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I like your big bounce scenario too, would it be possible without negative radiation density? Tweaking the w parameter might be the most plausible way
Yes, let's take a closer look at it! To make the universe collapse, I'll give it much greater than the critical density of matter. But to make it rebound before collapsing to zero size, I'll have to fill it with something that causes acceleration, and that thing will need to dominate the total mass-energy density when the universe is a very small size, and be negligible when the universe is larger. This means it must dilute with expansion faster than matter. Actually the most natural thing that dilutes in the required way is radiation. But we want to keep radiation in the model and keep the radiation gravitationally attractive (positive mass density).
So we'll change the dark energy, and give it w=1/3 so that it dilutes like radiation and dominates at small scale factor. But there's another problem if we do that: any substance with a positive energy density and with equation of state w>-1/3 will cause deceleration. And what we want is acceleration
. (Dark energy does not accelerate the expansion because it is "repulsive". It accelerates the expansion because it does not dilute!) So to make the dark energy dilute like radiation and still cause acceleration for a rebound, I must change its density to negative.
In this way, what we're describing is exactly equivalent to repulsive photons, anyway. But we'll just call
it dark energy with a negative energy density and a different equation of state w=1/3.
Let's run the model. Well set Ωm
=-0.5, and w=1/3. Maybe we'll call this "An'shur's Cyclic Universe"
Here's the scale factor over time:
This universe has no clear beginning or ending. It just endlessly oscillates between near-crunches. I have to have some sort of label for the initial simulation time though, and I set it to be t=0 at the moment of a bounce. Then I choose the present time to be when the universe is collapsing, not the first time, but the second time, 25.6 billion years later. The contraction rate at this moment is -100km/s/Mpc:
How do the matter, radiation, and "dark energy" densities change with time?
The dark energy density (green) is negative, so I plot the negative of it so that it shows up on a logarithmic scale. The absolute value of the dark energy density is always less than the matter, except for the brief moments that the universe is rebounding, where its density spikes and causes the sudden acceleration to re-expansion.
Plotting the densities in terms of their ratios to the critical density makes quite a pretty graphic as well. Here Ωk is 1 minus the sum of all the others and can be thought of as a "curvature density". The effect of this curvature density will become more clear in a moment.
And now, the thing which I think is the most interesting of all: the space-time diagram:
What the heck is happening here?!
Well, here I am showing something which I did not show earlier when we looked at the closed, collapsing universe model. That time I had treated the geometry of space as being flat (Euclidean), which is actually not true when the total density is greater than the critical density. This time I include the effect of the spatial curvature. Because this universe has such a high density, space curves back on itself, like the surface of a sphere, but in 3 dimensions. Travel far enough in any direction in this universe, and you will return to your origin! The distance to this boundary where space has curved back on itself and distances start diminishing again is shown with the solid white curve labelled "curvature horizon". Its size is related to the value of the curvature density, Ωk.
Because of the curvature, there is no space beyond that horizon. This universe is "closed", and its volume is finite.
Another odd feature of the curvature is that proper distances are greater than we would expect from a flat geometry. The 2D analogy with the curvature of a sphere helps here too: the distance to the opposite side of the Earth is greater as measured over the surface than if you tunneled straight through the middle. Near the antipodal point, distances over the surface grow rapidly, for just a small change in direct distance through the Earth. This property of the curvature explains why the light paths curve the way they do, with sharp cusps near the curvature horizon.
Light rays which are currently arriving at our location during this second contraction phase have had a crazy journey. Because of the closed spatial geometry, the light rays have circled around the universe multiple times during each bounce. We will see multiple images of the same galaxies! Also, because the universe bounces at a finite size rather than going full crunch to singularity, we can trace the paths of those light rays through the bounce! Previous bounces of the universe are visible! This would be a very trippy universe to live inside of, like the inside of a spherical mirror, but where moving toward the edge leads you back to where you started.
Would it be survivable? Maybe! But it sounds rather dangerous. If it has stars and galaxies and planets and so forth, then the rates of galaxy mergers must become extraordinarily high during the bounces. The energy density of radiation will also get more intense, with all the photons being brought together and blueshifted to higher energy. But in principle, there's nothing making a bounce unsurvivable to an observer who is well equipped to pass through it. I imagine it would be an amazing spectacle, if you lived long enough to watch the change.
A close-up of the galaxies and light rays through the bounce:
Wild... I think this is one of the more fascinating "types" of universes that can come out of the equations (and the physics).
Of course, the material requirements for it are quite unphysical. We know of no substance that dilutes like photons but has negative energy, and we are so confident that dark energy does not have w as high as 1/3 that it's insane. This is more of an academic exercise of "let's play with the parameters to make neat things happen." A deeper problem is that it's very ambiguous as to how such a universe would get started. Our universe has a clear evolution from the Big Bang, but what was the initial state of a cyclic universe?
Perhaps we must conclude it has existed like this forever.
Or maybe it is a simulation on a computer somewhere...