Redshift & Total Energy Density

In summary, the conversation discusses the contribution of vacuum, matter, and radiation to the total energy density of the universe at different redshifts. The first two questions seek to determine the redshift at which vacuum and matter were contributing equally, and at which dark matter and radiation were contributing equally. The third question explores the horizon problem in a hypothetical matter-dominated universe, while the fourth question discusses the flatness problem and the calculation of Omega at a specific redshift. The equation Omega0 = p0/pc,0 is mentioned, but it is unclear what the variable p represents. The conversation suggests that a relation between redshift and the scale factor a can provide answers to these questions.
  • #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!
 
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  • #2
You should be able to find a relation between the redshift z and the scale factor a. How do the different components of the energy density scale with a?
 

1. What is redshift and how is it related to total energy density?

Redshift is a phenomenon in which the wavelength of light from distant objects appears longer, or "shifted", towards the red end of the spectrum. This is caused by the expansion of the universe, which stretches the light waves as they travel through space. Redshift is directly related to the total energy density of the universe, as it is a measure of the rate of expansion and therefore the amount of energy present in the universe.

2. How is redshift measured?

Redshift is measured using a unit called "z", which is the ratio of the observed wavelength of light to the rest wavelength of that same light. This can be calculated using spectroscopy, which analyzes the light spectrum of an object to determine its redshift. The higher the z value, the greater the redshift and therefore the greater the distance and energy density of the object.

3. What is the significance of redshift in cosmology?

Redshift is a crucial tool in understanding the expansion and evolution of the universe. By measuring the redshift of distant objects, scientists can determine their distance, velocity, and energy density. This allows for the creation of models and theories about the past, present, and future of the universe.

4. How does redshift affect the observable universe?

Redshift has a significant impact on the observable universe. As the universe expands, the light from distant objects is redshifted, making them appear farther away and older than they actually are. This means that the observable universe is limited by the speed of light and the age of the universe, as objects beyond a certain distance and age will have a redshift too high to be detected.

5. Can redshift be used to measure the age of the universe?

While redshift is not a direct measure of the age of the universe, it is an important factor in determining it. By measuring the redshift of various objects and using models of the expansion rate, scientists can estimate the age of the universe. However, other factors such as the density of matter and dark energy also play a role in determining the age of the universe.

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