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# Why wouldn't the universe continue to expand at a greater rate? If F=G (m1m2)/r^2, and r^2 was to increase, ?

then wouldn't the resultant F effectively decrease (in all practicality)? It's not like we're talking about friction or some other resistance slowing things down. If r-5, then r^=25; but if r (through momentum) increased to 10, then r^=100. That's 4x the r for the same resultant (m1m2). You don't need dark energy to account for a never ending or even increasing rate of expansion. You simply needn't add more mass.

Demiurge42 & oldprof- My point exactly. The greater the distance between m1 & m2, the lower the effect of gravity which means less restraint on expansion.

neb- You mean E=mC^2? That's just another force equation (F=MA <which also assumes linear acceleration>). Any way you look at it, as r increases Fg's influence should decrease.

### 3 Answers

- nebLv 71 month ago
If you want to explain why the universe is accelerating it’s expansion, you have to use the right theory - and Newton’s gravity isn’t the right theory.

Einstein’s general relativity has replaced Newton’s gravity. Newton’s gravity is a weak field approximation to general relativity and doesn’t have the predictive power since it doesn’t account for ALL the sources of gravity.

The sources of gravity in general relativity are energy density (obviously including the energy equivalent of mass but also includes the energy density of massless fields), momentum density, and something specifically related to your question - pressure.

If you solve Einstein’s equations at the cosmological level (using energy density and isotropic pressure), the expansion rate of the universe will accelerate IF the pressure exceeds the energy density and if the pressure is negative.

So, if you include dark energy as a positive energy density, and dark energy that has a constant density even as the universe expands, then the dark energy will cause a negative pressure. The negative pressure will cause the universe to expand its intrinsic metric - a kind of repulsive gravity.

So, yes you do need dark energy density without actually needing the details of what that energy is. It just needs to be positive, and it’s density must be constant which means the total dark energy density must increase with the increasing volume of the universe.

Update - David, no E=mc^2 is not a force like F=ma. Mc^2 is the comoving T⁰⁰ component of the matter stress-energy tensor. My point in bringing that up is that Newton’s gravity doesn’t provide for fields with energy density such as dark energy and cannot deal with pressure components. Newton’s gravity CANNOT explain the accelerating expansion of the universe. The expansion came initially from the GUT symmetry breaking event that powered rapid expansion through gravity from negative pressure. Once that negative pressure was gone, the overall effect of gravity - excluding dark energy - has slowed the expansion rate and would continue to slow the expansion rate for ever. It CANNOT result in accelerated expansion without dark energy and modeling the gravity sources from general relativity. Forget Newton for this type of problem!!!

- oldprofLv 71 month ago
You have missed the point. The universe itself is expanding so it sort of forces an ever increasing and accelerating wedge of space between all the celestial bodies (i.e., the mass) in the global universe.

That expanding space has nothing to do with the gravity force except that the gravity forces between the masses and energy points will decrease due to the increasing space between them. My point is that the force f = kmM/r^2 is a result of the masses and the distances between them. It's not the net force causing space itself to expand.

In fact, as someone already pointed out, gravity is normally an attractive force resulting from the presence of mass and energy. It is not a repelling force, which is really what we need to explain the expansion, the repelling, of the universe.

So they've invented "dark energy" as the requisite repelling force. While there are several concepts as to what dark energy might be, there is still no empirical evidence to support any of the hypotheses. They are still in the dark about it.

- Demiurge42Lv 71 month ago
The force of gravitiy decreases with distance but the force is still there. Gravity is an attractive force, so it should still slow down the expansion. To have the universe expand faster, you'd need an outward force to cause that.