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

• I
• Arman777
In summary: So at some point the photon sent from ##50c/H## will have the same proper distance at ##0.1c/H_0## as the photon sent from ##0.1c/H_0##?
Arman777
Gold Member
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

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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## ?
Orodruin said:
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.

## 1. What is the maximum ##d_p(t_e)## value and how is it calculated?

The maximum ##d_p(t_e)## value is the highest point on a graph that represents the relationship between the concentration of a substance and the time it takes for that substance to reach a certain level. It is typically calculated by plotting the data points and finding the highest point on the curve.

## 2. What does the maximum ##d_p(t_e)## value indicate about the substance?

The maximum ##d_p(t_e)## value can indicate the rate at which the substance is absorbed, metabolized, or eliminated from the body. It can also provide information about the potency and effectiveness of the substance.

## 3. How does the maximum ##d_p(t_e)## value affect the dosing of a substance?

The maximum ##d_p(t_e)## value can help determine the optimal dosing of a substance. If the maximum value is too low, it may indicate that the substance is not being absorbed or metabolized efficiently and a higher dose may be needed. If the maximum value is too high, it may indicate that the substance is being eliminated too quickly and a lower dose may be more effective.

## 4. Can the maximum ##d_p(t_e)## value change over time?

Yes, the maximum ##d_p(t_e)## value can change over time as the body's metabolism and elimination processes may be affected by various factors such as age, health conditions, and other medications being taken.

## 5. How is the maximum ##d_p(t_e)## value used in drug development and testing?

The maximum ##d_p(t_e)## value is an important factor in determining the safety and effectiveness of a drug. It is often used in drug development and testing to establish the appropriate dosing and to assess any potential side effects or risks associated with the substance.

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