# Expressing the current Hubble rate as a temporary percentage increase in distance

1. Jul 8, 2009

### marcus

In this PF Cosmo forum context we have to be sensitive/practical about language. How to state cosmo basics, especially to newcomers who may not have assimilated technical terms like "scalefactor" yet. This does not mean we dumb everything to the max! Introductory terms should lay a basis of understanding that you can build on. So there are issues.

Here's an example and I'd like to hear your opinion.

The Hubble rate is 71 km/s per Mpc----with the new Riess numbers putting it at 74 and a gradual transition seems to be under way. But say, for now, 71.

According to the standard LCDM model, that should decline to about sqrt(0.75) of the current value and level out there. So we are looking at eventually getting down near 61, or with the new Riess numbers 64 km/s per Mpc.

Now a newcomer would not necessarily be familiar with Megaparsecs or be able to picture Hubble law expansion graphically from that number 71. So some of us have gotten into the practice of translating it into concrete terms of distances currently increasing by a certain (non-constant) percentage every million years. The percentage changes very very slowly so it will stay roughly right for a long time and the mental picture is, I think, adequate.
The point of using a percentage is to get across the idea that longer distances increase more.

The current Hubble rate of 71 translates into distances currently increasing 1/140 percent every million years. Do you think this is an OK way to describe things to newcomers? A good thing about it is it conveys the idea of the slowness (1/140 of a percent is a slight increase and a million years is a long time.) And it also implies superluminal rates of distance increase for long distances. If a distance is long enough then 1/140 of a percent of it can be more than a million lightyears, so in a million years it adds more than a million lightyears to its length. So saying things that way can give useful mental pictures.

Now there are some fine points to consider later after one gets across the main idea. The eventual decline to about sqrt(.75) of the current value means that this 1/140 will eventually get down near 1/160.

Or with the new Riess numbers closer to 1/150. So one can say that the asymptotic percentage rate, for Hubble law expansion, is slated to be about 1/150 of a percent per million years.

An important point to make is that currently the increase in distance is not exponential growth, because the percentage rate is declining.

If you would like to check the calculation yourself, type this into the google window and press return:
(71 km/s per megaparsec)*(10^6 year) in percent

The google calculator will give you this response:
(71 ((km / s) per megaParsec)) * ((10^6) year) = 0.00726109501 percent

and you can verify that 0.00726 is approximately 1/140.

2. Jul 8, 2009

### StandardsGuy

Since 2003 the measurements of H0 have been from 73 to 77. HST data (2009) is 74.2 (+/- 3.6). That is about the best uncertainty I've seen. Why not use it? I would round it down to 74 for newbies. I don't like fractions with percent, I think it is confusing. I would say 0.0075 % (or what 74.2 comes out to) or 75 PPM (parts per million) is even better. I may be biased from using PPM a lot.

3. Jul 9, 2009

### sylas

The units of the Hubble constant are effectively inverse time. I generally like giving it in inverse seconds. 74 km/s/MegaParsec is about 2.4*10-18 s-1.

This means you should be able to express the meaning of the Hubble constant as a time.... and indeed you can. Basically, everything is expanding away from everything else at a velocity which, if run back in time at the current velocity, would have everything compressed together a certain length of time ago. That time is about 13.2 billion years.

That is suspiciously close to the age of the universe... but this is pretty much a co-incidence; a consequence of the fact that dark energy and dark matter have a similar order of magnitudes. In current models, the expansion rate was decelerating for a bit over half the universe's life so far, and has been accelerating since then as matter density drops and dark energy becomes more significant. It's something of a co-incidence that we happen to be living in an epoch where dark energy and matter have comparable magnitudes. At least... most people think it is a co-incidence.

Cheers -- sylas

Last edited: Jul 9, 2009
4. Jul 9, 2009

### oldman

Yes I do. The Hubble rate is nothing more than a strain rate -- the (dimensionless) dilation strain of a model universe per second (2.4*10-18 s-1, as Sylas points out), or 1/140 percent per million years, as you say, Marcus ---- perhaps the latter is more easily grasped.

In "using introductory terms to lay a basis of understanding", I have a quibble with the way you sometimes do this, as when you ask people to accept that geometry is dynamic and stress that one has no right to expect distances, such as light wavelengths, to remain constant. I do agree that this is an excellent way of understanding geometry in GR and in particular the Hubble flow.

But: I think this approach need refining. Any dynamic behaviour, like uniform universal expansion, always implies change over time--- and change itself cannot be contemplated, imagined or quantified without making comparisons, preferably with some invariant standard.

When GR is used to describe gravity our usual SI standards are implicitly used for comparisons, to validate the concept of change. I have no problem with this (GR so far describes only gravity, not with the cohesion of say, solid rulers.) Or, since GR does require the invariance of light seconds --- is this modern definition of length therefore the implicit standard used?

I think one should be scrupulously explicit about what standards are being used when talking of distances being dynamic, most particularly in the context of universal uniform expansion.

5. Jul 9, 2009

### Rymer

Technically no complaint ... but do most people relate better to factions? (Just happens I don't so every time I see one I convert to decimal) ... suggest to include both for those of us so disabled.

6. Jul 9, 2009

### marcus

In that case, sylas, I should say that the current Hubble rate is 1/132 percent every million years, should I not?

The style of giving it as a fraction of a percent per million years, like that, is only a way of echoing the reciprocal of the Hubble rate--the "Hubble time".
If you say that the Hubble time is 14.0 billion years, then equivalently you say 1/140 percent per million years, and picture each distance increasing by 1/140 percent.
If you believe the Hubble time is 13.2 billion years, as per the new Riess numbers, then you tell everybody 1/132 of a percent, instead.

Always a pleasure to see your posts, clear organized knowledgeable. Improves the forum.
Similar thanks to Chalnoth and others doing likewise!

Oldman you are absolutely right! We must acquire a new understanding of what it means to be dynamic. And it will require a deeper understanding of quantum theory. The old idea of dynamical system involves a preferred timeclock. The clock on the laboratory wall that is outside of the box holding the system or the experiment. E pur se muove. Geometry is still dynamic even though the classical picture is a block universe. We just don't have the mental concepts to grasp it. George Ellis (Hawking's collaborator you recall) has a "what is time" essay that is fairly deep philosophically and explores the dynamicness and not-yet-determinedness of geometry. The ground is mined with paradoxes but with his help I will say that geometry is quantumdynamic and that the classic block universe is not valid. I disagree though your points are extremely well taken. If you possibly can, attend the George Ellis 70th birthday party in Cape Town. It is going to be a major event. I think the most important QG and QC event of 2009, it is in August. If there is a public lecture, go to it. If the public is admitted to the main talks, go. You won't regret. I wish I could but it is in the wrong hemisphere.

Look at what George Ellis says about the conference---his 70th birthday party, with Cambridge U. P. on board to do the festschrift:
And look at who will be giving talks:
http://www.mth.uct.ac.za/~jeff/Quantum_Gravity/Participants.html [Broken]

Last edited by a moderator: May 4, 2017
7. Jul 9, 2009

### sylas

I would prefer to say it is increasing at 1/132 percent of the current scale every million years.

The additional "of the current scale" phrase is just to be clear that it is not a compounding percentage, which the unadorned phrase appears to suggest.

In fact, this exactly the difference between simple and compound interest.

In compound interest, you earn a percentage of your balance every year.
In simple interest, you earn a percentage of your initial balance every year.

The Hubble expansion is actually more complex than either of these, and the "dark energy" component is in fact more like a compounding interest. But hey.