Some Simple Cosmology Questions

[EEWannabe]

Homework Statement
Estimate the pressure of the CMB photons today. [You will need to choose a reasonable value for the present value of the temperature of the CMB. The radiation
constant is α = 7.56 × 10−15erg cm−3K−4

Assume that a new population of stars is discovered, and their age is estimated to
be 19 Gyr.
From this observational result, derive an (approximate) value for the Hubble
parameter today, and express the result in kms−1Mpc−1

Homework Equations

First question . Energy Density = aT^4.
E(photon) = kT

2nd Question;
v = Hd

The Attempt at a Solution

Hey there, I've left it too late again ! And I have an exam tomorrow so any hints on these ones would be great;

1) Taking the current temperature as 2.7K, the energy density from radiation can be worked out. However I don't really get it when it asks for the pressure? How exactly do I work that out? I've never seen anything like it. The energy of a single photon at 2.7K can be worked out using E = kT, but I don't see how that will help.

2) I don't understand this one at all, what does it mean 19Gyear? Giga years? If so that's older than the universe surely... Any points in the right direction here would be fantastic.

 

[ideasrule]

1) Taking the current temperature as 2.7K, the energy density from radiation can be worked out. However I don't really get it when it asks for the pressure? How exactly do I work that out? I've never seen anything like it. The energy of a single photon at 2.7K can be worked out using E = kT, but I don't see how that will help.

I'm surprised that you've never talked about pressure in your cosmology class. Cosmology has 2 important equations: the Friedmann equations, and the equation of state. The equation of state gives you a fluid's pressure in terms of its density. See: http://en.wikipedia.org/wiki/Equation_of_state_(cosmology)

Be careful of the units, since it's conventional to set c=1.

2) I don't understand this one at all, what does it mean 19Gyear? Giga years? If so that's older than the universe surely... Any points in the right direction here would be fantastic.

Yes, 19 billion years. It is indeed older than the universe, which is why you're being asked to find the new Hubble constant for this new, imaginary universe.

The answer depends heavily on the other assumptions you want to make. Is the universe the same as ours, except older? What's the universe's matter, radiation, and cosmological constant density? For a very simple estimate, see here: http://en.wikipedia.org/wiki/Age_of_the_universe#Cosmological_parameters

 

[EEWannabe]

I'm surprised that you've never talked about pressure in your cosmology class. Cosmology has 2 important equations: the Friedmann equations, and the equation of state. The equation of state gives you a fluid's pressure in terms of its density. See: http://en.wikipedia.org/wiki/Equation_of_state_(cosmology)

Be careful of the units, since it's conventional to set c=1.

Ah I see! So for radiation the pressure = energy density / 3? That simple? :D

Yes, 19 billion years. It is indeed older than the universe, which is why you're being asked to find the new Hubble constant for this new, imaginary universe.

The answer depends heavily on the other assumptions you want to make. Is the universe the same as ours, except older? What's the universe's matter, radiation, and cosmological constant density? For a very simple estimate, see here: http://en.wikipedia.org/wiki/Age_of_the_universe#Cosmological_parameters

Hmm I see, so for example, if I assume it's matter dominated, would I just assume that the ageof those stars = the age of that universe? If so;

H = 2/3t , and using 19 billion for t?

Thanks a lot for your help, this is meant to be an introduction to cosmology course, but I've decided I'm not going to carry it on lol ;P

 

[ideasrule]

Ah I see! So for radiation the pressure = energy density / 3? That simple? :D

Yup.

Hmm I see, so for example, if I assume it's matter dominated, would I just assume that the ageof those stars = the age of that universe? If so;

H = 2/3t , and using 19 billion for t?

Yeah, but only if it's matter dominated and flat. For our universe, just taking the inverse of H0 gives (by coincidence) an amazingly good value for its age.

 

[EEWannabe]

Much obliged sir!