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In cosmological models the relationship between proper distance to a galaxy at the emission and absorption times can be written as ##d_p(t_e)(1 + z) = d_p(t_e)##
In this case in most cosmological models we get a maximum value for the ##d_p(t_e)##. This maximum value can be also seen from the graph. The problem is that I did not understand the "physical meaning" of the graph.
Let me describe what I understand. We know that the measurable quantity is the ##z##. So let's suppose we measured value of ##z = 0.1## and we can see that this corresponds to ##d_p(t_e) = 0.1## Hubble distance. At the same time, we measured another source which has a ##z=50##. From the graph, it seems that they have the same proper distance for ##t = t_e## but corresponding different ##z## values. How can this be possible? Thanks
Let me describe what I understand. We know that the measurable quantity is the ##z##. So let's suppose we measured value of ##z = 0.1## and we can see that this corresponds to ##d_p(t_e) = 0.1## Hubble distance. At the same time, we measured another source which has a ##z=50##. From the graph, it seems that they have the same proper distance for ##t = t_e## but corresponding different ##z## values. How can this be possible? Thanks