my experience a not unusual figure for that is z_eq = 3400

You know that the scale factor associated with any redshift z is 1/(z+1)
so the scale factor associated with z = 3400 is 1/3401 ≈ 3×10^-4

It struck me as curious that your textbook would imply that the scale factor at matter-radiation equality was considerably smaller namely 10^-4. But that is the same order of magnitude as 3×10^-4. So maybe it is all right. The textbook may merely be speaking approximately in rough orders of magnitude.

When you say you are studying at the OU, is that Oxford? I live in North America and we have places like Oregon, and Oklahoma, and Ohio, and Ontario.
So I can't be sure what OU means.

 

[George Jones]

Open University in the UK.

 

[mrjaffa]

Hi Mr. Jaffa, and welcome!
We have a "homework help" section for helping with textbook problems that are part of coursework and the moderators may want to move this thread over to that section.
I just want to say hello and compare notation, someone else may be able to help you with the actual problem.

I am used to the notation z_eq for "redshift at matter-radiation equality"

In my experience a not unusual figure for that is z_eq = 3400

You know that the scale factor associated with any redshift z is 1/(z+1)
so the scale factor associated with z = 3400 is 1/3401 ≈ 3×10^-4

It struck me as curious that your textbook would imply that the scale factor at matter-radiation equality was considerably smaller namely 10^-4. But that is the same order of magnitude as 3×10^-4. So maybe it is all right. The textbook may merely be speaking approximately in rough orders of magnitude.

When you say you are studying at the OU, is that Oxford? I live in North America and we have places like Oregon, and Oklahoma, and Ohio, and Ontario.
So I can't be sure what OU means.

Hi Marcus. OU is indeed just the Open University which is online online learning.

Thanks for your reply. I'm still not understanding this.

In the textbook, there is a graph showing the energy densities for radiation and matter on the y-axis and then on the x-axis is the scale factor R(t) / R(t0). The time whe the energry density for the radiation and matter is equal is shown as 10^-4.

I don't understand why we divide R(t) by R(t0) if the latter is just 1.

 

[marcus]

Some people do not use a normalized scale factor, so for them R(t₀) is not automatically 1.
If your scale factor R is not normalized and made to equal one, already, then when you use it you may need to
divide by R(t₀) all the time
So you use R(t)/R(t₀) as a normalized version of R
The normalized version WILL equal 1 at present.

I remember being puzzled when I first noticed that some people, some books, etc. use an unnormalized scale factor.