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

• B
• anonymous24
In summary, the conversation discusses the assumptions and uncertainties surrounding the expansion of the universe at a constant rate. The speakers touch on the concept of Hubble's Law and its implications for the age of the universe and the changing velocities of galaxies over time. They also address the misconception that the velocity of a given galaxy is constant with respect to distance, and explain how the Hubble Constant is not truly constant but rather decreases over time in a universe with constant expansion. They also mention ongoing efforts to measure the acceleration of the universe through advanced technology.
anonymous24
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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anonymous24 said:
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
nrqed said:
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.

anonymous24 said:
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".
anonymous24 said:
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
mfb said:
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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anonymous24 said:
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
nrqed said:
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.

nrqed said:
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
mfb said:
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
That's fascinating, thanks for the info!

## 1. How is the Hubble constant used to calculate the age of the universe?

The Hubble constant is a measure of the rate at which the universe is expanding. By using this constant in conjunction with other observations, such as the cosmic microwave background radiation, scientists can estimate the age of the universe.

## 2. What is the current value of the Hubble constant and how does it affect the age calculation?

The current accepted value of the Hubble constant is approximately 70 km/s/Mpc. This value is used in the calculation of the age of the universe, meaning that any changes to this value can significantly impact the estimated age.

## 3. How accurate is the Hubble constant in determining the age of the universe?

The accuracy of the Hubble constant in determining the age of the universe depends on the precision of the measurements used. With improved technology and observations, the accuracy of the Hubble constant and age calculations have improved over time.

## 4. Are there any other methods besides the Hubble constant for calculating the age of the universe?

Yes, scientists also use other methods such as the study of the cosmic microwave background radiation, the expansion rate of the universe, and the ages of the oldest stars in the universe to estimate the age of the universe.

## 5. How does the age of the universe calculated with the Hubble constant compare to other estimates?

The age of the universe calculated with the Hubble constant is currently estimated to be around 13.8 billion years. This estimate is consistent with other estimates using different methods, providing more evidence for the accuracy of the Hubble constant in determining the age of the universe.

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