How is the universe expanding if the speed of light is finite?

[Arman777]

How do u know this? I thought it was accelerating cause of dark energy?

Well Expansion rate can be defined as $H(t)$ where $H(t)=\frac {\dot {a}(t)} {a(t)}$. Now we can write the Friedmann Equation in the form of,

$\frac {H^2} {(H_0)^2}=Ω_ma^{-3}+Ω_Λ$ and Now in here $H$ is Hubble parameter at any time t. $H_0$ Hubble parameter now. $Ω_m$ matter density
$Ω_Λ$ dark energy density and $a$ is the value of the scale factor at that time respeect to the $a(t_0)=1$.

Note: $Ω_m$ and $Ω_Λ$ should be current (Now) values

Now we can re-write the equation as,

$H^2={(H_0)^2}[Ω_ma^{-3}+Ω_Λ]$

take square root and we get,

$H=H_0\sqrt{Ω_ma^{-3}+Ω_Λ}$

Since, $H_0$, $Ω_m$ and $Ω_Λ$ are constant numbers, we can simply think this equation like this,

$H=\sqrt{x^{-3}}$

and I graphed it in desmos and I get,

As PeterDonis Said $\ddot {a}(t)$ is icreasing but it doesn't mean $H(t)$ is also increasing.

 

[graybass]

In layman terms, are we saying that the dark energy is/will eventually expand faster than C but that actual matter of the galaxies can not move faster than C because of common relativity? So this is why the standard model does not work?
Pardon my ignorance.

 

[phinds]

In layman terms, are we saying that the dark energy is/will eventually expand faster than C but that actual matter of the galaxies can not move faster than C because of common relativity? So this is why the standard model does not work?
Pardon my ignorance.

Dark energy does not expand, but I think what you mean to ask is will the effect of dark energy cause expansion faster than C. It ALREADY causes recession velocities faster than c. The objects at the outer regions of our observable universe are already receding from us at about 3c. Recession velocity is not proper motion, so no speeding tickets are issued.