# Observational data for evolution of Hubble rate

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1. Dec 4, 2014

### Sudesh Kumar

Is there any observational data available for evolution of Hubble rate? To give some context, read the dark energy FAQ by Sean Caroll here.

He says:

"If the universe is decelerating, the Hubble constant is decreasing. If the Hubble constant is increasing, the universe is accelerating. But there’s an intermediate regime in which the universe is accelerating but the Hubble constant is decreasing — and that’s exactly where we think we are."

My question is: is there any observational data to prove that Hubble rate is decreasing, or is he just stating that the concordance model of cosmology predicts it to decrease with time?

Looking at the Supernova data from Perlmutter et al, it seemed to me that the value of Hubble rate is actually increasing with time, but I may be wrong here!

2. Dec 4, 2014

### Chalnoth

Well, yes. This is precisely what supernova observations are used for.

What is measured is the distance as a function of redshift, and distance can be computed as a particular integral over the Hubble expansion rate (technically, it's an integral over the inverse of the Hubble expansion). So each individual supernova gives you an estimate of the integral of the Hubble expansion rate from the time that supernova exploded to now. Add up the data from lots and lots of supernovae at different redshifts and you get an experimental estimate of how the Hubble expansion rate has changed over time.

3. Dec 4, 2014

### marcus

And it has clearly been decreasing over time, from the earliest time from which we can get data up to the present!

the H(t) is not a SPEED (badly chosen units give that misleading impression) it is, rather, a fractional growth rate of distances. It is conveniently expressed as percentage increase per million years. If you look at the history you can see the decline very clearly.

The current Hubble rate is measured at about 1/144 percent per million years. To check this get google to convert to more familiar units.
(1/144) percent per million years in km/s per Mpc
you should get 67.9 km/s per Mpc, close to the most recent Planck mission report figure.

Or play around with google calculator and try, for example, 1/143 or 1/142 percent, it should give values slightly larger than 67.9

This table shows the decline. In year 67 million the Hubble expansion rate was 1% per million years.
In year 135 million it was 1/2 of one percent per million years
In year 271 million it was 1/4 of one percent per million years
In year 543 million it was 1/8 %
In year 1.085 billion it was 1/16 %
In year 2.159 billion it was 1/32 %
...
...
In year 13.787 billion (now) it is 1/144 %

you see how to read the table:

$${\scriptsize\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline T (Gy)&R (Gly) \\ \hline 0.067&0.1\\ \hline 0.135&0.2\\ \hline 0.271&0.4\\ \hline 0.543&0.8\\ \hline 1.085&1.6\\ \hline 2.159&3.2\\ \hline 4.243&6.1\\ \hline 8.009&10.4\\ \hline 13.787&14.4\\ \hline 20.917&16.4\\ \hline 28.613&17.1\\ \hline \end{array}}$$

The table gives the Hubble RADIUS, which is the reciprocal of the distance growth RATE.
R = c/H
So the Hubble radius R grows in proportion as the percentage expansion rate H declines.
and our calculator happens to give the Hubble radius, so one mentally converts to get H.

Last edited: Dec 4, 2014
4. Dec 5, 2014

### Sudesh Kumar

Thanks for your inputs. Can you please let me know how these values of Hubble rate over time were measured? It would be great if you can point me to the source of these calculations.