Cool post, and a lot to cover with it so apologies in advance for the length!

Gnargenox wrote:Source of the post Is not Gravity the force that keeps the bowling balls from becoming larger? Gravity has also been keeping all other matter from being ripped apart, ever since the expansion rate started accelerating 7 billion years after the universe came into being.

The bowling balls are held together by the inter-atomic forces, which is far stronger of a binding than their gravitation.Gravitation becomes the dominant binding for much larger masses like planets, stars, galaxies, and galactic clusters. The space within galactic clusters is also not expanding anyway, because the gravitation causes it to change from the expanding FLRW metric to the non-expanding Schwarzschild metric. In a sense, the space within these regions has "broken off" from the expansion.But, does that mean the force of Gravity also changed since things before this rate change where still the same size as after it accelerated?

Not quite. The gravitational force stays the same. G is a constant, and the laws of gravitation (whether Newtonian or general relativistic) also stay the same.

Something else does happen with this shift of the universe from being radiation dominated to matter dominated to dark energy dominated: the rate of change of the expansion changes. That is, the acceleration changes. For a radiation dominated universe, the scale factor is proportional to the square root of time. For matter dominated it's proportional to time to the 2/3rd power, and for dark energy dominated it's exponential. The reason for this has to do with how the density of matter, radiation, and dark energy change as the universe expands.Gnargenox wrote:Source of the post Also around this same time the universe switched from being dominated by photons and neutrinos to being dominated by both normal matter and Dark Matter. The universe was fairly equal in density in all directions, but can it not stay stable without expansion?

The universe being equal in density in all directions is *always* true, as far as data can show. This is the cosmological principle: on large enough scales the universe looks the same no matter where you are (homogeneity) or which direction you look (isotropy), and it was as true very close to the Big Bang as it is true today. But I'm not quite sure what you mean about it being stable. Are you talking of being able to be static -- remaining neither expanding or contracting? This is possible if the dark energy density exactly balances the tendency for matter and radiation to pull the universe back together, but it is an unstable equilibrium. Einstein himself tried to model a static universe by introducing the cosmological constant, but alas a universe balanced this way would be like balancing a pencil on its point. Even the smallest fluctuation would immediately result in the universe collapsing or expanding.Gnargenox wrote:Source of the post For some reason when Dark Energy reached 33% of the total energy density in the Universe, the expansion rate began accelerating.

That's right, and we can show that this follows from the Friedmann equations, which describe the universe's expansion rate as governed by general relativity and its contents (matter, radiation, and dark energy). Let's do a bit of math. We can write the first equation asThe term on the left side describes the expansion rate of the universe. Specifically, **a** is the scale factor ("size" of the universe), and **a** with a dot over it is the time derivative (its expansion velocity). So [math]\frac{\dot{a}}{a} is the expansion velocity per distance, which is Hubble's constant.The right side of the equation describes the universe's contents. Each of the Ω's represents a type of mass or energy density. The one with subscript **m** represents matter density, **r** is for radiation, and **Λ** is for dark energy. These are all expressed in terms of the critical density (the specific density which would make the spatial curvature of the universe flat.) In fact the spatial curvature is very close to flat, so total density is close to the critical density and the sum of these Ω's is about 1. The actual values today are about 10^{-4} for radiation (pretty negligible), 0.3 for matter, and 0.7 for dark energy.Let's use this equation to figure out something about the universe's acceleration (in effect, deriving the acceleration equation). To do this, start by moving the denominator a

^{2} over to the right hand side:

Now take the time derivative of both sides [remember to use the chain rule: e.g. derivative of a

^{2} is 2a(da/dt)].

Finally, solve for the acceleration (the

**a** with two dots over it, meaning 2nd time derivative of the scale factor)

The universe switching from decelerating to accelerating corresponds with

[math]\ddot{a} = 0. So we can set this equation to zero to see what conditions on the dark energy density will satisfy that. Let a=1 across the board, and also let Ω

_{r }be zero, since by the time dark energy can start to dominate, the radiation density will already be negligible. We then get Ω

_{Λ} = 1/2Ω

_{m}. But the total density is Ω

_{Λ + }Ω

_{m}, which is 3Ω

_{Λ}. So the dark energy density at the onset of acceleration is 1/3 of the total density. Neat!

Gnargenox wrote:Source of the post Since that time, some 6 billion years ago, the matter density has continued to drop, while dark energy has remained a constant. As time goes on in the future, the matter density will continue to drop, while the dark energy density will remain constant, meaning dark energy becomes more and more dominant. Does perhaps Dark Energy also keep things from "snapping" or turning into atomic vapor?

Dark energy is the agent that would snap them, if it is strong enough.

For an analogy (which is not quite correct, but a decent starting point), you can think of dark energy as acting like a small repulsive force between particles. In a solid, the atoms or molecules or whatever are bound together like masses attached by springs. What then happens if you introduce a small repulsive force between two masses connected by springs? It simply increases the equilibrium position. If the force becomes too strong, it may tear them apart.

In reality dark energy's effect is, like the basic expansion, only really meaningful on large scales -- larger than galactic clusters. However, in the hypothetical "Big Rip" scenario, where dark energy is assumed to have an equation of state that leads to it getting stronger over time, it could very well overwhelm all structures, tearing things apart from top down. Galaxies in clusters would be separated first, then the stars from each other, then the planets from their stars, and finally down to the atoms.

I think most cosmologists view this scenario as unlikely on physical grounds, though the best we can do with data is constrain how far into the future it would have to happen, if it happens at all. For more detail and data about it I can refer to the second half of my post

here.

Gnargenox wrote:Source of the post Another neat thing about Expansion is that, on average, 20,000 stars transition every second from being reachable by us at the speed of light to being unreachable. The light they emitted a second ago will someday reach us, but the light they emit this very second never will.

I've never checked the actual number, but that is a neat thing to think about.

Or maybe depressing, I'm not sure... Another interesting (and often confusing) thing is that we can continue to see those objects, even though their recession speeds are faster than light. It just means we don't receive signals they are releasing "now", and we can't ever reach or send signals to them.

We look outward and see all these distant galaxies, yet as time goes on they are pulled out of our reach, though not from view. What a cruel thing. The size of our playground gets bigger, but the amount of stuff we are allowed to play with grows smaller.