Maximum ##d_p(t_e)## value and its meaning

[Arman777]

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

 

[Orodruin]

The universe is initially expanding so fast that the proper distance between the signal from z = 50 and the observer starts out increasing. As the universe’s expansion slows down, the signal will start catching up and at some point have the same proper distance to the observer as it started out with. This occurs at z=0.1 in your example. A signal sent at that time will have been sent from the same proper distance at emission.

Note that the emission times are different so the same proper distance at emission for the two signals correspond to different comoving coordinates.

 

[Arman777]

So the photon sended from $50c/H$ cannot reach the observer due to the expansion of the universe but later on when universe slows down the photon catches up the same proper distance at $0.1c/H_0$ ?

Note that the emission times are different so the same proper distance at emission for the two signals correspond to different comoving coordinates.

I see.