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Das apashanka
for the matter+lambda universe why is Ω[Λ,o]=1-Ω[m,0]?
Das apashanka said:for the matter+lambda universe why is Ω[Λ,o]=1-Ω[m,0]?
Because the sum of the ##\Omega## terms is defined to be equal to one, and a matter+lambda universe has only matter and a cosmological constant term.Das apashanka said:for the matter+lambda universe why is Ω[Λ,o]=1-Ω[m,0]?
will you please explain the reason for being total omega to be 1kimbyd said:Because the sum of the ##\Omega## terms is defined to be equal to one, and a matter+lambda universe has only matter and a cosmological constant term.
There's no deep meaning. The parameter is just defined that way.Das apashanka said:will you please explain the reason for being total omega to be 1
Das apashanka said:for the matter+lambda universe why is Ω[Λ,o]=1-Ω[m,0]?
kimbyd said:Because the sum of the ##\Omega## terms is defined to be equal to one, and a matter+lambda universe has only matter and a cosmological constant term.
Whichever ##\Omega## values you include in your model, their sum is always identically equal to one. That's how they're defined: as density fractions. If you have matter, cosmological constant, and curvature, then it's:George Jones said:This only is true for spatially flat matter/Lambda universes, i.e., it is not true for general matter/Lambda universes.
kimbyd said:Whichever ##\Omega## values you include in your model, their sum is always identically equal to one. That's how they're defined: as density fractions. If you have matter, cosmological constant, and curvature, then it's:
$$\Omega_m + \Omega_\Lambda + \Omega_k = 1$$
PeterDonis said:Where are you getting this equation from? Do you have a reference?
That's more or less the point I was getting at. There's no deep reason here. It's just the way the terms are defined.George Jones said:Of course. As you say, this is true **by definition**. But this is not what the original poster asked about. A question equivalent to the OP's question is "Why is ##\Omega_k = 0##?"
The Matter+Lambda Universe Equation, also known as the Friedmann equation, is a fundamental equation in cosmology that describes the evolution of the universe. It is derived from the Einstein field equations and takes into account the matter density (Ωm) and the cosmological constant (ΩΛ). The equation is set equal to 1, which represents a flat universe, because observations have shown that the universe is nearly flat. This means that the matter density and the energy density from the cosmological constant must balance each other out to maintain a flat geometry.
The Matter+Lambda Universe Equation is significant because it helps us understand the overall structure and evolution of the universe. It allows us to calculate the expansion rate of the universe and make predictions about its future. It also provides evidence for the existence of dark matter and dark energy, which are necessary components to balance the equation and maintain a flat universe.
The Big Bang theory is the prevailing theory of the origin and evolution of the universe. The Matter+Lambda Universe Equation is a crucial component of this theory as it describes the expansion of the universe and its overall geometry. In fact, the equation was first derived by Alexander Friedmann, a Russian mathematician, in the 1920s when he was trying to find a solution to Einstein's equations that would support the idea of the expanding universe.
Yes, the value of Ω can change over time. In fact, it is believed that the value of Ω for matter (Ωm) has decreased over time due to the expansion of the universe. This is because as the universe expands, the matter becomes more spread out, resulting in a lower density. On the other hand, the value of Ω for the cosmological constant (ΩΛ) is thought to remain constant, which is why it is referred to as a "constant."
The Matter+Lambda Universe Equation is tested and verified through various observations and experiments. For example, the cosmic microwave background radiation, which is leftover radiation from the Big Bang, can be analyzed to determine the matter density and energy density in the universe. Additionally, observations of the large-scale structure of the universe and the expansion rate of galaxies also support the equation. The equation has been extensively tested and is widely accepted by the scientific community as an accurate description of the universe.