Resolve Universal Expansion: Can We Measure It in the Lab?

[JollyOlly]

There seem to be an extraordinary number of coincidences here!

Thank you for your reference to Ned Wrights site. I have found it very illuminating. In particular on http://www.astro.ucla.edu/~wright/cosmo_03.htm" of his cosmology tutorial he plots various possibilities for the variation of a(t) with time. The black line is the matter dominated line which predicts an age for the universe of 9.2 Gyr. The green line is a linear one which I understand is not a solution to the Friedmann equations (see my post on is the cosmological constant constant) but which gives an age of 13.8 Gyr. The magenta line is the one currently favoured. It gives an age of coincidentally almost the same age and, to my mind, unacceptably puts us exactly at the epoch when the curve changes from slowing down to speeding up.

I can, however, see now that the coincidence of the age of the CMB is not a coincidence because we are all agreed that in that early universe, matter dominated so the magenta line approximates to the black one.

If you build a large scale triangle in a "flat" universe, you'll find the sum of angles to be different from 180°. From the difference, you'd deduce a positive curvature of 1/H².

I cannot agree with you here. In a 'flat' universe the angles of a triangle add up to 180° by definition. You must have some other definition in mind.

 

[Ich]

I cannot agree with you here. In a 'flat' universe the angles of a triangle add up to 180° by definition. You must have some other definition in mind.

You have to understand that "space" depends on coordinates.
When cosmologists talk about space being flat, they mean the spatial slicings defined by constant cosmological time. These are dynamic coordinates.
Triangles don't know about cosmological expansion and cosmological coordinates. They are just there, defined by their structure, which is assumed to be as rigid as possible. They are static, and such is the relevant "space". It is curved, the sum of angles is >180°.
Operationally, if you set the corners in motion according to Hubble's law, the relevant angles are changed due to aberration. Thus, their sum becomes 180° again if the corners are moving.

 

[utesfan100]

Can't \Lambda in GR be interpreted as an intrinsic expansion of the underlying space? In this case universal expansion is a local property of space.

Two objects at rest relative to each other separated by a distance would tend separate further if no other force or curvature is present. A volume element would tend to increase three times faster.

The existence of a cosmological constant or dark energy imply a fifth force of nature exists, we just don't know how it works yet. Or we don't know how one of the existing forces works completely and the perturbation from our understanding is what is causing the acceleratin of the universe.

The definition of a gravitationally bound mass is when the gravity is stronger than this undetermined force. At the solar system level this force is of the scale of the Pioneer anomoly, but this anomoly is a contraction not an expansion.

The reason we don't see it is because the effect is so small. If this effect is so much smaller than gravity at our scales it is even less significant at the scale of particles.

Based on a DeSitter universe with the observed Hubble expansion the length of an object doubles every 2.8E17 seconds, or 8.8 billion years. An electron expanding at this rate would hardly blink at this effect.

 

[JollyOlly]

When cosmologists talk about space being flat, they mean the spatial slicings defined by constant cosmological time. These are dynamic coordinates.

I am afraid you have lost me there Ich!
Are you saying that three comoving observers in a Friedmann universe in which k = 0 would still measure an angular defect?

 

[Ich]

Are you saying that three comoving observers in a Friedmann universe in which k = 0 would still measure an angular defect?

No, their relative angles add to 180°.
If you build a static triangle to test curvature, its angles would be more than 180°.

 

[Ich]

\Lambda in GR be interpreted as an intrinsic expansion of the underlying space? In this case universal expansion is a local property of space.

It can be interpreted as repulsive gravity, an acceleration. It's rather the time derivative of expansion \ddot a , which is velocity\dot a.

Two objects at rest relative to each other separated by a distance would tend separate further if no other force or curvature is present. A volume element would tend to increase three times faster.

Yep, but starting with dx/dt=0, if the objects are at rest. To get expansion, dx/dt=Hx, you have to set the objects in motion accordingly. Or wait some time, in a de Sitter universe things eventually become comoving at nozero H.

The existence of a cosmological constant or dark energy imply a fifth force of nature exists, we just don't know how it works yet.

It's gravity. We don't know it source, but the force itself seems to be gravity.

The definition of a gravitationally bound mass is when the gravity is stronger than this undetermined force.

...and strong enough to overcome motion. Yes.

At the solar system level this force is of the scale of the Pioneer anomoly, but this anomoly is a contraction not an expansion.

No, it's several OOM smaller than the anomaly. And don't forget that there's even more dark matter, which acts contracting. Still 5 OOM too small, IIRC.

The reason we don't see it is because the effect is so small. If this effect is so much smaller than gravity at our scales it is even less significant at the scale of particles.

There's another reason, as I said just before: in Galaxies, Dark Matter is much denser than Dark Energy. As you'd treat both effects as cosmological corrections to the gravity of ordinary matter, the net correction is positive (contracting).

Based on a DeSitter universe with the observed Hubble expansion the length of an object doubles every 2.8E17 seconds, or 8.8 billion years. An electron expanding at this rate would hardly blink at this effect.

I get 3e17 s, and almost 6e17 s if the ends of the object were at rest initially.
This is my point during the whole thread: if things aren't moving from the start, they won't follow the expansion. Even in de Sitter space, the difference is remarkable. Without Lambda, or with a sufficient DM density, objects at rest wouldn't start receding at all. They would accelerate towards each other.
That's one of the reasons why atoms don't expand.
The other is, as you said, that they can absorb this little Lambda easily.
I don't know if I mentioned it, but such a repulsive force doesn't let bound systems grow. Instead, they settle in a slightly larger stable configuration.

 

[utesfan100]

It's gravity. We don't know it source, but the force itself seems to be gravity.

For dark energy I agree completely. For dark energy and the cosmological constant responsible for the increasing expansion rate of the universe I am not so set. My point is, unti lwe can account for it in a testable way, we can't say whether it is an unaccounted for effect in a known force or a new force.

Maybe it is the negative gravity from all the negative energy gravitons floating through "empty space". I have yet to see a model of such a system. I think the lack of a good model for a graviton is a major obsicle.

I get 3e17 s, and almost 6e17 s if the ends of the object were at rest initially.
This is my point during the whole thread: if things aren't moving from the start, they won't follow the expansion. Even in de Sitter space, the difference is remarkable. Without Lambda, or with a sufficient DM density, objects at rest wouldn't start receding at all. They would accelerate towards each other.

let us take an observer in a DeSitter frame. Two objects comoving with this DeSitter frame double their distance in 3e17 seconds. Two objects whose distance is constant at a given point in time will double their distance in 6e17 seconds, twice as long. Essentially, their rate of separation needs to accelerate from rest.

At 3e17 the rest objects will be moving slower than their comoving objects, but will also be closer to the origin of the DeSitter space with a %velocity closer to their local region of DeSitter space than they originally had. Asymtotically they will approach the Hubble velocity.

... assuming a perfectly flat DeSitter space. I think they go next to the frictionless planes and massless springs in the physics lab. :)

 

[Ich]

My point is, unti lwe can account for it in a testable way, we can't say whether it is an unaccounted for effect in a known force or a new force.

Well, you're right in principle. But I'm not aware of any research that doesn't treat the effect as gravitational (which includes Lambda in my way of thinking).

... assuming a perfectly flat DeSitter space. I think they go next to the frictionless planes and massless springs in the physics lab. :)

Just visit a void and wait some 120 Gy there. Not much left then except DE.