Normalized LightCone7 Graphs

[Jorrie]

The LightCone7 cosmological calculator has been under collaboratively development on this forum for over three years now. It has sprouted a branch following Marcus' definition of a 'natural timescale of the present universe' - the long term Hubble time, which we collaboratively labelled one "zeit". So there are presently two versions: LightCone7s (for 'standard'), which is also linked to simply as LightCone7, and then LightCone7zeit. They are presently in a few signatures around here.

LightCone7 is essentially a table-making calculator, but one of the great features that emerged is a charting option. It has a predefined set of 12 curves, which can be selected for inclusion in the table or chart. What LightCone7zeit taught us is that the degree of normalization resulting from using zeit and light-zeit units is very useful when comparing different graphs with each other. The normal values of cosmological parameters in their usual units have widely different scales.

Just for illustrating the point that I want to make (and without claiming any usefulness for the full set of graphs), here are the whole lot in one chart. Apart from the light-green D_particle graph, all the others have comparable normalized magnitudes over a very useful range of time.

Despite the naturalness of the zeit timescale in cosmological terms, it has a certain "unnatural" ring in human terms, e.g. the present cosmological time is about 0.8 zeit and the present Hubble radius R is 0.83 lzeit.
I experimented a little with other normalization values and found that the present Hubble radius (R_0) and the present cosmological time (T_now) 'looks more natural', to me at least.

I'm aware of the fact that this destroys some of the mathematical simplicity of the zeit-scale normalization, but I would like to know other opinions on it.

 

[marcus]

My first reaction was favorable. It seems like it could be a useful alternative. In effect what it does is use the present age (T_now) as the unit of time, and the present rate of expansion H₀ as the unit rate, to which other rates of expansion can be compared. That seems natural and intuitive. I just now saw the new version of Lightcone for the first time, so I'm just beginning to imagine situations where it might be especially helpful.

A newcomer to cosmology might find comparing past rates with the present more meaningful than comparing percentages per million years. For example someone might wonder when was the expansion rate TWICE what it is today?
and then looking back at the graph of normalized-Lightcone, at the light turquoise H/H₀ curve, one sees that ratio was 2 at an age about 0.4 of the present age.

 

[anorlunda]

I would love to learn from those graphs. I need a legend to define the terms. I need more than just the words but perhaps a paragraph on each term. Where can I find that?

 

[Jorrie]

I would love to learn from those graphs. I need a legend to define the terms. I need more than just the words but perhaps a paragraph on each term. Where can I find that?

Start with the 'tooltips' (question marks) on the calculator face. Many are hidden under the 'Column Selection and Definition' button.

 

[Bandersnatch]

I have to say I was never really fond of the zeit scale. I understand how it's a mathematically 'sensible' normalisation, but it always felt like yet another mental hurdle to overcome as one struggles to imagine what's going on - a natural tendency for the mind, mine at least, is to view the history of the expansion from some manageable mental anchor point, like the universe at the present day.
In my opinion, any normalisation that takes present values for its basis is going to be more palatable for anybody who is not already an advanced student of the subject.
So yeah, I do like the new approach.
Of course, in the end we want all of them to be available - the original not normalised one, the new scale, and the zeit one too. Same as with the three lightcone graphs with different scaling Lineweaver & Davies employed in their oft-cited paper, the more ways there are to help form a mental picture of the expansion, the better.

 

[Jorrie]

I am working on a LightCone7 version that will combine the three normalization strategies as options inside one program, with some 'tooltips' help. As soon as that's released, I will propose an Insights article to explain the strategy and use.

 

[Jorrie]

I am working on a LightCone7 version that will combine the three normalization strategies as options inside one program, with some 'tooltips' help. As soon as that's released, I will propose an Insights article to explain the strategy and use.

OK, the draft version of LightCone7Combo is ready - possibly still with the odd bug. I would appreciate any feedback on bugs, tooltip errors, omissions, spelling, etc.

You will notice that it has sprouted another 'version' (for distance scaling to Gigaparsec), which I hope will please the occasional professional user.

I have started the 'project' for creating an Insights Tutorial for LightCone7Combo. I will post pieces here for comment before finalizing the Tut.

 

[Jorrie]

OK, the draft version of LightCone7Combo is ready - possibly still with the odd bug. I would appreciate any feedback on bugs, tooltip errors, omissions, spelling, etc.

I found one minor bug and fixed that, but a more serious matter is that the latest Microsoft IE does not seem to render the charts perfectly. They work correctly in FF and Chrome - I have not tested other browsers yet, but I suspect that is a MS issue and will look further for a solution.

This sort of thing may happen to any browser, but MS is making a bit of a habit...

 

[Jorrie]

I could not find a solution to the MS IE issue yet, so for IE users I suggest as a workaround: open a separate Chrome window and and then open LightCone7 there (by a right click and Copy Link Location). This means you have two windows to work from, next to each other, if you so want.