Undergrad Is the Hubble constant a constant or is it a parameter?

[Angela G]

TL;DR

Hello!
I was solving an exercise about the Hubble constant and the Hubble parameter and got that the Hubble parameter ( at t = 1/2 t_0, where t_0 is the actual age of the universe) is 8/9 smaller than the Hubble constant. So my question is if we should consider this difference and talk about the Hubble parameter instead of the Hubble constant? In other words: Does the "Hubble constant" variate with time?

(P.S! this is an open question, feel free to answer)

 

[Orodruin]

Yes. The Hubble rate varies with time. The nomenclature of the "Hubble constant" comes from the original observations of recession velocity being proportional to distance and the proportionality constant being the "Hubble constant".

 

[Bandersnatch]

As far as nomenclature goes, Hubble constant is the value of the Hubble parameter at t_0. By definition $H_0$ doesn't vary in time. If you want to talk about the time-dependent variable you refer to the Hubble parameter $H(t)$.

 

[Bandersnatch]

Also, if you ended up calculating the value of H at an earlier time as being lower than $H_0$, then you need to check your work.

 

[mathman]

Open problem. Two different methods to determine value get different nos. (67 and 74) which are too far apart.

 

[elcaro]

Yes. The Hubble rate varies with time. The nomenclature of the "Hubble constant" comes from the original observations of recession velocity being proportional to distance and the proportionality constant being the "Hubble constant".

If I'm correct, we in fact do not measure the Hubble constant at a given time, but its average value over the time period for the observed object. So, looking at different objects at different distances from us, we would also in fact measure different values for the Hubble constant., as with increasing distance we also look further into the past in which the value of the Hubble constant would have take on different values.

 

[Bandersnatch]

If I'm correct, we in fact do not measure the Hubble constant at a given time, but its average value over the time period for the observed object. So, looking at different objects at different distances from us, we would also in fact measure different values for the Hubble constant., as with increasing distance we also look further into the past in which the value of the Hubble constant would have take on different values.

For low z, as was the case with early observations, the change in the Hubble parameter is low enough that it approximates a constant. For higher z there is indeed a growing deviation from linearity. However, the recession velocities for individual objects don't change fast enough to be observed, so there's no need to average them.

 

[kimbyd]

For low z, as was the case with early observations, the change in the Hubble parameter is low enough that it approximates a constant. For higher z there is indeed a growing deviation from linearity. However, the recession velocities for individual objects don't change fast enough to be observed, so there's no need to average them.

Also, the difference from non-linearity is a result of looking into the past. According to the main model currently used, recession velocities are exactly proportional to distance. But that proportionality changes over time, so when we look far away we are observing an older (and higher) value of this proportionality.

 

[Angela G]

Thanks, for all your answers! I understand now