# Detectability of cosmological redshift in an empty part of universe

I'm pretty new to the concept and I want to get a better idea about it. I've seen a video in which a light wave is stretched since the space itself is stretching. Another analogy is that cosmological redshift is like some ball bearings stuck to a rubber sheet that's stretching. I also looked at this question (and the top answer there): As the universe expands, why do some things stretch but not others?.

Suppose we just consider a huge part of the universe that's empty. Some object emits a blue light wave from one end of this void towards an observer at the other end of the void. This space in this void itself will be expanding or "stretching" - so the light wave itself will get "stretched". But will the observer notice any difference in wavelength between the stationary-space and expanding-space cases?

I have this scenario in mind: suppose I notice some small rock A suspended in space that's at rest w.r.t. me, and another rock B at rest w.r.t. me but sufficiently far away from A so that the gravitational attraction between them is negligible. I define the distance between A and B as "1 unit". If the space isn't expanding, let's say n crests of the light wave fit between A and B. But even if space expands, even though the light wave gets "stretched", the rocks A and B will also move away from each other and again n crests of the stretched wave will fit between A and B (assuming uniform expansion of space everywhere).

In summary - initially we have a finer grid of space and small "ruler" to measure the distances, and later we have a stretched grid of space and a "stretched ruler" to measure the distances. So the notion of distance won't get altered, which means the wavelength of the emitted light will also remain the same, right?

Just want to understand the flaw in the above argument and clear up my concepts.

• I am not sure why you say that "all hypothetical rulers" get stretched. You said you read the top answer to "As the universe expands, why do some things stretch but not others?."... this tells you, that while the spacetime in an "empty" part of the universe, for example between galaxies, will get stretched, hypothetical rulers, like we, or the Earth or something on it, will not, due to much stronger electromagnetic forces. Commented Jun 20, 2023 at 15:27
• @Koschi: You're right, the "all hypothetical rulers" part isn't correct for the reason you mentioned. Let me think about it some more and I'll try to rephrase it in a better way. Commented Jun 20, 2023 at 15:51
• @Koschi: I have edited the question and removed the erroneous part. Thanks for pointing it out Commented Jun 21, 2023 at 9:21

Space isn't stretching in an objective sense. That's a common misconception, unfortunately repeated in the answer to the question that you linked. Other contributors and I have discussed this point elsewhere; for example

If you place two objects at rest with respect to each other, in an empty background (no matter, radiation, dark energy, etc.), they will remain at rest with respect to each other. Light traveling between them will not be redshifted. This is true irrespective of whether or how rapidly the Universe is expanding.

Now, in the presence of a dark energy background (as seems to be the case today), the gravitational influence of the dark energy would cause the two objects to begin receding from each other. Since they are receding, there will be a redshift. People sometimes explain these effects as a consequence of "space stretching", but that's pretty misleading, because the induced recession is not linked to the cosmic expansion rate. It's just related to the density of dark energy.

Note also that the most natural interpretation of the cosmological redshift is that it is just a Doppler shift due to objects receding. This point is discussed at length in the pedagogical academic article "The kinematic origin of the cosmological redshift".

• Thanks! I'll have a look at the links you provided and try to understand them. But regarding your last paragraph, not saying that it's wrong but I've seen a couple of places (e.g. in the video I linked to in the question) where they say that cosmological redshift isn't due to regular movement-based doppler effect. See here: youtu.be/LE_wbOw39Mk?t=222. After reading the abstract of that arxiv paper though, it seems there are people arguing both for and against this. Commented Jun 21, 2023 at 12:07
• @ShirishKulhari Yes, and in the first page of the Bunn & Hogg paper, they list physics/astronomy textbooks that also claim the cosmological redshift is different from a Doppler shift. As they note, it's a common belief! It's not correct though.
– Sten
Commented Jun 21, 2023 at 12:31

A blue light being beamed at us through a large region of empty space that is expanding will get stretched out and appear redder. Its specific spectral lines (coming from, for example, excited hydrogen, etc.) will be shifted "off center" towards longer wavelengths too.

Key to making this effect measurable by our instruments is the idea that the stretched distance through which the light propagates is truly gigantic compared to the amount by which the length of our rulers here on earth get stretched.

• So in the scenario that I mentioned in the question - in which there's some observer at the other end of the void - they'll have to use something to measure the light beam's wavelength. And the core argument is that that something would be less affected by the space expansion as compared to the effect of the expansion on the light beam itself. Did I understand that correctly? Commented Jun 20, 2023 at 15:55
• yes you did. -NN Commented Jun 20, 2023 at 17:20