# 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?

• Anyway, it is not that any galaxy move away at the speed of light. There are many discussions on SE that treat this argument. Mar 21, 2014 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!
– user96
Mar 21, 2014 at 13:15

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.

• Can you explain this in simple terms? I am not familiar with the mathematical description of Friedman models. Mar 21, 2014 at 16:29
• D'oh! What exactly you do not understand? Let's try to narrow the problem. Mar 24, 2014 at 0:38
• What exactly is the cosmological constant? Mar 24, 2014 at 10:15
• Did you try this? en.wikipedia.org/wiki/Cosmological_constant Would you like some math or a more physical explanation? Mar 24, 2014 at 10:45

Well, the original idea of the Big Crunch came about when it was thought that gravity was slowing down the expansion of the universe and that one day it will stop expanding (a finite universe). At which point the gravitational pull of all the objects in the universe would make it contract, growing smaller into itself until eventually it is just a singularity.

However, today we see that the universe is expanding and accelerating due to dark energy's effect on gravity making it an infinite universe. This makes the original idea of the Big Crunch not possible (since the universe would be infinite), but a big crunch can still occur in an alternate way if dark energy becomes too weak to counteract gravity which would set in motion the Big Crunch. However there is still so much unknown about dark energy that it is also possible that it will never weaken and the universe will just keep expanding, which opens different end of the universe theories.

• This is not correct. A Big Crunch scenario is still possible even in a presently accelerating Universe. It depends on the density of matter and cosmological constant (dark energy). Please edit your answer. Mar 20, 2014 at 1:47
• Yeah you are right, I forgot about the idea of dark energy weakening, I edited it to include that the infinite universe made it so the original Big Crunch theory not possible but that a Big crunch could still occur if dark energy were to diminish in strength. Mar 20, 2014 at 13:51
• 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. Mar 21, 2014 at 0:21
• So can we say that we cannot say anything for sure about the future of the Universe? And if the Universe is infinite then there's no way we could say that a thing called the Big Bang took place and the universe originated from a singularity. Mar 21, 2014 at 16:33
• @polyphant Yes, you are right. I thought you mentioned it being infinite in both directions. Jun 9, 2014 at 8:42