# B Calculating the age of the universe with the Hubble constant

Hello,
When we assume the universe is expanding at a constant rate, we could say the age of the universe is 1/Ho. but I always feel unsure about that because 1/Ho is the distance over the velocity. However, the velocity changes over time, that is, when something is closer to us, the move slower and when they are further, they move faster according to Hubble's Law. So my question is how can we assume the velocity is constant while it's accelerating ? Thank you in advance.

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nrqed
Homework Helper
Gold Member
Hello,
When we assume the universe is expanding at a constant rate, we could say the age of the universe is 1/Ho. but I always feel unsure about that because 1/Ho is the distance over the velocity. However, the velocity changes over time, that is, when something is closer to us, the move slower and when they are further, they move faster according to Hubble's Law. So my question is how can we assume the velocity is constant while it's accelerating ? Thank you in advance.

Do not confuse "constant or not with respect to time" with "constant or not with respect to distance". When we assume a constant rate, the velocities with respect to us are constant with respect to time but it is true that the velocities of galaxies at different distances are different. But if you pick a given galaxy, we take its velocity to have been constant since the Big Bang. Of course, this approximation of constant velocities is far from what is actually going on and must taken with a huge grain of salt. Even in a universe with constant Hubble parameter, there are subtle effects to take into account.

• anonymous24 and mfb
Do not confuse "constant or not with respect to time" with "constant or not with respect to distance". When we assume a constant rate, the velocities with respect to us are constant with respect to time but it is true that the velocities of galaxies at different distances are different. But if you pick a given galaxy, we take its velocity to have been constant since the Big Bang. Of course, this approximation of constant velocities is far from what is actually going on and must taken with a huge grain of salt. Even in a universe with constant Hubble parameter, there are subtle effects to take into account.
Thank you for your reply. However, there is one point i'm not so sure about. You mentioned we assume the velocity with respect to us of a given galaxy is constant with respect to time, does it imply that it is moving away from us with constant velocity since the big bang? If so, how does this not imply that the velocity is also constant with respect to distance, i.e. as it certainly gets further away from us. Thank you.

mfb
Mentor
does it imply that it is moving away from us with constant velocity since the big bang?
That is exactly the meaning of "constant expansion".
If so, how does this not imply that the velocity is also constant with respect to distance, i.e. as it certainly gets further away from us.
"with respect to distance" compares two different objects at different distance but at the same time. The distance to something that is now 10 billion light years away from us increases faster today than the distance to something 5 billion light years away.

• anonymous24
That is exactly the meaning of "constant expansion"."with respect to distance" compares two different objects at different distance but at the same time. The distance to something that is now 10 billion light years away from us increases faster today than the distance to something 5 billion light years away.
Thank you so much, that clears up a lot of my confusion. I just have one last question that does it mean the recession speed against distance from our earth diagram (gradient = Ho) changes over time? like it will look really different a thousand years in the future? Thank you. Is it also why Hubble Constant changes over time?

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nrqed
Homework Helper
Gold Member
Thank you so much, that clears up a lot of my confusion. I just have one last question that does it mean the recession speed against distance from our earth diagram (gradient = Ho) changes over time? like it will look really different a thousand years in the future? Thank you. Is it also why Hubble Constant changes over time?
That's right. Hubble's "constant" is a misnomer as it is not at all a constant with respect to time. In a constant rate expansion universe, the formula age of universe = ##1/H_0## remains valid at all times which shows that as time passes, Hubble's "constant" has to change. It actually decreases linearly with time in such a universe. A thousand years would be too short to notice the variation (unless much much more precise measurement tools are made available) but, say, in a billion years it would be clear that ##H_0## would have decreased.

• anonymous24
That's right. Hubble's "constant" is a misnomer as it is not at all a constant with respect to time. In a constant rate expansion universe, the formula age of universe = ##1/H_0## remains valid at all times which shows that as time passes, Hubble's "constant" has to change. It actually decreases linearly with time in such a universe. A thousand years would be too short to notice the variation (unless much much more precise measurement tools are made available) but, say, in a billion years it would be clear that ##H_0## would have decreased.
Thank you so much, it's really clear to me now.

mfb
Mentor
A thousand years would be too short to notice the variation (unless much much more precise measurement tools are made available)
Those tools are under construction. The E-ELT (first light expected 2024) will have a mirror as large as the 20 largest existing telescopes combined. The CODEX experiment there plans to directly measure the accelerated expansion of the universe within a few years. The idea is simple: measure the redshift of some galaxies, repeat the measurements a few years later. The challenge is the required precision, the redshift has to be measured with a precision of 1 part in a billion.
Reference

• nrqed
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