Cosmology question.

[reds4ever]

I wonder if anyone could help me? I'm doing an Astronomy course, but the last module has desended into the black art of "basic" (ha!) Cosmology and I'm stumped. I need to get a basic pass on the module (>40%), I've answered all the "easy" questions and figure I'm in the mid 30's, this question is worth 10% and would make sure.

(Sorry in advance for the equation notation, I don't know how to do it in HTML)

It's all to do with the temperature of the universe at a different times.

R(t) is the scale factor at cosmic time 't'
t0 is the present time
t1 is the time that the universe changed from being radiation dominated to being matter dominated.
the age of the universe is 13.7 billion years.

I've been given the information that R(t)/R(t0) = 10^-4 for t1 but I can't make this help.



1) How do I find R(t1)/R(t0)?

2) Given that the background radiation is 2.73K how do I find the temperature at t1?
and then find at what time t1 occured.

I'm totally lost on 1). The second part of 2) is tied up with

(T/K)=1.5*10^10*(t/s)^.5

But I'm unsure how to go about getting the answer from the first part to plug into the equation?

Any help would be app.

[Urban Ranger]

Okay, something went boom and the universe was formed. Then it started expanding, and thus as a result the temperature started to drop. When the temperature dropped below a certain point energy condensed to become matter. That would be t1. Then the temperature continued to drop, and after 13.7 billion years it is 2.73K.

What does R(t) mean? Is t any arbitrarily point?

[Sava]

lies

none of this was in the bible

[DeathByTheSword]

dont you have the R(t0) in BINAS?

[Whaleboy]

http://scienceworld.wolfram.com/physics/CosmicBackgroundRadiation.html

[Ramo]

What does R(t) mean? Is t any arbitrarily point?

R is the scale factor of the line element of the constant time hypersurface of the metric for a homogenous, isotropic universe.

Your metric looks somethign like this:
ds^2 = -dt^2 + R^2(h_ij)dx^i*dx^j

It's important because well...

When the universe was radiation dominated, rho*R^4 was a constant, when it's matter domianted, rho*R^3 is a constant (take the covariant derivitive of the energy momentum tensor for a perfect fluid, etc., etc.). So, we're only talking about the second regime. So, if you plug in your metric and the previously mentioned expression for density, into Einstein's equations, you eventually get some expression for R which I can't possibly remeber.

Anyways, you can relate luminosity with distance, and eventually get an expression for Hubble's constant, H = R'(t)/R(t). So, you'd be able to find out an expression for R if you happened to know H. So I think there's some missing info on question 1.

For question 2, you can, through adiabatic expansion, say that the microwave background ratiation temperature is inversely proportional to R. So, you'd need the answer to question 1 for that, and thus be able to say T(t1)/T(t0) = R(t0)/R(t1). And you plug the T(t1) into the equation you posted to get t1.

[reds4ever]

Cheers Ramo , thats a big help!


Wheres KH?

[duke o' york]

Good luck reds.

I scraped one of my accountancy exams that I thought I had done all right in, and did really well in the one I was sure I had failed. It's a funny old game...

[reds4ever]

Originally posted by duke o' york
Good luck reds.

I'll need it. After Ramos post I'm more confused than ever1

THB it's all over my head, I just need the fooking 10%

[Ramo]

I'm just saying that you're missing info on question one. Look over the question again.

On two, again T ~ 1/R, so T1/T0 = R0/R1. And that's your answer.

[reds4ever]

Ramo,

I really don't understand question 1, is it calculus? My math isn't up to this!

Reds

[Ramo]

Differential geometry, actually...

I might be able to give you a simplified equation, if I knew what info you had. As I said, I think something's missing.

[reds4ever]

Originally posted by Ramo
Differential geometry, actually...

I might be able to give you a simplified equation, if I knew what info you had. As I said, I think something's missing.

Thanks Ramo,

I'll get my books tomorrow, I REALLY need this 10%. If you could bare with me....

reds

[duke o' york]

It's bear with me!!!!! Whaleboy just posted the same thing earlier.

Any chance that you can type out the entire question then? I assume that you have it with you.

[reds4ever]

Originally posted by duke o' york
It's bear with me!!!!! Whaleboy just posted the same thing earlier.

Any chance that you can type out the entire question then? I assume that you have it with you.

Can I mail you the PDF? It's embarassing to admit, but this question is totally beyond me.