What Values Can Ωk Take in the Equation Ωm+Ωr+Ωk=1?

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Arman777
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Let's suppose we have an equation,
$$Ω_m+Ω_r+Ω_k=1$$
In this equation what's the values that ##Ω_k## can take ?
Only 1,0 or -1 ?

Also this equation is true for only "now" or any time in the universe ?
 
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Arman777 said:
Let's suppose we have an equation,
$$Ω_m+Ω_r+Ω_k=1$$
In this equation what's the values that ##Ω_k## can take ?
Only 1,0 or -1 ?

Also this equation is true for only "now" or any time in the universe ?

Assuming the omegas are positive, then ##0 \le \Omega_k \le 1##

If you allow negative values, then ##\Omega_k## can be any real number.

That was the mathematical answer. Rereading your question, I guess you want a cosmological answer. I'll leave that to others.
 
PeroK said:
Assuming the omegas are positive, then ##0 \le \Omega_k \le 1##

If you allow negative values, then ##\Omega_k## can be any real number.
For flat universe we can take ##Ω_k=0##. In example for positive curvature universe then what could be the value of ##Ω_k## ?
A negative value ?

Cause ##Ω_k=-\frac {κ} {a^2H^2}##

Something seems wrong to me. Either this equation only hold for ##Ω_k=0##.

Oh okay I understand
 
For a negative value of ##Ω_k## corresponds to ##Ω>1## which its positively curved universe
For ##Ω_k=0## corresponds to ##Ω=1## which flat universe
For a positive value of ##Ω_k## corresponds to ##Ω<1## which its negatively curved universe

where ##Ω=Ω_m+Ω_r##
 
Arman777 said:
Let's suppose we have an equation,
$$Ω_m+Ω_r+Ω_k=1$$
In this equation what's the values that ##Ω_k## can take ?
Only 1,0 or -1 ?

Also this equation is true for only "now" or any time in the universe ?
##\Omega_k## can be any real number that makes the equation above true. Because ##\Omega_m## and ##\Omega_r## must be positive, ##\Omega_k## cannot be greater than 1. But it can be as negative as you like.

Arman777 said:
For a negative value of ##Ω_k## corresponds to ##Ω>1## which its positively curved universe
For ##Ω_k=0## corresponds to ##Ω=1## which flat universe
For a positive value of ##Ω_k## corresponds to ##Ω<1## which its negatively curved universe

where ##Ω=Ω_m+Ω_r##
This is accurate.
 
kimbyd said:
##\Omega_k## can be any real number that makes the equation above true. Because ##\Omega_m## and ##\Omega_r## must be positive, ##\Omega_k## cannot be greater than 1. But it can be as negative as you like.This is accurate.
Thanks, its more clear now