When was the matter density equal to the vacuum energy density?

In summary, the conversation is discussing the values of ΛCDM parameters and their relation to the universe being spatially flat. The question is asked about the matter and vacuum energy density being equal and how it relates to the Hubble parameter. The response suggests using the equation Ωm,0(1+zeq)^3 = ΩΛ,0 to find the value of zeq and then plugging it into a cosmological calculator to obtain the corresponding time.
  • #1
LeoChan
5
1
TL;DR Summary
In ΛCDM, to find t and z when the matter density equal to the vacuum energy density.
In ΛCDM, H(t0) = 70km/s/Mpc,
Ωd(t0) = 0.3, Ωr(t0) = 0 and ΩΛ(t0) =0.7,
so that Ω(t0) = Ωd(t0) + Ωr(t0) + ΩΛ(t0) = 1and the universe is spatially flat.

I want to know the t and z when the matter density equal to the vacuum energy density. By total energy density equation, I think Ωd(t) + ΩΛ(t) = 1, so they are both equal to 0.5 .

Maybe 0.5 = Λ / ( 3 * H(t) ^ 2 ). As for the matter, I am not sure since I only know it is proportional to a^-3. Is it related to the redshift dependent Hubble parameter, H(z)?

Thank you for your attention.
 
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  • #2
Just use

$$\Omega_{m,0}(1+z_{eq})^3 = \Omega_{\Lambda,0}$$
to find ##z_{eq}## and then type it into some cosmological calculator to obtain ##t##
 
  • #3
Arman777 said:
Just use

$$\Omega_{m,0}(1+z_{eq})^3 = \Omega_{\Lambda,0}$$
to find ##z_{eq}## and then type it into some cosmological calculator to obtain ##t##
Thank you.That is quite straight forward.
 

1. What is the significance of the matter density being equal to the vacuum energy density?

The matter density being equal to the vacuum energy density is a key concept in understanding the expansion and evolution of the universe. This equality marks a critical point in the history of the universe, known as the "matter-radiation equality". At this point, the energy density of matter and radiation are equal, and the expansion of the universe shifts from being dominated by radiation to being dominated by matter.

2. When did the matter density and vacuum energy density become equal?

The exact time when the matter density and vacuum energy density became equal is not known with certainty. However, based on current models and observations, it is estimated to have occurred approximately 50,000 years after the Big Bang, when the universe was around 1,000 times smaller than it is today.

3. How does the equality of matter density and vacuum energy density affect the expansion of the universe?

The equality of matter density and vacuum energy density marks a transition in the expansion of the universe. Before this point, the expansion was driven primarily by the energy of radiation. However, after this point, the expansion is driven by the energy of matter, which is less dense but more dominant due to its larger contribution to the total energy of the universe.

4. Is the matter density and vacuum energy density still equal today?

No, the matter density and vacuum energy density are not equal today. The expansion of the universe has continued, and the matter density has decreased while the vacuum energy density has remained relatively constant. This is due to the phenomenon of dark energy, which is causing the expansion of the universe to accelerate.

5. How does the equality of matter density and vacuum energy density relate to the fate of the universe?

The equality of matter density and vacuum energy density is a crucial factor in determining the ultimate fate of the universe. If the matter density were greater than the vacuum energy density, the universe would eventually collapse in a "Big Crunch". However, if the vacuum energy density dominates, the universe will continue to expand indefinitely, leading to a "Big Freeze". The equality of these two densities suggests that the fate of the universe is likely to be a balance between these two possibilities.

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