# Universe expansion and general relativity [closed]

If the universe is expanding faster and faster, won't we reach a moment where the general relativity will make the mass so big, that the universe will have to decrease its acceleration?

• It was answered in the following response., but thanks. – Kaloka Feb 19 '16 at 22:16
• How does general relativity "make the mass so big"? – Kyle Kanos Feb 20 '16 at 11:43

The expansion of the universe is stranger than it appears at first glance. For a start, the Big Bang didn't happen at a point like some kind of explosion. When we say the universe is expanding we mean that the distance between any two stationary points (I'll get on what we mean by stationary in a moment) increases with time.

Suppose we take two points $A$ and $B$. For convenience we'll put $A$ at the origin then we can write the position (in space) of $B$ as $(x, y, z)$. Here the $x$, $y$ and $z$ coordinates are comoving coordinates, and when we say $A$ and $B$ are stationary we mean their comoving coordinates do not change with time. If you remember Pythagoras' theorem then you'll remember that the distance $d$ between $A$ and $B$ is:

$$d^2 = x^2 + y^2 + z^2$$

(This only applies to a flat universe, but our universe appears to be flat so that's OK)

When we say the universe is expanding we mean that the distance is actually given by:

$$d^2 = a^2(t)(x^2 + y^2 + z^2)$$

where $a(t)$ is a function called the scale factor that changes with time. If $a$ is increasing with time that means the distance between $A$ and $B$ is increasing with time and that means the universe is expanding i.e. the distances between stationary objects are increasing with time. We generally take the value of $a$ to be one right now, so $a$ was smaller than one in the past and will be bigger than one in the future.

If you're interested I talk about how we calculate $a$ in How does the Hubble parameter change with the age of the universe?.

But to get back to your question:

I would guess that when you say mass increases you mean the fact that relativistic mass increases as you approach the speed of light. So if distant galaxies are speeding away from us their mass must be increasing. However those distance galaxies are (approximately) stationary with respect to us just like $A$ and $B$ in my discussion above. All that is happening is that the distance between us and the distant galaxies is increasing with time. So the distant galaxies aren't getting more massive, and for completeness they aren't suffering any relativitic time dilation either.

But there is a sense in which you are correct that mass could stop the expansion, though in our universe it doesn't appear this will happen. The way the scale factor changes with time depends on the average density of the universe. If the density is lower or equal to the critical density then $a$ just increases smoothly with time and the universe keeps getting bigger. If the average density is higher than the critical density then $a$ increases at first, but then peaks and starts to decrease again, which means the expansion of the universe slows to a stop then reverses.

As far as we can tell the density of our universe is too low for the expansion to reverse. In fact the presence of dark energy means the expansion will keep getting faster and in the far future the scale factor will increase exponentially with time.

• Your answer was incredible neat. I had these two hypothesis, like, is it expanding in the space or the space itself. But I just wonder why now, that "we"defined a space-time, when we talk about the expansion since big bang, every body talks about the space expansion only, and nothing about time. It is an intuition that the universe has different ages in differents regions of the universe, since space time is stretching in an unknown manner. – Kaloka Feb 19 '16 at 22:03
• @Kaloka: time is (approximately) the same everywhere in the universe. See for example this question, this question and this question. – John Rennie Feb 20 '16 at 6:28
• @Kaloka: for a (alightly technical) discussion of how time differences between different bits of the universe can arise see Is the cosmological time grosso modo isochrone? – John Rennie Feb 20 '16 at 6:29

Because relativistic mass only arises because of motion through space, not motion with space. For more details google "peculiar velocity" and "recessional velocity". Susskind explains this here.

• and dark energy ? is it counted as gravitational energy ? – user46925 Feb 19 '16 at 22:04
• To quote Wikipedia: "Dark energy is thought to be very homogeneous, not very dense and is not known to interact through any of the fundamental forces other than gravity." and "According to general relativity, the pressure within a substance contributes to its gravitational attraction for other things" - dark energy has a negative pressure, so it manifests as gravitational repulsion. – Yukterez Feb 19 '16 at 22:48
• then it weighs even if its property of negative pressure accelerates the expansion. I just want to understand its role when we say that it is 70% of the whole energy and that contibutes to get the universe flat. Anyway there is a shell effect. TY – user46925 Feb 19 '16 at 23:08

Per dark energy hypothesis -

It does not increase mass or kinetic energy, because it is expansion of space itself, and universe is expanding with space, not into it.

Actually, it is supposed to be other way, expansion increases the dark energy in the universe, which is expected to be cause of the acceleration to begin with.

In one speculation, the process is expected to continue till everything flies apart including atoms and subatomic particles.

Not my opinion, it is per the hypothesis.

However, there are other speculations that the dark energy may change from repulsion to attraction some time in the future, and then, yes, the expansion would slow down.

They have already detected at least one cycle of accelerated expansion, and slowdown in the past. Last switch from slow down to acceleration is supposed to have happened nearly 5 billion years ago.

• "The process is expected to continue till everything flies apart including atoms and subatomic particles. Not my opinion, it is per the hypothesis." > This is not correct, this only happens in the Big Rip scenario where not only the expansion accelerates because the Hubbleparameter converges to a constant value, but the Hubbleparameter would also increase because the amount of dark energy per cubic meter would increase, which is not the case in standard cosmology. We only have accelerated expansion because the Hubbleparameter will converge to a constant, therefore the "cosmological constant" – Yukterez Feb 19 '16 at 20:33
• Dark energy is a speculation and so are the consequences in different scenarios, big rip is one such scenario. So my answer was more in general terms rather than trying to being theoretically correct because the whole thing is still a speculation. A made up concept to explain the otherwise in-explainable. – kpv Feb 19 '16 at 20:58
• If you say "In one speculation" there's nothing wrong with your text, but the observations from WMAP and Planck lead to the conclusion that dark energy is constant. Speculation or not, it is an established part of mainstream physics. – Yukterez Feb 19 '16 at 22:43
• Dark energy is constant per volume of space, or it is constat in the whole universe? – kpv Feb 19 '16 at 22:52
• Constant energy density, not constant energy. Also see physics.stackexchange.com/questions/168101/… – Yukterez Feb 19 '16 at 22:53