Discover the Relationship Between CMB's Temperature and Redshift z in Cosmology

[Li Jiaxuan]

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

 

[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.​

 

[Li Jiaxuan]

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.​

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?)

 

[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.

 

[George Jones]

Li Jiaxuan, welcome to Physics Forums!

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

 

[Li Jiaxuan]

Li Jiaxuan, welcome to Physics Forums!

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

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!

 

[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.

 

[Li Jiaxuan]

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.

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)

 

[WannabeNewton]

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

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.

 

[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.