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In Barbara Ryden's introduction to cosmology book its written that

Then later on, in the book energy density of the ##\Lambda## defined as ##\epsilon_{\Lambda} = \frac{c^2\Lambda}{8\pi G}##

But this not make much sense. Since in this case

$$\epsilon_{\Lambda} = \frac{c^2 4\pi G\rho}{8\pi G} $$

$$\epsilon_{\Lambda} = \rho/2 c^2 $$

Which is not correct.

From other sources I see that actually

##\Lambda = 8\pi G\rho## and

##\epsilon_{\Lambda} = \frac{c^4\Lambda}{8\pi G}##

Also,

##\epsilon_{\Lambda} = \frac{c^4\Lambda}{8\pi G}## and we know that ##\Omega_{\Lambda} = \frac{\epsilon_{\Lambda}}{\epsilon_c}##

and ##\epsilon_c = \frac{3H^2c^2}{8 \pi G}##

so we get

$$\Lambda = \frac{3H^2\Omega_{\Lambda}} {c^2}$$

*"Introducing ##\Lambda## into the Poisson's equation allows the universe to be static, if you set ##\Lambda = 4\pi G\rho##"*Then later on, in the book energy density of the ##\Lambda## defined as ##\epsilon_{\Lambda} = \frac{c^2\Lambda}{8\pi G}##

But this not make much sense. Since in this case

$$\epsilon_{\Lambda} = \frac{c^2 4\pi G\rho}{8\pi G} $$

$$\epsilon_{\Lambda} = \rho/2 c^2 $$

Which is not correct.

From other sources I see that actually

##\Lambda = 8\pi G\rho## and

##\epsilon_{\Lambda} = \frac{c^4\Lambda}{8\pi G}##

**And it seems that other sources definiton is the correct one. So the information on the book is wrong ? Or the ##\Lambda## for the static universe case is different then the general ##\Lambda## ?**Also,

##\epsilon_{\Lambda} = \frac{c^4\Lambda}{8\pi G}## and we know that ##\Omega_{\Lambda} = \frac{\epsilon_{\Lambda}}{\epsilon_c}##

and ##\epsilon_c = \frac{3H^2c^2}{8 \pi G}##

so we get

$$\Lambda = \frac{3H^2\Omega_{\Lambda}} {c^2}$$

**So is this means that ##\Lambda## is actually a time dependent thing since it involves ##H(t)## and ##\Omega_{\Lambda}## ?**
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