# Cosmological expansion of earth orbit

1. May 5, 2012

### 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".

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

From the 1998 paper:

2. May 5, 2012

### Ich

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.

3. May 5, 2012

### Staff: Mentor

What is the "cosmological background density"?

4. May 6, 2012

### 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

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:

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

5. May 6, 2012

### Naty1

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

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)

6. May 7, 2012

### Ich

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.

7. May 7, 2012

Ah ok.

8. May 8, 2012

### Naty1

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

Last edited: May 8, 2012
9. May 8, 2012

### Staff: Mentor

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?

10. May 9, 2012

### Ich

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.

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.

11. May 9, 2012

### Staff: Mentor

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

12. May 9, 2012

### Ich

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

13. May 9, 2012

### 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.

14. May 9, 2012

### 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.

15. May 9, 2012

### 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:

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

Last edited: May 10, 2012