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I understand that the expansion of the universe causes unbound structures to move apart from each other. This means that unbound structures have negative relative momentum due to universal expansion.

When a photon was emitted from a galaxy that was receding relative to Earth at the time of emission due to expansion, the momentum it had relative to Earth at the time of emission would have been proportional to the relative (to Earth) momentum of the mass from which it was emitted at the time of emission. Since the momentum of a photon is inversely proportional to its wavelength, this would have resulted in a longer wavelength. And if the momentum of that photon was conserved during its journey through empty space, then it would also have that longer wavelength at its time of arrival on Earth.

If this is true, then the redshift we see represents the recession velocity of the emitting mass relative to Earth at the time of emission. Furthermore, if we see more redshift per unit distance at longer distances (as I believe we do), it simply indicates that the rate of expansion was greater further back in time than it is now, so the expansion of the universe is decelerating over time. That's logical.

But I am told by Cosmologists that there is another reason for the redshift. Space itself is expanding over time and the doppler effect I described, although quite logical to me, is actually not applicable to this scenario.

Why is that?

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You can find the answer here: http://curious.astro.cornell.edu/physics/104-the-universe/cosmology-and-the-big-bang/expansion-of-the-universe/610-what-is-the-difference-between-the-doppler-redshift-and-the-gravitational-or-cosmological-redshift-advanced

In both cases, the light emitted by one body and received by the other will be "redshifted" - i.e. its wavelength will be stretched, so the color of the light is more towards the red end of the spectrum. But there's a subtle difference, which you sort of allude to.

In fact, only in the first case (a nearby body moving away from the earth) is the redshift caused by the Doppler effect. You've experienced the Doppler effect if you've ever had a train go past you and heard the whistle go to a lower pitch (corresponding to a longer wavelength for the sound wave) as the train moves away. The Doppler effect can happen for light waves too (though it can't be properly understood without knowing special relativity). It turns out that just like for sound waves, the wavelength of light emitted by an object that is moving away from you is longer when you measure it than it is when measured in the rest frame of the emitting object.

In the case of distant objects where the expansion of the universe becomes an important factor, the redshift is referred to as the "cosmological redshift" and it is due to an entirely different effect. According to general relativity, the expansion of the universe does not consist of objects actually moving away from each other - rather, the space between these objects stretches. Any light moving through that space will also be stretched, and its wavelength will increase - i.e. be redshifted.

(This is a special case of a more general phenomenon known as the "gravitational redshift" which describes how gravity's effect on spacetime changes the wavelength of light moving through that spacetime. The classic example of the gravitational redshift has been observed on the earth; if you shine a light up to a tower and measure its wavelength when it is received as compared to its wavelength when emitted, you find that the wavelength has increased, and this is due to the fact that the gravitational field of the earth is stronger the closer you get to its surface, causing time to pass slower - or, if you like, to be "stretched" - near the surface and thereby affecting the frequency and hence the wavelength of the light.)

Practically speaking, the difference between the two (Doppler redshift and cosmological redshift) is this: in the case of a Doppler shift, the only thing that matters is the relative velocity of the emitting object when the light is emitted compared to that of the receiving object when the light is received. After the light is emitted, it doesn't matter what happens to the emitting object - it won't affect the wavelength of the light that is received. In the case of the cosmological redshift, however, the emitting object is expanding along with the rest of the universe, and if the rate of expansion changes between the time the light is emitted and the time it is received, that will affect the received wavelength. Basically, the cosmological redshift is a measure of the total "stretching" that the universe has undergone between the time the light was emitted and the time it was received.

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    $\begingroup$ Link-only answers are generally frowned upon as they become useless if the link breaks or its content changes. Please put the essence of what you link here into your answer. $\endgroup$ Jan 2, 2022 at 14:49
  • $\begingroup$ I'm not suggesting that's not a useful answer, but I don't agree with all of it, particularly the apparent suggestion that mass has expanded at the same rate as space. What I'm really asking is why there was any need for anything other than the Doppler effect to explain the red shift we see due to inflation. $\endgroup$
    – Alan Gee
    Jan 3, 2022 at 15:48
  • $\begingroup$ See: only in the first case (a nearby body moving away from the earth) is the redshift caused by the Doppler effect. In the case of distant objects where the expansion of the universe becomes an important factor, the redshift is referred to as the "cosmological redshift" and it is due to an entirely different effect. According to general relativity, the expansion of the universe does not consist of objects actually moving away from each other - rather, the space between these objects stretches. $\endgroup$
    – Aveer
    Jan 3, 2022 at 16:29
  • $\begingroup$ doppler effect: nearby objects where they are moving away (this is dominant over the expansion of the universe) cosmological ("due to inflation") redshift : when the objects are far away and the space between them expands and becomes much more dominant over two moving objects $\endgroup$
    – Aveer
    Jan 3, 2022 at 16:31
  • $\begingroup$ @Aveer I am well aware that there is a theory that claims that space is expanding and that the effect of that is seen by us as cosmological red shift. But why does such a theory exist if there is a more logical explanation for the red shift known as the Doppler effect. $\endgroup$
    – Alan Gee
    Jan 4, 2022 at 10:14

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