<p>As per the above comments, there will still be v=Hd, if v is the rate of change of current distance, and d is the current distance-- as long as the universe continues to obey the cosmological principle.  The nearby version of that will still look like correlating Doppler-shift velocity to distance indicators, and the faraway version will require a dynamical model, albeit a very simple one due to dark energy.  It will lead to a constant H that will not be anything like the inverse of the age of the universe.  And if you go too far into the future, you won't be able to see the CMB, or quasars, so alien cosmology will really struggle.</p>

CC BY-SA 3.0
2016-10-17T20:58:31.850Z
2016-10-17T20:58:31.850Z
Ken G
<p>We have Hubble's law:</p>

<p>$$v=Hd$$</p>

<p>where H is the Hubble parameter, which is decreasing in value, but it will be constant in the distant future. So, assuming the Standard Model of Cosmology holds true, will Hubble's law be accurate when the Hubble parameter becomes a constant?</p>

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2016-10-17T15:25:16.780Z
I think @RobJeffries assessment is correct here. What's more, even if you knew the current distance, that distance wouldn't correspond to the recessional velocity you might measure because you're measuring the velocity based on observables from light that is millions or billions of years old.
zephyr
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2016-10-17T20:51:09.290Z
The key to Hubble's law is to say what you mean by v and d.   Historically, they were Doppler shift velocity and some distance indicator.  But if v is the rate of increase of current distance, and d is the current distance, then Hubble's law is exact whenever there is a cosmological principle, the idea that the whole universe is doing more or less the same thing spatially at any given age.  But you always need a dynamical model to take observable redshifts and distance indicators and infer the v and d that would work in an exact Hubble law.
Ken G
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2015-06-06T15:50:04.813Z
Not clear what you are asking. The Hubble parameter is *defined* to be $\dot{a}(t)/a(t)$, so by definition Hubble's law will be still applicable. Do you mean will it be accurate to a greater range of distance?
ProfRob
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2015-06-06T16:20:13.007Z
I thought Hubble's law was currently accurate for all distances. Is that not true?
set5
CC BY-SA 3.0
2015-06-06T16:36:26.130Z
No, that isn't true. The universal expansion was decelerating, it is now accelerating; that is why the Hubble parameter is changing. If the parameter changes with time, then when we look at distant objects in the past, it is clear that today's Hubble parameter will not accurately predict their recession velocities.
ProfRob
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2015-06-07T23:57:39.653Z
Peculiar Velocity in cosmology: http://en.wikipedia.org/wiki/Peculiar_velocity#Cosmology
Wayfaring Stranger
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2015-06-08T00:12:21.423Z
@Rob But  I'm talking about the velocity-distance law, not the redshift-distance law. My understanding is that the velocity-distance law is applicable to all distances, whereas the redshift-distance law is only valid for small redshifts. Or has  dark energy changed this?
set5
CC BY-SA 3.0
2015-06-08T08:47:04.290Z
You got me thinking quite hard about this. You are correct, but only if the distance is the *proper distance* - the distance away *now*. In practice we cannot measure this for distant galaxies. Have a look at http://www.astro.ucla.edu/~wright/cosmo_02.htm
ProfRob
<cosmology><distances><expansion>
Will Hubble's law always be accurate?
set5
# Will Hubble's law always be accurate?

(Asked by: username_0 on 2015-06-06)

We have Hubble's law:

$$v=Hd$$

where H is the Hubble parameter, which is decreasing in value, but it will be constant in the distant future. So, assuming the Standard Model of Cosmology holds true, will Hubble's law be accurate when the Hubble parameter becomes a constant?

**Tags:** cosmology, distances, expansion

> **Comments:**
> **username_3**: Not clear what you are asking. The Hubble parameter is *defined* to be $\dot{a}(t)/a(t)$, so by definition Hubble's law will be still applicable. Do you mean will it be accurate to a greater range of distance?  
> **username_0**: I thought Hubble's law was currently accurate for all distances. Is that not true?  
> **username_3**: No, that isn't true. The universal expansion was decelerating, it is now accelerating; that is why the Hubble parameter is changing. If the parameter changes with time, then when we look at distant objects in the past, it is clear that today's Hubble parameter will not accurately predict their recession velocities.  
> **username_4**: Peculiar Velocity in cosmology: http://en.wikipedia.org/wiki/Peculiar_velocity#Cosmology  
> **username_0**: @Rob But  I'm talking about the velocity-distance law, not the redshift-distance law. My understanding is that the velocity-distance law is applicable to all distances, whereas the redshift-distance law is only valid for small redshifts. Or has  dark energy changed this?  
> **username_3**: You got me thinking quite hard about this. You are correct, but only if the distance is the *proper distance* - the distance away *now*. In practice we cannot measure this for distant galaxies. Have a look at http://www.astro.ucla.edu/~wright/cosmo_02.htm  
> **username_1**: I think @RobJeffries assessment is correct here. What's more, even if you knew the current distance, that distance wouldn't correspond to the recessional velocity you might measure because you're measuring the velocity based on observables from light that is millions or billions of years old.  
> **username_2**: The key to Hubble's law is to say what you mean by v and d.   Historically, they were Doppler shift velocity and some distance indicator.  But if v is the rate of increase of current distance, and d is the current distance, then Hubble's law is exact whenever there is a cosmological principle, the idea that the whole universe is doing more or less the same thing spatially at any given age.  But you always need a dynamical model to take observable redshifts and distance indicators and infer the v and d that would work in an exact Hubble law.  

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## 1 answers

### Answer by username_2 on 2016-10-17. Score: 1

As per the above comments, there will still be v=Hd, if v is the rate of change of current distance, and d is the current distance-- as long as the universe continues to obey the cosmological principle. The nearby version of that will still look like correlating Doppler-shift velocity to distance indicators, and the faraway version will require a dynamical model, albeit a very simple one due to dark energy. It will lead to a constant H that will not be anything like the inverse of the age of the universe. And if you go too far into the future, you won't be able to see the CMB, or quasars, so alien cosmology will really struggle.


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