# How can we predict a Big Crunch when all galaxies are moving further apart?

I've read that the further away a Galaxy is from us the faster it moves away.

By this logic how can scientists predict that there will eventually be a big crunch when every piece of matter is seemingly getting further and further apart?

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Anyway, it is not that any galaxy move away at the speed of light. There are many discussions on SE that treat this argument. –  Py-ser Mar 21 at 9:09
Hi there, I gave this a quick edit to focus more on the question you would like answered. Good luck and welcome to the site! –  RhysW Mar 21 at 13:15
@RhysW Thanks. Feel free to edit. –  Yashbhatt Mar 22 at 17:39

In a homogeneous and isotropic Universe (even if recent observations challenge this hypothesis), you can derive the Friedmann equations, which describe the evolution of the Hubble constant with time: $\frac{\dot{a}}{a} = H(t) = \frac{8 \pi G}{3}\rho - \frac{k}{a^2} + \frac{\Lambda}{3}$ (with $c=1$) (Equation $1$)

where $a=a(t)$ is the scale factor, $\dot{a}$ its derivative, $G$ the gravitational constant, $\rho$ the matter density, $\frac{k}{a^2}$ the spatial curvature (a parameter that describes the metric of the Universe), and $\Lambda$ the cosmological constant (an integration constant added by Einstein). It could be useful to rewrite the equation as:

$H^2 = \frac{8 \pi G}{3}(\rho + \rho_{\Lambda}) - \frac{k}{a^2}$

where $\rho_{\Lambda} = \frac{\Lambda}{8 \pi G}$ is the "density of cosmological constant".

We can also expand the matter density as $\rho = \rho_{matter} + \rho_{radiation}$.

So we have a "total" density $\rho_{tot} = \rho_{matter} + \rho_{radiation} + \rho_{\Lambda}$. The destiny of the Universe depends on this amount.

In case of $\rho_{tot} > \rho_{crit}$, or equivalently a closed Universe ($k=+1$), the equation $(1)$ becomes:

$\dot a^2 = \frac{8 \pi G}{3}\rho a^2 -1$

Which points out that the scale factor must have an upper limit $a_{max}$ ($\dot a^2$ must be positive). This in turn means that the second derivative $\ddot a$ of the scale factor must be negative, when approaching $a_{max}$, that is the scale factor function inverts its behavior:

Look at here and here if you want to go deeper.

@Bardathehobo This figure shows what I mean when I say that a currently accelerating Universe can still crunch. This is because we are basically ignorant upon the dark energy issue.

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Can you explain this in simple terms? I am not familiar with the mathematical description of Friedman models. –  Yashbhatt Mar 21 at 16:29
D'oh! What exactly you do not understand? Let's try to narrow the problem. –  Py-ser Mar 24 at 0:38
What exactly is the cosmological constant? –  Yashbhatt Mar 24 at 10:15
Did you try this? en.wikipedia.org/wiki/Cosmological_constant Would you like some math or a more physical explanation? –  Py-ser Mar 24 at 10:45
I am sorry, but this is not correct anyway. We don't know the behavior of the $\Omega_{\Lambda}$ function with time. We don't how was in the past, why it is increasing now, and what it will do in future. This means that the Big Crunch scenario is still possible, and a presently accelerating Universe does NOT necessarily bring to an infinite Universe. We just don't know that much about the observed acceleration. –  Py-ser Mar 21 at 0:21