# A question on cosmology

1. Jun 29, 2014

### Li Jiaxuan

I have a question about cosmos microwave background.
Can we get a relationship between CMB's temperature and redshift z??
THX!!!

2. Jun 29, 2014

### Simon Bridge

Welcome to PF;
iirc that's one of the ways the Universe gets dated.
As the universe expands, the CMB photons are redshifted, making the radiation's temperature inversely proportional to a parameter called the universe's scale length. The temperature Tr of the CMB as a function of redshift, z, can be shown to be proportional to the temperature of the CMB as observed in the present day (2.725 K or 0.235 meV)...
--- Noterdaeme, P.; Petitjean, P.; Srianand, R.; Ledoux, C.; López, S. (February 2011). "The evolution of the cosmic microwave background temperature. Measurements of TCMB at high redshift from carbon monoxide excitation". Astronomy and Astrophysics 526: L7. arXiv:1012.3164. Bibcode:2011A&A...526L...7N. doi:10.1051/0004-6361/201016140.​

3. Jun 29, 2014

### Li Jiaxuan

Thanks for your answer. I find a function on the internet: T=2.73k*(1+z),and 2.73k is the current temperature of CMB. Hence T/Tnow=1+z.
I know that R2/R1=1+z , R is the universe scale length. And can we get that T~R?
Thank you!!
(P.s. Can you introduce a book to me?)

4. Jun 29, 2014

### Simon Bridge

Very roughly - and most books giving a mathematical treatment of cosmology will have the relations you are after.
I've had: Introduction to mathematical cosmology by J Islam recommended to me - I have only skimmed the first chapter so I cannot comment on how good it is.
It doesn't seem to be terrible and I see it is on Cambridge Universities text list FWIW.

5. Jun 29, 2014

### George Jones

Staff Emeritus
Li Jiaxuan, welcome to Physics Forums!

At what level would you like your questions answered? What is your background in physics and mathematics?

6. Jun 29, 2014

### Li Jiaxuan

I am a senior student and I want to take part in an astronomy competition in our city. I can master calculus and mechanics. I want a detail answer about CMB.
Thx!

7. Jun 29, 2014

### Simon Bridge

That's impressive - it usually takes people another 4-6years of college study to "master" calculus or mechanics ;)
The problem then is to figure out what level of detail the competition would like to see.
Have a skim of that link I gave you and see how much you follow.
You may need a more elementary work.

8. Jun 29, 2014

### Li Jiaxuan

Well, I mean I can use a little calculus to solve problems. English is not my native language so my English is poor. I regard "master" as "use".(I often fail in English,forgive me)

9. Jun 29, 2014

### WannabeNewton

The CMB temperature is inversely proportional to the scale factor so you can use that to get a relationship between the CMB temperature and redshift.

10. Jun 29, 2014

### Simon Bridge

Actually your English is better than most native speakers.
Master, as a verb related to a subject matter, means: to acquire complete knowledge or skill in (a subject, technique, or art).

i.e. someone who can ride a little is not a master of horsemanship.
A common use would be "chess is easy to learn and difficult to master."

Academically, "a Master" is someone with at least the post-graduate University degree "Master of" <subject>.

Have you had a look at that book yet?
It's tricky to get references at a lower level that also have the maths you want.