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As I understand the metric expansion of space, space itself is expanding uniformly, isotropically. Distant light, passing through our solar system expands, as does the distance between atoms on earth. Any matter that is gravitationally bound does not expand, presumably, because gravity compensates by holding everything together, but it must be stretched apart before being held back together by stronger local forces.

So I did the calculations based on the current Hubble constant, and I determined that space everywhere is expanding by about 7% every billion years. So if the space between the sun and earth has expanded 7%, then I would expect it the orbit increase, and the length of a year to be shortened. Problem is, it seems like this is not accounted for in models of earths orbit.

So my question is, does light not expand as it passes through the solar system? And if not, then, how can that be explained in an isotropic universe? My understanding is that it is space that is expanding not the matter within it. If that is true, then I would expect all distances to be affected even between gravitationally bound objects like the sun and earth.

Thomas Tiger
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  • "Any matter that is gravitationally bound does not expand, presumably, because gravity compensates by holding everything together, " is correct, but it is not clear what you mean by "it must be stretched apart before being held back together by stronger local forces". The answers to these questions may help: "Is the expansion of space universal or local?", "Does gravity keep nearby galaxies from flying apart in space expansion?". – David Bailey Dec 13 '22 at 02:29
  • Thanks David for your quick response, and I need to study the equations in the link that you sent, but my initial thought is they confirm my suggestion that there is a balance between gravity and cosmic expansion. The way that I’m visualizing this is that expansion slowly moves the sun and the earth apart, which increases the potential energy of the earth, changing the period of its orbit, although it remains gravitationally bound. In other words, the stretching of space should increase the potential energy of the earth, or of two galaxies for that matter, since they are further apart gravitat – Thomas Tiger Dec 13 '22 at 04:27
  • So if I can try it one more time, the expansion of space is linear, independent of any gravitational well, so expanding the space within a deep gravitational well, like the sun and earth, will require an input of energy. You could take this to an extreme around the edge of a black hole, where even a small stretching of space could potentially require a huge amount of energy, since some particle would be ever so slightly drawn back from the edge – Thomas Tiger Dec 13 '22 at 04:41
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    @ThomasTiger but, but, but the planetary systemis gravitationally bound. there is no "slowly moves" . The interactions happen instantaneously and the expansion is not felt by the gravitational interaction. – anna v Dec 13 '22 at 05:24
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    I think this is a duplicate of Why does space expansion not expand matter?, but almost all of the answers to it are wrong, except for this one. See also this answer and this article. – benrg Dec 13 '22 at 07:51
  • The space-time around solar system is, to a good approximation, given by Schwarzschild geometry and not the FLRW geometry, which we use in cosmological scale. I don't think it's justified to extrapolate FLRW geometry all the way upto solar system scale – KP99 Dec 14 '22 at 04:19
  • Davis & Lineweaver, in many preprints and published articles whose titles all contain the phrase "expanding confusion", have made clear that spatial expansion is not a "force or drag" carrying massive objects with it: Space expands only into itself ("intrinsically"), and my impression's that this expansion is, currently, perceptible only as occurring at a slow rate, in spite of its faintly perceptible acceleration and the hypothetical potential it has for expansion at a rate greater than the speed of light. How would space (whether described as vacuum or simply emptiness) move anything? – Edouard Jan 15 '23 at 09:19

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In my question above, I was visualizing the expansion of space as an expanding balloon, where the expanding space carries matter along with it, kind of like a moving stairway that is conveying matter along as it expands. Hence, my thought experiment that light passing through our solar system on its way to some distant galaxy must be stretched as it traverses the path from earth to the sun, but the length of that same path between the earth and sun is not stretching at all. If it were, then energy would be added to earth's orbit and the length of a day would increase perceptibly over a billion years.

Thanks to the comments and links I now understand that the expanding space does not carry the galaxies along with it, rather galaxies are comoving because they are expanding at the same rate as space and therefore have no momentum relative to the comoving coordinates. As the expansion of space slows due to gravity or speeds up due to dark energy, matter and space are equally affected so that there is no change of momentum of the universe overall.

Now when, in the distant past, our local group of galaxies became gravitationally bound, there was an exchange of momentum, such that the center of mass of our local group remains comoving with the universe, but the individual galaxies and stars have a peculiar velocity relative to comoving space, but overall continue to expand with the universe around the center of mass of our local group.

So to answer my own question, the light passing along the path from the earth to the sun is always comoving and therefore is stretching along with space, but that stretching space is just flowing past the earth like a teflon sheet, it does not carry the earth along with it. It is the peculiar velocity of the earth relative to comoving space that preserves local relative distances as space is stretched around it.

I would appreciate any feedback to this answer, I know that other commenters explained this already, but I hope that my explanation would be helpful to someone who is still contemplating and trying to visualize the concept.

Thomas Tiger
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