# Scale factor

1. Apr 14, 2015

### 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 text book, 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 :-)

2. Apr 14, 2015

### 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 zeq for "redshift at matter-radiation equality"

In my experience a not unusual figure for that is zeq = 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.

3. Apr 14, 2015

### George Jones

Staff Emeritus
Open University in the UK.

4. Apr 15, 2015

### mrjaffa

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

In the text book, 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.

5. Apr 15, 2015

### 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.