- #1
Eulalie
- 1
- 0
- Homework Statement
- Thank you for taking a look! I've been pouring over my textbook trying to figure out the right formulas for these problems, but have been unable to do so. My professor did not teach some of these problems and I basically need a point in the right direction. If I knew what formulas to use I could easily solve these myself. This was all for an Intro to Cosmology course. I was able to solve the rest of the problems apart from these four.
- Relevant Equations
- unknown
1. If today vacuum and matter contribute 71 % and 29 % to the total energy density of the universe, at what redshift z were they contributing equally?
2. If today vacuum, matter, and radiation contribute 71 %, 29 %, and 0.01% to the total energy density of the universe, at what redshift z were dark matter and radiation contributing equally?
3. (horizon problem) In a (hypothetical) matter-dominated universe, consider two galaxies that are exactly at the Hubble distance today: d = dH, where dH ≡ c/H. Calculate d dH |z – the ratio of the distance between the galaxies to the Hubble distance at redshift z.
4. (flatness problem) Assume that Ω = 1.01 today (see PV, I didn’t introduce Ω in the lectures). Assume that radiation contributes 0.01% to the total energy density of the universe. Calculate Ω at redshift z = 106 .
While searching for the solutions to #1 and #2, I came across the equation Omega0 = p0/pc,0. However, I can't find any equations involving redshift, which is basically where I'm stumped. I also could not figure out what the variable p represents as it unfortunately was not defined in my textbook.
Any help at all would be awesome!
2. If today vacuum, matter, and radiation contribute 71 %, 29 %, and 0.01% to the total energy density of the universe, at what redshift z were dark matter and radiation contributing equally?
3. (horizon problem) In a (hypothetical) matter-dominated universe, consider two galaxies that are exactly at the Hubble distance today: d = dH, where dH ≡ c/H. Calculate d dH |z – the ratio of the distance between the galaxies to the Hubble distance at redshift z.
4. (flatness problem) Assume that Ω = 1.01 today (see PV, I didn’t introduce Ω in the lectures). Assume that radiation contributes 0.01% to the total energy density of the universe. Calculate Ω at redshift z = 106 .
While searching for the solutions to #1 and #2, I came across the equation Omega0 = p0/pc,0. However, I can't find any equations involving redshift, which is basically where I'm stumped. I also could not figure out what the variable p represents as it unfortunately was not defined in my textbook.
Any help at all would be awesome!