Cosmological expansion of earth orbit

[Naty1]

I came across the following at Ned Wrights website and wondered
[a] What does the boldface statement mean?
What is thought about the statement that "Cosmological expansion of the Earth orbit around the sun is negligible but not zero" instead of "its not been determined".

" For the technically minded, Cooperstock et al. computes that the influence of the cosmological expansion on the Earth's orbit around the Sun amounts to a growth by only one part in a septillion over the age of the Solar System. This effect is caused by the cosmological background density within the Solar System going down as the Universe expands, which may or may not happen depending on the nature of the dark matter. The mass loss of the Sun due to its luminosity and the Solar wind leads to a much larger [but still tiny] growth of the Earth's orbit which has nothing to do with the expansion of the Universe..."

http://www.astro.ucla.edu/~wright/cosmology_faq.html

From the 1998 paper:

... it is reasonable to pose the question as to whether there is a cut–off at which systems below this scale do not partake of the expansion. It would appear that one would
be hard put to justify a particular scale for the onset of expansion. Thus, in this debate,
we are in agreement with Anderson (1995) that it is most reasonable to assume that the
expansion does indeed proceed at all scales...The recurrent attention paid to this issue indicates that to this point a definitive answer is still lacking. However, it is our sense that the prevalent perception is that the physics of systems which are small compared to the radius of curvature of the cosmological background is essentially unaffected by the expansion of the universe...Thus, the effect of the cosmological
expansion is seen to be negligible locally and grows in significance with distance, reaching
full import on the cosmological scale. This conclusion is qualitative, and is certainly
well–known to most relativists but, to the best of the authors’ knowledge, has yet to be
well–formulated quantitatively...

 

[Ich]

[a] What does the boldface statement mean?

It means that Ned Wright is great. Thank you for digging this up, Naty1, you have no idea how difficult it is to explain the conclusion of the Cooperstock paper without having some respected cosmologist affirming what you say.
This has to do with what I said here.
Cooperstock assumes that the universe is completely homogeneous, and places the solar system in this background. So he calculates that now there are some 90000 tons of "universe" inside the Earth orbit, contributing to the Sun's gravitation and therefore narrowing the orbit. As the universe expands, the amount of "universe" inside the orbit decreases, with it the gravitational attraction, so the orbit becomes wider. That's it.

The problem is that Cooperstock et al. fail to interpret their result correctly. Instead of concluding that expansion has exacly zero effect on local dynamics, which is only governed by the local mass density, they claim that there is a subtle nonzero effect.

The "missing link" for the correct interpretation is the Friedmann Equation
$$\frac{\ddot a}{a} =-\frac{4}{3\pi G } (\rho + 3p),$$which explains the dynamics of the scale factor with the (almost Newtonian) gravitation of the cosmological fluid. Ned Wright is aware of this, but Cooperstock et al. weren't.

 

[Drakkith]

What is the "cosmological background density"?

 

[Naty1]

Ich: thanks for your post...your reference to an earlier thread post from Drakkith was in fact the thread that brought this subject to mind [and I could not find it] when I bumped into the Wright statement ...

so I am concluding with you

,,,,expansion has exactly zero effect on local dynamics...

Drakkith:
I thought 'cosmological background density' referred to the energy density of the 'vacuum' which I think several sources have indicated is 'constant'...that is, 'new' expanding space is just like 'old' space...[if it were 'different' that would be really fascinating] they have a constant energy density, a constant negative pressure, so over time we are moving towards a 'dark energy dominated universe'...more space and constant density means total dark energy increases...

Wikipedia seems to say the same:

Note that this definition is tied to the critical density of the present cosmological era: the critical density changes with cosmological time, but the energy density due to the cosmological constant remains unchanged throughout the history of the universe.

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

 

[Naty1]

Here is another possible take on 'cosmological background density' from another recent thread: [from the original 'inflationary era']

...characteristics of the state of the universe at the onset of inflation are not diluted by the inflationary expansion and can be imprinted in the spectrum of primordial inhomogeneities. …

http://arxiv.org/abs/1106.4240

Stimulated creation of quanta during inflation and the observable universe
Ivan Agullo, Leonard Parker
(Submitted on 21 Jun 2011)

https://www.physicsforums.com/showthread.php?t=590798&page=2

 

[Ich]

What is the "cosmological background density"?

The universe has an average density of ~10^-27 kg/m³. In Cooperstocks test universe it's a bit more, with no Dark Energy there. Cooperstock assumes for his calculations perfect homogeneity, which means that the density is everywhere exactly the same - the "background density".
That's why there are suddenly 90000 tons "averaged universe" within Earth's orbit, leading to a tighter orbit.

 

[Drakkith]

The universe has an average density of ~10^-27 kg/m³. In Cooperstocks test universe it's a bit more, with no Dark Energy there. Cooperstock assumes for his calculations perfect homogeneity, which means that the density is everywhere exactly the same - the "background density".
That's why there are suddenly 90000 tons "averaged universe" within Earth's orbit, leading to a tighter orbit.

Ah ok.

 

[Naty1]

Found these comments in my notes [which I totaly forgot] which directly pertain [April 2007]:

https://www.physicsforums.com/showthread.php?t=162727&highlight=current+flow&page=4

thread # 162727

“ If anything there is a vanishingly small FRW element to the metric of bound structures. If the FRW metric 'prevail(ed) on all scales and everywhere, even inside gravitationally bound structures or within atoms' then why do galaxies maintain a constant size as the distance between them expands? Commonly we are told that the local mass concentration 'overcomes' the expansion preventing this from occurring. This is one of the worst and most fallacious explanations you could possibly give someone! What really happens then?The FRW metric is the inevitable result of the cosmological principle, CP. which is that the universe is homogeneous and isotropic. The metric is only valid if these principles hold. Consider now a galaxy, solar system or planet. Does the CP hold? No. Is it a remotely useful approximation? Not at all! Unsurprisingly then the dynamics of bodies in these systems and on these scales bears no resemblance to the dynamics of galaxies. So for instance, there is no redshift of light due to a(t) when we observe light from the other side of our galaxy, or from say Andromeda. The FRW metric simply is not valid on these scales.

….. The better way to look at it is that the presence of the mass in the galaxy gives the metric of space-time around this mass a form that would look much more like a Schwarzschild metric than FRW (though we cannot fully solve GR for a galaxy.). The point is though that there is not expansion to 'overcome' since the 'expansion' is merely the result of the metric [variable over time] formed by a homogeneous and isotropic mass distribution. If the mass doesn't obey these principles we shouldn't be surprised that we don't see any 'expansion'.

If you don't believe me hold an object in each hand with outstretched arms. When you let them go what happens? I think you will find that they both plummet towards the local centre of mass (the centre of the Earth) rather than drift off into the Hubble flow! The local mass concentration can hardly be described as a mere perturbation to the FRW metric!Wallace: Wallace: #63
….the 'expansion' (which we both definitely agree is a bad term for it!) is a result of the FRW metric, in particular a(t). The metric in the region of bound structure looks nothing like the FRW metric, in particular it has no global time dependence (though will of course evolve). For this reason I stand by the statement that the FRW metric is not valid on scales which are significantly inhomogeneous, since the metric has no component that reflects the global a(t), and hence the FRW picture does not relate to the dynamics of the system.

 

[Drakkith]

So the expanding universe thing is the FLRW calculation correct? Since the metric is different around clumps of matter due to their mass, then the FLRW metric isn't valid. And this means our standard view of cosmological expansion doesn't apply. Since we don't have an exact solution to GR's equations for something like our own solar system or galaxy, would it be correct to say that we simply don't know?

 

[Ich]

Since the metric is different around clumps of matter due to their mass, then the FLRW metric isn't valid. And this means our standard view of cosmological expansion doesn't apply.

No, not at all. The FRW metric is valid as a large scale approximation. That's what it is good for.
The have been some people questioning the validity of such an approximation - google "cosmological backreaction" -, but from my perception that issue is no longer been taken seriously.

Since we don't have an exact solution to GR's equations for something like our own solar system or galaxy, would it be correct to say that we simply don't know?

We don't have an exact solution to anything out there. Not even in Newtonian gravity. That doesn't mean we don't know.
You use perturbation techniques instead: Starting from an exact solution, say flat metric or FRW metric, you add components and assume that you can simply add the perturbation to the background metric. That is true in most cases. With this assumption, you can for example first add the sun (an additionan Schwarzschild metric) and the a planet, which you treat as having no gravitational field at all.
This approach is very poweful, and it is what Cooperstock et al. did.

Wallace correctly critizises the use of the FRW-metric as a starting point, because it introduces a factor (metric expansion) that has nothing to do with local dynamics. It just makes the calculations and the interpretation much more difficult (Cooperstock knew that, too, so they used a different set of coordinates).
You better start with flat space, which you can always do. Then add all the matter there is, the add the sun, and then a planet. You can safely ignore the expansion, as it introduces only slow motion of the local background matter, and as the rest of the universe has no effect due to Birkhoff's theorem.

 

[Drakkith]

No, not at all. The FRW metric is valid as a large scale approximation. That's what it is good for.
The have been some people questioning the validity of such an approximation - google "cosmological backreaction" -, but from my perception that issue is no longer been taken seriously.

Of course, I mean it isn't valid on small scales such as our Solar System. Is that correct?

 

[Ich]

Yes. It is a valid background for perturbation analysis, though.

 

[sweet springs]

Hi. Let me say something that I have been pondering.

In the part of space where expansion is taking place, the expansion is very homogeneous in micro scale of at most nanometer. I tell you. Wave packet of traveling one photon whose length is one meter or so and wave length is order of nanometer undertake red shift by expansion. It shows that expansion is homogeneously occur in nanometer scale at most.

Is it OK? Regards.

 

[Ich]

It merely shows that spacetime is continuous at these scales. If it were quantized at length scales comparable (*) to the wavelength, we'd see for example a different speed of light for different wavelengths.
But this has nothing to do with expansion.

(*) "comparable" meaning "only some 15 orders of magnitude smaller" or so, depending on the theory that predicts the quantization.

 

[Naty1]

I've been plowing thru thread 162727 and was going to post the following here.
I see it has already come up in discussion and confirms the above posts:

Wallace, post #73:

... so there is no harsh cut-off point where the metric goes from FRW suddenly to some other non-expanding form. I would have expected that the expansion would not be dominant on the scale of the local group, so that results is unexpected for me. Thanks for pointing it out, I will have to follow this up.

It remains that case though, that as the local region becomes more and more inhomogenous, the metric must have less and less 'FRWness' in it. The expansion most certainly does not occur on galactic scales or smaller, such as the scale of a solar system for instance.

This lack of a 'harsh cut off' is just what I expected in a previous post without understanding the detail Wallace provided.