Does the Equation 1=Ω_k+Ω_m+Ω_Λ Hold for All Universe Types?

• Mysteryciel
In summary, the equation ##1=Ω_k+Ω_m+Ω_Λ## is true for all types of universes (open, flat, closed) as long as there is no other component of energy density present. The equation for ##Ω_k## is also correct, with values greater than 1 indicating a closed universe, values less than 1 indicating an open universe, and a value of 1 indicating a flat universe. For further proof, consult any introductory cosmology text.
Mysteryciel
I was searching a cosmology calculator and In one calculator I saw this equation.
##1=Ω_k+Ω_m+Ω_Λ##
is that true true for all type universe's (open,flat,closed) ?
and is here ##Ω_k={-k\over H^2_0 /a^2_0}## isn't it.
(And If you can give me an article about this issue I will be very happy,I need exact proof)
Thanks

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It's true for globally isotropic universes with matter and cosmological constant. For proof, consult any introductory cosmology text.

Mysteryciel said:
I was searching a cosmology calculator and In one calculator I saw this equation.
##1=Ω_k+Ω_m+Ω_Λ##
is that true true for all type universe's (open,flat,closed) ?
and is here ##Ω_k={-k\over H^2_0 /a^2_0}## isn't it.
(And If you can give me an article about this issue I will be very happy,I need exact proof)
Thanks
That equation is part of the definition of the ##\Omega## parameters. It's true as long as there is no other component of the energy density (e.g. it's true as long as the radiation density is small enough to be ignored). If you have some other component, such as ##\Omega_r## for radiation, then you have to add that to the equation:

$$1 = \Omega_k + \Omega_m + \Omega_\Lambda + \Omega_r$$

And yes, that equation for ##\Omega_k## is correct.

Sum = 1 implies a flat universe. > 1 implies closed, < 1 implies open.

mathman said:
Sum = 1 implies a flat universe. > 1 implies closed, < 1 implies open.
Not when $\Omega_k$ is included, as Chalnoth said the sum is unity; $\Omega_k$ absorbs the k term.

$\Omega_k$ > 0 implies open, $\Omega_k$ = 0 implies flat and $\Omega_k$< 0 implies closed, (see the OP definition of $\Omega_k$).

Garth

What is the "Universe density types equation"?

The "Universe density types equation" is a mathematical equation that describes the different types of density that exist in the universe. It includes the density of matter, radiation, and dark energy.

What are the different types of density in the universe?

There are three types of density in the universe: matter density, radiation density, and dark energy density. Matter density refers to the amount of matter in a given volume, radiation density refers to the amount of energy carried by radiation in a given volume, and dark energy density refers to the energy associated with the expansion of the universe.

How is the "Universe density types equation" calculated?

The "Universe density types equation" is calculated using the mass-energy density parameter, which is the ratio of the density of a given type of energy to the critical density of the universe. This parameter is represented by the Greek letter omega (Ω).

What is the significance of the "Universe density types equation" in cosmology?

The "Universe density types equation" is significant in cosmology because it helps us understand the composition of the universe and how it has evolved over time. By studying the density of different types of energy, we can gain insights into the expansion and fate of the universe.

How does the "Universe density types equation" relate to the concept of dark energy?

The "Universe density types equation" is closely related to the concept of dark energy, as it helps us measure and understand the density of dark energy in the universe. It also plays a crucial role in theories about the accelerated expansion of the universe, which is thought to be driven by dark energy.

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