Universe re-collapse and time reversal

[Ranku]

If the universe were to re-collapse, the Hubble constant would increase over time. Since the age of the universe is the inverse of the Hubble constant, the age of the universe will decrease. Does that mean time reversal?

 

[Orodruin]

No. In a recollapse the Hubble constant would first decrease to eventually go negative.

It is also not true that the age of the Universe is as simple as the inverse of the Hubble parameter. It depends on what you assume about what dominates the expansion.

 

[Bandersnatch]

The inverse of the Hubble parameter tells you how long it'd take to cover the distance between any two points, given their recession velocity.
This equals the actual age of the universe only if the scale factor grows linearly. I.e. the recession velocities stay constant - Which requires an empty universe. In our universe, up to this moment, there was a period of deceleration, and a period of acceleration, in roughly equal measure. Just so that the growth of the scale factor can be roughly approximated as linear. The approximation was much more off in the past, will be better in a few billion years, and will be increasingly more off for the reminder of time. It's only in this sense that the inverse of H gives the age of the universe. There's no fancy-shmancy arrow-of-time physics involved.

 

[Ranku]

In a recollapse the Hubble constant would first decrease to eventually go negative.

What do you mean by 'go negative' - as in having a negative sign?

 

[Ibix]

What do you mean by 'go negative' - as in having a negative sign?

Yes. The further away things are in a collapsing universe, the faster they move towards us.

 

[Ranku]

Yes. The further away things are in a collapsing universe, the faster they move towards us.

But isn't that counterintuitive, since gravitational attraction, and therefore acceleration only increases as objects approach each other.

 

[Orodruin]

But isn't that counterintuitive, since gravitational attraction, and therefore acceleration only increases as objects approach each other.

No. It is a direct consequence of homogeneous expansion/contraction.

 

[Bandersnatch]

But isn't that counterintuitive, since gravitational attraction, and therefore acceleration only increases as objects approach each other.

You're making the mistake of thinking of Hubble's law as if it were describing the motion of a single point across a range of distances, whereas it describes the state of motion of different points at a moment in time.

Start with the moment when an initially expanding universe is decelerated so that it's neither expanding nor contracting (it's at the inflection point, just before the contraction begins).
At this moment, every recession velocity, of any distant point, is zero, and the Hubble parameter is zero.
Then the points start approaching. The point A at distance d from the observer is accelerated inward by all the mass that is contained within a sphere of radius d. Point B at distance 2d is accelerated by all the mass within a sphere of radius 2d. I.e. points further away are accelerated more, so the velocity they gain is greater. Just as Hubble's law describes, only with the Hubble parameter now going negative (which only means the direction being reversed from expansion to contraction).

After some time, those same points will have moved closer to the observer, and will have gained speed. But they still obey Hubble's law, with points twice more distant having twice more speed. It's the changing Hubble parameter (in this case, becoming more negative), that reflects the increasing approach velocity of points A and B as they get closer together.
edit: I should clarify - it's how H is changing, since it'd be changing even in a coasting universe, where all velocities remain constant for all time.

 

[Ranku]

You're making the mistake of thinking of Hubble's law as if it were describing the motion of a single point across a range of distances, whereas it describes the state of motion of different points at a moment in time.

Start with the moment when an initially expanding universe is decelerated so that it's neither expanding nor contracting (it's at the inflection point, just before the contraction begins).
At this moment, every recession velocity, of any distant point, is zero, and the Hubble parameter is zero.
Then the points start approaching. The point A at distance d from the observer is accelerated inward by all the mass that is contained within a sphere of radius d. Point B at distance 2d is accelerated by all the mass within a sphere of radius 2d. I.e. points further away are accelerated more, so the velocity they gain is greater. Just as Hubble's law describes, only with the Hubble parameter now going negative (which only means the direction being reversed from expansion to contraction).

After some time, those same points will have moved closer to the observer, and will have gained speed. But they still obey Hubble's law, with points twice more distant having twice more speed. It's the changing Hubble parameter (in this case, becoming more negative), that reflects the increasing approach velocity of points A and B as they get closer together.
edit: I should clarify - it's how H is changing, since it'd be changing even in a coasting universe, where all velocities remain constant for all time.

To be clear, negative Hubble constant will increase in value over time in a contracting universe?

 

[Ibix]

To be clear, negative Hubble constant will increase in value over time in a contracting universe?

Depends what you mean by "increase". It would be 0 at some time, -1 at a later time, -2 at a still later time, which I would call a decrease. Its magnitude increases, though, if that's what you mean.

(Yes there should be units, but it doesn't matter which ones they are here.)

 

[Ranku]

Depends what you mean by "increase". It would be 0 at some time, -1 at a later time, -2 at a still later time, which I would call a decrease. Its magnitude increases, though, if that's what you mean.

(Yes there should be units, but it doesn't matter which ones they are here.)

Yes, that's what I meant.

 

[Imager]

Just clarify for me, is it the "things" in universe grow closer together or is it space that is that is getting smaller?

Should I should said space-time?

 

[Ranku]

Just clarify for me, is it the "things" in universe grow closer together or is it space that is that is getting smaller?

Should I should said space-time?

If there is enough matter in the universe for it to re-collapse, the universe would be spatially closed like a sphere. So the re-collapsing spacetime universe will become smaller along with the matter in it growing closer.

 

[Ibix]

Just clarify for me, is it the "things" in universe grow closer together or is it space that is that is getting smaller?

That isn't either-or. "Things get further apart/closer together" is a direct observation you can make by bouncing radar pulses off distant galaxies (in principle anyway - there are a few practical challenges). The question is how you interpret that - as "space expanding/contracting between stationary objects" or as "objects moving through space". There isn't a right answer to that. The usual interpretation is the first one and it has a lot of advantages, notably that it directly reflects the "everything's the same everywhere" cosmological principle. But the other isn't wrong.

Should I should said space-time?

Definitely not. Spacetime includes space now, space in the past, and space in the future. It doesn't change, it just is. In fact, the choice of interpretation above is a choice of different ways to slice ("foliate" is the technical term) 4d spacetime into a stack of 3d "space at one time" slices.

 

[Imager]

Ranku and Ibix, thank you for your help!