Matter density parameter = 1

In summary, the person is trying to solve for a range of values for a where Ωm is approximately equal to 1. However, setting Ωm to 1 leads to imaginary values for a, so the person is unsure how to proceed. They suggest using a computer to plot Ωm(a) and finding values of a where it is greater than a specified number, such as 0.95.
  • #1

Homework Statement

Starting with the equation below, I need to:
- Show that there is a range of values for a for which Ωm≈1
- Derive expressions for the values of a at the endpoints of this range.

Homework Equations

Ωm(a) = Ωm0/[Ωm0r0/av0a3].

(0 signifies present day values, m=matter, r=radiation, v=vacuum)

The Attempt at a Solution

Just setting Ωm=1 leads to a4 = -Ωr0v0, which gives imaginary values for a, which is obviously not right. However, I can't see any other way of solving this problem to get real values...Thanks in advance,
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  • #2
The question is unclear to me. What does [itex]\Omega_m \approx 1[/itex] mean? Clearly, the expression gives [itex]\Omega_m \left( a \right) < 1[/itex] always. To get a handle on things, I had my computer plot [itex]\Omega_m \left( a \right)[/itex]. Try finding the values of [itex]a[/itex] for which [itex]\Omega_m \left( a \right) > 0.95[/itex]. Instead of 0.95 you could use some other number nearer to or farther from 1.

1. What is the significance of matter density parameter = 1?

The matter density parameter, denoted as Ωm, is a measure of the relative amount of matter in the universe compared to the critical density needed for the universe to be flat. A value of Ωm = 1 indicates that the universe contains exactly the critical density of matter, which means it will continue to expand at a constant rate indefinitely.

2. How is matter density parameter = 1 determined?

The matter density parameter is calculated by measuring the average density of matter in the universe and comparing it to the critical density. This can be done using various methods, such as studying the distribution of galaxies and their velocities or analyzing the cosmic microwave background radiation.

3. What does a matter density parameter ≠ 1 mean for the fate of the universe?

If the matter density parameter is less than 1, it suggests that the universe will continue to expand forever at an accelerating rate. On the other hand, if the matter density parameter is greater than 1, it indicates that the universe will eventually stop expanding and begin to collapse in a "big crunch" scenario.

4. How does matter density parameter = 1 relate to dark matter?

Dark matter is a type of matter that does not interact with light and is thought to make up a significant portion of the matter in the universe. The matter density parameter includes both regular matter and dark matter, so a value of 1 implies that the amount of dark matter is equal to the critical density needed for a flat universe.

5. Can the matter density parameter change over time?

Yes, the matter density parameter can change over time as the universe expands. As the universe expands, the amount of matter stays the same, but the volume of space increases, thereby decreasing the overall density of matter. This means that the matter density parameter will decrease over time. However, the rate of expansion and the presence of dark energy can also affect the value of the matter density parameter.