# Net curvature of the universe

1. Jul 19, 2006

### kmarinas86

In order for the universe to remain flat, doesn't the contribution to curvature by mass have to be cancelled out by the contribution by dark energy? If the mass contributes to positive curvature, then dark energy would be there to make a negative contribution to curvature.

And yet, without dark energy, the universe would be open and not flat (so that Omega=1), thus dark energy would have a positive contribution to curvature (as if it had mass which contributed to positive pressure)? Yet it makes the universe accelerate with negative pressure (thus a reason for having an open universe)?

Wouldn't dark energy cause the big bang as well? Or is that type-2 dark energy, something that is even more mysterious?

If one wrongly used SR to explain the recession of galaxies, one would have an effective "Hubble potential" = .5m(HD)^2, where HD is the Hubble velocity. This would make "Hubble potential" proportional to the square of the distance. For the General Relativistic case, would dark "energy" increase with the square of the distance (actually less than the square, since H is decreasing)?

But if dark energy makes a positive contribution to the curvature (towards closed geometry), providing 2/3rds of Omega=1, how does it make galaxies diverge (as if the universe were open)?

Or am I wrong in assuming that dark energy is the only thing causing the expansion?

The radius of the curvature of the entire universe, i suppose remains the same (i.e. no curvature) - does it?

I'm confused.

How can a flat universe accelerate it expansion? If dark energy couples with matter, how can an accelerated expansion promote flat universe? How can a open universe be flat? How can a hyperbolic system be Euclidean? How can the universe be flat, if it has no sign of halting its expansion? How can it be open when Omega=1?

Is this a mystery or just nonsense?

Last edited: Jul 19, 2006
2. Jul 19, 2006

### hellfire

Dark energy has a positive energy density and contributes to the curvature of space like any other component of the universe. This positive energy density contributes also to decelerate the expansion of space. However, unlike any other component of the universe, dark energy has a negative pressure that contributes to accelerate the expansion of space three times stronger than the deceleration caused by the energy density.

3. Jul 20, 2006

### Jorrie

I understand it that 'flat' and Omega=1 nowadays mean flat space, but that spacetime is open due to the accelerated expansion. Omega=1 simply says that the energy density equals the critical (balancing) value.

4. Jul 20, 2006

### hellfire

IMO the terms closed, open and flat should be used only when talking about geometry of space, but not when taking about the fate of the universe.

The source of confusion might be that in cosmological models without dark energy there is a clear relation between the geometry of space and the fate of the universe. Open and flat models expand forever and closed models collapse.

However, this relation is lost in models with dark energy. For example, a closed universe may expand forever if it contains enough amount of dark energy.

Last edited: Jul 20, 2006
5. Jul 21, 2006

### Chaos' lil bro Order

Recent WMAP data shows a preferred inhomogenity size of 1 degree, this supports the idea that the Universe's curvature is flat. Note that flat space doesn't neccesarily imply a static Universe. The best analogy of how the Universe expands when its curvature is flat (whilst neglecting dark energy of course), is considering a baseball thrown upwards into the sky with just enough velocity to escape Earth's gravitational field, so that the basedball constantly decelerates towards 0 velocity, but never reaches it. This is also consistant with Omega-matter = 1, if we again ignore dark energy.

The critical density (as I recall it) is equivalent to 6 Hydrogen atoms/ meter cubed. I find it funny that Omega-matter = only 27% of this tiny density (WMAP) and it makes one appreciate just how empty space really is between nebulae and galaxies. Imagine if a human which is approximately a meter cubed in volume, contained only 6 Hydrogen atoms, we would not be talking right now :).

6. Jul 21, 2006

### Chaos' lil bro Order

kmarina

If you could simplify your question or order them by number, it would be easier to help you.

7. Jul 22, 2006

### Jack Bauer

Not sure where to post this but I am puzzled by what seems to be a paradox concerning "wraparound" in 3-sphere universe and the expansion of the universe. If we could see to the edge of the universe and saw the opposite side because of "wraparound", would we see a red or a blue shift? Looking at the opposite side from "outside" as it were would mean blue shift, if the universe is expanding. Yet since the non-opposite outermost edge is also expanding, one could argue that it should appear with a red shift. Or would we see both? Could such an observation be used to prove we live in a 3-space?