How do we know the expansion of the universe is not centered around our position?

Question

It is my understanding that the red shift of galaxies in whatever direction we look shows the universe is expanding in every direction around us. That could be explained in two ways:

A (accepted): The universe is expanding in every point, like the stretched surface of a balloon, and therefore it's expansion looks the same whatever is your position as an observer.

B (unlikely): Earth is somehow at the center of the universe, who is expanding from this point.

I am not contesting A, but I am curious about how B was discarded although we only ever have been able to observe the universe from Earth or it's vicinity for a (astronomicaly speaking) brief period of time (and therefore a relatively small portion of space even though our solar system and galaxy, etc are also moving). Is there some positive reason to think we are not at the center of the universe, or is it more of a "it would be very unlikely that we just happen to be at the center of the expansion" type of reasoning?

Answer 1

Taken from my answer to https://physics.stackexchange.com/a/534684/123208, which is a duplicate on Physics SE.

We observe that galaxies appear to move away from us, in an isotropic fashion, at a rate that is proportional to their distance from us (Hubble's law).

Whilst one could argue that we are at (or near) the centre of a very uniform expansion, one would have to explain why Hubble's law should exist (it wouldn't if it were some sort of explosion-driven event) and why the universe appears isotropic to us, but wouldn't from a different position in the universe. The simplest explanation is that General Relativity applies (as we observe in a number of other cases) and we live in an expanding universe - this then means we do not need to occupy some privileged position in the universe (an erroneous assumption that has proved wrong every other time it has been made).

In such a universe, the redshift of distant galaxies is not caused by relative motion, but by the expansion of space. At high redshifts, these phenomena become distinct in that the relationship between "velocity" and redshift is different, for instance allowing "faster than light" (apparent) speeds. What this means is that in order to explain the observed relationship between distance and redshift (naturally explained by Hubble's law in scenario A) you would have to posit an exact relationship between the recession velocity and distance for scenario B that yielded the observed distance-redshift relationship in just such a manner that it appeared to match Hubble's law and scenario A at high redshift. That seems unlikely.

So basically at present, expansion fits the facts (far) better and more simply than any of the alternatives.

A further piece of indirect evidence comes from a careful analysis of the physical conditions of gas at high redshifts, illuminated by background quasars (out to $z \sim 3$) and subtle alterations to the cosmic microwave background (CMB) spectrum, caused by the Sunyaev-Zel'dovich effect, towards galaxy clusters at low redshifts ($z \leq 1$). Both of these methods give the temperature of the CMB at those locations.

In the expanding universe model, the temperature should increase as $1+z$, where $z$ is the redshift. If one instead has a non-expanding universe, and explain the CMB as due to some expanding shell of material, then the average temperature "seen" by distant galaxies would differ from this unless the shell gas has been uniformly cooling by an amount that just happens to agree with redshift of that galaxy.

Avgoustidis et al. (2015) review the evidence for the temperature evolution of the CMB and conclude that it agrees with an adiabatic expansion to better than 1%.

Direct evidence for the expansion is on the horizon though. In an expanding universe, the speed at which galaxies move away from us can change slowly with time (and with distance) by of order 10 cm/s per year, despite their being no force on them. This is known as the redshift drift. There are plans to measure this tiny effect with the European Extremely Large Telescope and the Square Kilometre Array over the course of a decade. See fr example https://astronomy.stackexchange.com/a/53762/2531 .

Answer 2

Things are observed to recede with velocity $\vec v$ proportional to their separation $\vec x$ from us, $$\vec v=H\vec x,\tag{1}\label{1}$$ where $H$ is a constant (the Hubble rate). This relationship is special, because consider an observer at the position $\vec x^\prime$ elsewhere in the Universe. Equation \eqref{1} implies that their velocity relative to us is $\vec v^\prime=H\vec x^\prime$. Hence, from their perspective, an object at separation $\vec x-\vec x^\prime$ from them ($\vec x$ from us) recedes with velocity $$\vec v-\vec v^\prime = H\vec x-H\vec x^\prime=H(\vec x-\vec x^\prime)\tag{2}\label{2}$$ from them. By comparing equations \eqref{1} and \eqref{2}, it is evident that they see the exact same cosmic expansion as we do!

That is, the cosmic expansion that we observe is precisely of the right nature that every observer will see expansion radially away from them. This is only true because of the particular form of equation \eqref{1}. Had we observed a different velocity-distance relationship, then we could have inferred that we are the center of expansion. But we observed exactly the velocity-distance relationship that is consistent with every observer being on equal footing.

Answer 3

A model in which we aren't at the center of the universe is both homogeneous and isotropic, while a model in which we are at the center is only isotropic.

The universe looks homogeneous. Homogeneity is a very special property; it's not impossible that a merely isotropic universe could be close enough to homogeneous to fool us, but there's no apparent reason why it should be. Generically, you'd expect it to be inhomogeneous enough that it would be obvious that we were at the center. So until there's clear evidence to the contrary, it makes sense to assume that the universe looks homogeneous because it is.

I also want to point out that your options A and B aren't as different as the wording of the question suggests. If everything is receding from us in a certain way, that is a homogeneous universe. You don't need a distinct stretching mechanism to have an expanding universe with no center. There is no center because there's a symmetry that means you can equally well take any other point to be the center.

Answer 4

First let's start from a simple point : Newtonian physics provides no explanation for what we can observe, regardless of what position you consider Earth to have in the expansion of the universe.

We have observations showing redshifts that denote expansion at faster than light speeds. That's a key problem to explain if you're trying to develop a theoretical model for the universe because relativity doesn't immediately suggest these redshifts are possible.

So when General Relativity was developed attempts were made to explain the observed apparent expansion away from us in all directions. The key point about relativity is that physics must follow the same rules everywhere. We've found no contradiction of that idea.

The model developed that could explain what was seen was the FLRW metric, named after it's discoverers. This is model has been refined into the Lambda-CDM model over time.

This model explains how it is possible for spacetime to be expanding and specifically requires that every point in the universe will see the same effect - i.e. that they in the center of an expansion. In a way it says that the oldest place in the universe is the place you're standing in - everything you see is younger.

There is no other model that explains what we observe so well. That makes this the model we use, because the gold standard in physical sciences is that the best model is the one that explains the observations best.

The model also provides a vital tool : different distances represent different timeslices of the universe to observe. The further away an object is, the further into the past of the universe we're looking. This provides yet more tests of the theory and our understanding of the universe and how it evolves.

This model ("there is no center") provides not just a match to observations, but predictions about what we expect to see. We expect to see (and do) objects at different stages of evolution as we peer into the distance (and hence the past).

B (unlikely): Earth is somehow at the center of the universe, who is expanding from this point.

We cannot accept this view simply because, while we have a working model for hypothesis-A, hypothesis-B has no model that explains what we see. In science you don't go with an idea that doesn't explain anything when you've already got one that does explain things.

Is there some positive reason to think we are not at the center of the universe

This comes down to your idea of "positive". Most scientists would regard choosing a theory that works over the absence of a theory that works a positive choice. That makes choosing the "no center" model a positive choice.

Answer 5

The expansion of the universe is centred around our position. The thing is, it is also centred around every other position in the universe.

Put another way: when you say "the center of the expansion", you are implicitly assuming that the expansion has a unique centre. Which is false.