How can we predict a Big Crunch?

[Yashbhatt]

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?

 

[Simon Bridge]

Same way you can predict that any object currently getting farther from you will eventually return: it is decelerating.

If the expansion is slowing enough, then it will eventually reverse.
ifaik, it looks like the expansion is accelerating so - no big crunch.

 

[Yashbhatt]

Has there been any evidence or theory which predicts deceleration?
If not so, how did the concept of Big Crunch originate

 

[Mordred]

The big crunch was one of the possibilities of the universes fate. Evidence today from WMAP and Planck data no longer supports the big crunch as a possible fate. Today we know the universe is approximately flat with a cosmological constant causing expansion.

The article written by myself with help from PF members will show the metrics involved on the three most likely possible fates. Currently unless something changes we are heading towards "heat death".

https://www.physicsforums.com/showpost.php?p=4697773&postcount=30

 

[phinds]

Has there been any evidence or theory which predicts deceleration?
If not so, how did the concept of Big Crunch originate

Not very many years ago, it was believed that the universe's expansion was slowing down under that force of gravity and that the expansion would reverse and end up in the big crunch. To everyone's surprise, it turned out not only to not be slowing down but to actually be accelerating. This was SUCH a surprise that at first people thought that the data might be wrong but soon realized that no, the data is right and the acceleration is real and the big crunch isn't going to happen.

 

[Simon Bridge]

Executive summary:

Has there been any evidence or theory which predicts deceleration?

Yes.

... how did the concept of Big Crunch originate

It was made up in someone's brain like all theories originate ;)

There was a time when less was known about the Universe than now and such possibilities abounded.
The progress of empirical research is (simplistically) to remove theories that are wrong, so old possibilities vanish and new one spring up in their places as we learn more about the Universe.

The quite recently observed and confirmed "acceleration" is why we need a theory of "dark energy" and the cosmological constant has been restored to Einsteins equations.

Einstein originally introduced the cosmological constant for somewhat different reasons.
You can look up the history online. i.e.
http://ned.ipac.caltech.edu/level5/Sept02/Padmanabhan/Pad1_2.html

 

[Yashbhatt]

Friedman proposed three models for the universe. One of them was about the Big Crunch. But why did he introduce such a model when Hubble had already discovered that all galaxies are not only moving away but accelerating?

 

[Simon Bridge]

The data may have been wrong. Do you have a reference for that?
It is also possible to gain insights from postulating a known incorrect model... if only to demonstrate formally that it is inconsistent with observations.

Did you read the link?

 

[George Jones]

Hubble had already discovered that all galaxies are not only moving away but accelerating?

I think you are confusing "accelerating" with Hubble's law of recessional speed increasing with distance. These are two different things. At the risk of further confusion:

consider a toy universe and galaxies A, B, C, D at three different instants of cosmological times, t = 1, t = 2, and t = 3.

At times t = 1, t = 2, and t = 3, the proper distances to galaxies A, B, C, D are given by the table:

$$\begin{matrix} & | & A & B & C & D \\ -- & | & - & - & - & - \\ t = 1 & | & 1 & 2 & 3 & 4 \\ t = 2 & | & 4 & 8 & 12 & 16 \\ t = 3 & | & 9 & 18 & 27 & 36 \end{matrix}$$

At times t = 1, t = 2, and t = 3, the recessional speed of galaxies A, B, C, D are given by the table:

$$\begin{matrix} & | & A & B & C & D \\ -- & | & - & - & - & - \\ t = 1 & | & 2 & 4 & 6 & 8 \\ t = 2 & | & 4 & 8 & 12 & 16 \\ t = 3 & | & 6 & 12 & 18 & 24 \end{matrix}$$

What are the values of the Hubble constant $H$ at the three times? Since $v = H d$, the Hubble constant is given by $H = v/d$. This give that $H$ equals 2, 1, and 2/3 at times 1, 2, and 3.

Note: 1) at each instant in time, the Hubble constant is constant, i.e., independent of the galaxy used to calculate it; 2) the Hubble constant decreases with time.

What about acceleration or deceleration of the expansion of this universe? During the time interval from $t = 1$ to $t = 2,$ Galaxy A "moves" a distance $\Delta d = 4 - 1 = 3$. During the later but equal-length interval from $t = 2$ to $t = 3,$ the same galaxy, Galaxy A, "moves" a greater distance, $\Delta d = 9 - 4 = 5$. This is an indication that the expansion of the universe is accelerating. The fact that this universe is accelerating is independent of which galaxy is used.

This toy model is a Freidman-Robertson-Walker universe that has its scale factor given by $a(t) = t^2.$

As an example of a decelerating (but still expanding) universe that has a Hubble constant that decreases with time, Consider a toy universe and galaxies A, B, C, D at three differents instants of cosmological time.

Table of proper distances $D$ from Milky Way:

$$\begin{matrix} & | & A & B & C & D \\ -- & | & - & - & - & - \\ t = 1 & | & 1 & 2 & 3 & 4 \\ t = 2 & | & 1.4 & 2.8 & 4.2 & 5.7 \\ t = 3 & | & 1.7 & 3.5 & 5.2 & 6.9 \end{matrix}$$

Table of recessional speeds $v$ from Milky way:

$$\begin{matrix} & | & A & B & C & D \\ -- & | & - & - & - & - \\ t = 1 & | & 0.5 & 1 & 1.5 & 2 \\ t = 2 & | & 0.35 & 0.71 & 1.1 & 1.4 \\ t = 3 & | & 0.29 & 0.58 & 0.87 & 1.2 \end{matrix}$$

The Hubble constant equals 1/2, 1/4, and 1/6 at times 1, 2, and 3.

Also, as can be seen, the universe is decelerating.

This toy model is a Freidman-Robertson-Walker universe that has its scale factor given by $a(t) = t^{1/2}$, and, qualitatively, echos the way we thought the universe behaved (near t = now) before we had the 1998 supernova data.

 

[Simon Bridge]

Yep, on checking...

Friedman proposed three models for the universe. One of them was about the Big Crunch. But why did he introduce such a model when Hubble had already discovered that all galaxies are not only moving away but accelerating?

... there was no reason for Freidman to discard a big-crunch solution in 1922 [1] since the cosmological acceleration was not discovered until 1998 [2].

Looking a bit further:
Hubble showed expansion in 1929. [3] The Hubble Expansion was actually first proposed in a 1927 paper by George Lamatre [4].

Freidman seems to have been just working the (then new) Einstein equations (1915) [5] to some logical conclusions with no more reason to reject those solutions that suggest an eventual contraction than those solutions that suggest expanding forever.

So: where are these questions coming from?

---------------------------

[1] Friedman, A (1922). "Über die Krümmung des Raumes". Z. Phys. 10 (1): 377–386.
[2] Nobel Prize for Physics (2011): Permutter, Reiss, and Schmidt for work done in 1998.
[3] Hubble, E., 1929, Proc. Nat. Acad. Sci. USA 15, 168.
[4] Lemaître, G. (1927). "Un universe homogène de masse constante et de rayon croissant rendant compte de la vitesse radiale des nébuleuses extra-galactiques". Annales de la Société Scientifique de Bruxelles A 47: 49–56.
[5] Einstein, Albert (November 25, 1915). "Die Feldgleichungen der Gravitation". Sitzungsberichte der Preussischen Akademie der Wissenschaften zu Berlin: 844–847.

 

[Yashbhatt]

I am sorry. I thought the acceleration was discovered at the same time when the expansion was discovered.

 

[Simon Bridge]

Easy mistake ... but even if it had been, the expansion appears to have been discovered too late to help Freidman discard the crunch and steady-state solutions.

... but that would be your question answered?

 

[timmdeeg]

Friedman proposed three models for the universe. One of them was about the Big Crunch. But why did he introduce such a model when Hubble had already discovered that all galaxies are not only moving away but accelerating?

Friedmann discovered these three models, which makes a difference. They are solutions of the Einsteinian equations and thus don't include any observations or proposals. However those are necessary to select one of the possible models.

 

[Yashbhatt]

@ Simon Bridge Yes. @timmedeeg I get your point.