Acceleration of Universe Expansion: 1/r2

[Gannet]

It seems to me as the space between galaxies expands it reduces the gravitational attraction between them. Assuming that this is happening between the majority of the galaxies in our Universe it would cause the acceleration of expansion by a factor of 1/r².

 

[Bandersnatch]

No, it reduces the deceleration. Even as the force of gravity decreases with increasing distance, its direction of stays inward, and it's the only one acting (without counting dark energy).

The expansion of the universe is not like a force, but like inertial motion in a gravitational field with some initial impulse. In a universe without dark energy the expansion is always decelerating.

Same as with shooting a projectile or launching an (unpowered) space probe - the weakening gravitational field as you get higher/further doesn't cause acceleration, just reduced deceleration, and the objects rely on the initial velocity to carry them along.

 

[jEANNE RUPPERT]

How does/would this relate to the 'cosmological constant'?

 

[PeroK]

How does/would this relate to the 'cosmological constant'?

The cosmological constant in modern cosmology is the vacuum energy (or "dark" energy) that drives an accelerated expansion. Without the vacuum energy there would still be expansion, but it would be slowing down.

Originally, Einstein introduced a different cosmological constant to prevent expansion (because at the time it was assumed that the universe was static). If he had had the courage, he could have predicted an expanding universe when he published his theory of GR in 1915.

https://en.wikipedia.org/wiki/Cosmological_constant

 

[PeroK]

It seems to me as the space between galaxies expands it reduces the gravitational attraction between them. Assuming that this is happening between the majority of the galaxies in our Universe it would cause the acceleration of expansion by a factor of 1/r².

That's like saying that a rocket fired from Earth will speed up as it gets further from the Earth, as the gravitational attraction reduces. Instead, of course, it slows down less quickly - which is equivalent to a decelerating expansion. And, depending on whether it has the required escape velocity, it either continues to move away at an ever decreasing rate, or eventually stops and falls back to Earth.

 

[Gannet]

Prior to the discovery that the expansion of the Universe was accelerating in 1998, it was assumed that the expansion of the Universe would be decelerating because of gravitational attraction.

Since gravitational attraction is based on the Mass between the two galaxies of interest which is not changing and the inverse square of the distance between them which is changing because the space between the galaxies is expanding.

Then, what I am indicating the gravitational attraction between most of the galaxies are reducing at an inverse square rate and is contributing to the acceleration of the expansion of space. In other words, there is a positive feedback mechanism existing in the gravitational attraction formula.

 

[PeroK]

Prior to the discovery that the expansion of the Universe was accelerating in 1998, it was assumed that the expansion of the Universe would be decelerating because of gravitational attraction.

Since gravitational attraction is based on the Mass between the two galaxies of interest which is not changing and the inverse square of the distance between them which is changing because the space between the galaxies is expanding.

Then, what I am indicating the gravitational attraction between most of the galaxies are reducing at an inverse square rate and is contributing to the acceleration of the expansion of space. In other words, it is a positive feedback mechanism existing in the gravitational attraction formula

It's been explained clearly in this thread why that is very wrong.

 

[Gannet]

That's like saying that a rocket fired from Earth will speed up as it gets further from the Earth, as the gravitational attraction reduces. Instead, of course, it slows down less quickly - which is equivalent to a decelerating expansion. And, depending on whether it has the required escape velocity, it either continues to move away at an ever decreasing rate, or eventually stops and falls back to Earth.

Yes, it would have speed up if the thrust remains constant and if it is outside the Earth's atmosphere

 

[PeroK]

Yes, it would have speed up if the thrust remains constant and if it is outside the Earth's atmosphere

Galaxies don't have engines, so the analogy is with a rocket cruising through space. If it has working engines, it can go where it likes.

 

[Gannet]

It's been explained clearly in this thread why that is very wrong.

No, it hasn't been explained. The only one

Galaxies don't have engines, so the analogy is with a rocket cruising through space. If it has working engines, it can go where it likes.

The space between the galaxies is expanding, carrying the galaxies with it.

 

[PeroK]

No, it hasn't been explained. The only one

The space between the galaxies is expanding, carrying the galaxies with it.

And without dark energy that expansion must slow down. The correct analysis is to use the Friedmann equation, but heuristically it's like decelerating due to gravitational attraction.

This was explained in the second post:

No, it reduces the deceleration. Even as the force of gravity decreases with increasing distance, its direction of stays inward, and it's the only one acting (without counting dark energy).

The expansion of the universe is not like a force, but like inertial motion in a gravitational field with some initial impulse. In a universe without dark energy the expansion is always decelerating.

Same as with shooting a projectile or launching an (unpowered) space probe - the weakening gravitational field as you get higher/further doesn't cause acceleration, just reduced deceleration, and the objects rely on the initial velocity to carry them along.

A post which you "liked".

 

[Gannet]

And without dark energy that expansion must slow down. The correct analysis is to use the Friedmann equation, but heuristically it's like decelerating due to gravitational attraction.

This was explained in the second post:A post which you "liked".

Which came closest to understanding the question

 

[PeroK]

Which came closest to understanding the question

We all understand the question. If you expect objects to speed up under gravity as they move further apart, then you're wrong. Unless, there is another "force" pushing them apart: the role of that force is played by dark energy. Without it, you simply have deceleration due to mutual gravity.

 

[Gannet]

And without dark energy that expansion must slow down. The correct analysis is to use the Friedmann equation, but heuristically it's like decelerating due to gravitational attraction.

This was explained in the second post:A post which you "liked".

What is being claimed is that Dark Energy is the cause of the acceleration of the expansion. And if the deceleration of the expansion is due to the gravitational attraction, then the opposite is true the acceleration is due to the reduction in gravitational attraction because of the positive feedback that continue to occur as the space expands even at a constant velocity.

 

[PeroK]

What is being claimed is that Dark Energy is the cause of the acceleration of the expansion. And if the deceleration of the expansion is due to the gravitational attraction, then the opposite is true the acceleration is due to the reduction in gravitational attraction because of the positive feedback that continue to occur as the space expands at a constant velocity.

This is where the Newtonian model breaks down, as there is no such thing as "expansion of space" in Newtonian gravity. This question came up recently - how far can you push the heuristic Newtonian model?

The model you're using maps the concept of expansion of space (GR and the Friedmann equation) to objects moving apart (Newtonian). It's one or the other. You're mixing the two.

In the Newtonian model, the expansion of space is modeled by objects moving apart. There's no additional expansion of space.

In the GR model, the objects are not moving, but space is expanding.

It's one or the other; but not both.

 

[Gannet]

This is where the Newtonian model breaks down, as there is no such thing as "expansion of space" in Newtonian gravity. This question came up recently - how far can you push the heuristic Newtonian model?

The model you're using maps the concept of expansion of space (GR and the Friedmann equation) to objects moving apart (Newtonian). It's one or the other. You're mixing the two.

In the Newtonian model, the expansion of space is modeled by objects moving apart. There's no additional expansion of space.

In the GR model, the objects are not moving, but space is expanding.

It's one or the other; but not both.

OK Thanks I did not know that.

 

[Bandersnatch]

In the GR model, the objects are not moving, but space is expanding.

That's not strictly true, is it? Whether objects are moving apart or the space is expanding is due to the choice of coordinates. In comoving coordinates it's the latter, in proper coordinates it's the former. There's no real physical difference between the two.

 

[PeroK]

It's not false, either. At the level of this thread, implicitly using comoving coordinates seemed appropriate - especially given we're debating the heuristic Newtonian model.

 

[Bandersnatch]

That doesn't make it not true. And I don't see why you think comoving coordinates are more appropriate here. If anything, proper coordinates are more intuitive, as they map to Newtonian intuitions.
In any case, the issue here seems to be how the OP understands, or misunderstands, Newtonian mechanics. It doesn't look to me as having anything to do with using the wrong model.

 

[PeroK]

That doesn't make it not true. And I don't see why you think comoving coordinates are more appropriate here. If anything, proper coordinates are more intuitive, as they map to Newtonian intuitions.
In any case, the issue here seems to be how the OP understands, or misunderstands, Newtonian mechanics. It doesn't look to me as having anything to do with using the wrong model.

You're more than welcome to pick up from post #10:

The space between the galaxies is expanding, carrying the galaxies with it.

I explained things using (implicitly) comoving coordinates. If that's not to your taste, then give an alternative explanation in proper coordinates or in a coordinate-free way.

 

[Bandersnatch]

And if the deceleration of the expansion is due to the gravitational attraction, then the opposite is true the acceleration is due to the reduction in gravitational attraction

Look. To ever get any acceleration, you need the nett force vector to change direction. The force of gravity, even as it's decreasing with the square of the distance, always points in the same direction. No matter how large r you choose, it is always decelerating. You need that additional effect of dark energy (or, for a rocket, it's engine being on, as opposed to unpowered flight after launch), acting as a force with opposite direction, to (eventually) cause acceleration. Only then can you talk about how the different scaling between the two forces (1/r^2 for gravity vs r for DE) leads to deceleration changing into acceleration.

 

[Gannet]

Look. To ever get any acceleration, you need the nett force vector to change direction. The force of gravity, even as it's decreasing with the square of the distance, always points in the same direction. No matter how large r you choose, it is always decelerating. You need that additional effect of dark energy (or, for a rocket, it's engine being on, as opposed to unpowered flight after launch), acting as a force with opposite direction, to (eventually) cause acceleration. Only then can you talk about how the different scaling between the two forces (1/r^2 for gravity vs r for DE) leads to deceleration changing into acceleration.

Thank you for helping me understand

 

[elcaro]

The feedback mechanism of the cosmological expansion is due to the simple fact that the energy density of space is constant and this energy also causes the expansion, so the more it expands, the more space with constant energy density, the faster the cosmological expansion.

 

[PeterDonis]

The feedback mechanism of the cosmological expansion is due to the simple fact that the energy density of space is constant and this energy also causes the expansion

I assume you mean specifically the energy density associated with the cosmological constant (aka dark energy), correct?

 

[elcaro]

I assume you mean specifically the energy density associated with the cosmological constant (aka dark energy), correct?

Yes, you are right. Because (unlike any other form of energy or mass) it has negative pressure, and that is what causing the expansion. Normal forms of energy/matter and radiation only decelerate the expansion.