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In all the measurements taken over the years, has anyone ever observed any effect of gravitational lensing on red shift?

So: if we would look at 2 galaxies at, say, 250 million lightyears away, where the light of one travels directly towards us while the light of the other passes another galaxy on its way and is thereby gravitationally lensed before it reaches our telescopes. Would we find any difference in red shift between the two?

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In principle yes, in practice no.

When light passes through a gravitational potential it will experience a delay compared to a signal not passing through a potential. This effect is known as the Shapiro Delay. Consequently, the light passing through the potential will be stretched a little bit more due to the metric expansion of space. Hence the delayed light is redshifted a little bit more. Put differently, when see two gravitationally lensed images of the same distant galaxy, one will show the galaxy at an earlier time than the other, the scale factor at that time was also smaller, hence the older image is also more redshifted.

However, since the Shapiro delay is typically (on a cosmological scale) very small, this effect is almost certainly negligibly small, and absolutely insignificant compared to the accuracy with which you can measure the redshift.

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  • $\begingroup$ Thank you so much! That is exactly the answer I was looking for. I've been wondering why expansion is implied from red shift, even though there could also be another explanation similar to what would happen to extremely loud sound waves shot straight up into the atmosphere: they would elongate as the pressure drops and create the doppler effect without the source moving away at all. But according to this model, you'd expect gravitational potential to reduce red shift, not amplify it. If the net effect of gravity is red shift amplification, the density explanation of red shift is ruled out. $\endgroup$
    – Daniel Malkin
    Nov 15, 2017 at 11:00
  • $\begingroup$ To be clear: If the universe were not expanding, you would expect no effect on the redshift/blueshift from a gravitational potential at all. $\endgroup$
    – TimRias
    Nov 15, 2017 at 14:49
  • $\begingroup$ Not at all. If you're assuming red shift is caused by low density in the fabric of the vacuum itself, then it follows that high density would cause blue shift. $\endgroup$
    – Daniel Malkin
    Nov 15, 2017 at 17:52
  • $\begingroup$ But the redshift is not "caused by low density in the fabric of the vacuum itself" at all. Anyway, it is simple to check by analytic calculation that travelling through a gravitational potential has no effect on the redshift. The only thing that matters is the difference in potential between the source and the observer. $\endgroup$
    – TimRias
    Nov 15, 2017 at 18:31
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Strong gravitational lensing does NOT change redshift of the background object. A gravitational lens is a potential; a photon will gain energy as it falls through (i.e. gets blueshifted) and has to give up the same amount as it gets out of that potential (i.e. gets redshifted). Hence, the energy of the photon is unaltered and the background galaxies will have its original redshift.

Light travels two different paths of different lengths for asymmetric lens systems, resulting in time delay. Since this effect is on the galactic scale, the cosmological expansion will not have a measurable effect on the two light.

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