# Calculating average density of the Universe

• I
• bobo1455
In summary, the conversation discusses the calculation of average density of the universe at the time the light was emitted by a galaxy with a red-shifted wavelength of 6.56. The formula for calculating density of matter in an expanding universe is given, as well as the formula for energy density of photons. The speaker also mentions calculating the average density correctly and asks for help in expressing it as the number of Hydrogen atoms per cubic meter. They suggest multiplying the calculated density by the number of Hydrogen atoms that would fit in one cubic meter.

#### bobo1455

Q: What was the average density of the universe at the time the light was emitted by the z = 6.56 galaxy?

For the question we know the current average density of the universe and red-shift wavelength z = 6.56. It says to calculate the average density of the universe at the moment when light was emitted by the galaxy at red-shifted wavelength 6.56. I have the linear scale factor but I'm not really sure what to do next. I've read equations about density on the internet but haven't found one that uses a wavelength or linear scale factor. Any help is appreciated.

In order to calculate the densities we use a cubic model of expansion for both.

Density of matter (expanding universe): ##\rho(t) = \frac{M}{L(t)^3} = \frac{M}{L_0^3a(t)^3} = \frac{\rho_0}{a(t)^3}##.

where ##M## is mass inside a "cube"
##L(t)## is expanding side of "cube"
##\rho_0## is current density
##a(t)## is scale factor of universe
##\rho(t)## is density at time t

Energy density of photons (expanding universe): ##\rho(t)c^2 = \frac{N E(t)}{L(t)^3} = \frac{\frac{N E_0}{a(t)}}{L_0^3a(t)^3} = \frac{\rho_0c^2}{a(t)^4}##.

where ##N## is number of photons in "cube"
##E(t)## is photon energy at time t
##\rho_0c^2## is current density

Alright I calculate the average density and it is correct because I checked against the book's answer. If I were asked to express the density as the number of Hydrogen atoms per cubic meter, how would I go about it?

What I've done is calculated the number of H atoms that would fit in one cubic meter to be 1.06 x 10^30 and just multiplied it by the density I calculated previously. Am I on the right track or way off?

## 1. What is the average density of the Universe?

The average density of the Universe is estimated to be about 9.9 x 10^-30 grams per cubic centimeter. This is equivalent to about 5.9 protons per cubic meter.

## 2. How is the average density of the Universe calculated?

The average density of the Universe is calculated by dividing the total mass of the Universe by its total volume. This is a challenging task as the mass and volume of the Universe are constantly changing and difficult to measure accurately.

## 3. How do scientists measure the total mass of the Universe?

Scientists use a variety of methods to estimate the total mass of the Universe, including studying the gravitational effects of large structures such as galaxy clusters, analyzing the cosmic microwave background radiation, and observing the rotational speeds of galaxies.

## 4. What factors affect the average density of the Universe?

The average density of the Universe is affected by several factors, including the amount of dark matter and dark energy present, the expansion rate of the Universe, and the distribution of matter and energy throughout the Universe.

## 5. Has the average density of the Universe changed over time?

Yes, the average density of the Universe has changed over time. As the Universe expands, the average density decreases. In the past, the Universe was much denser, and in the future, it is expected to become even less dense as the expansion continues.