Looking for a chart showing various growths of the Universe

[Buzz Bloom]

TL;DR Summary

I would like to see such charts with the appropriate corresponding values for the four Omega variables which add to unity. I have done a search, but the results have not been satisfactory for reasons I explain in the body of this thread.

The following is the closest chart to what I want that I could find.

https://map.gsfc.nasa.gov/media/990350/990350b.jpg

This chart has four curves, but only two of them has
Omega_m + Omega_Lambda = 1.

I would like to see a curve (of several) which expands and then contracts, like the orange curve, but one in which the Omegas sum to 1.

 

[Bandersnatch]

I would like to see a curve (of several) which expands and then contracts, like the orange curve, but one in which the Omegas sum to 1.

You can't have such curves. 1 is the critical density, which by definition separates the recollapsing group of curves from the forever expanding ones. With 1 you can only have curves on or above the green one, gradually looking more exponential as you turn the knob up on lambda density.

 

[Buzz Bloom]

Hi @Bandersnatch:

Thank you very much for your response. If I understand it correctly, the Friedmann equation with Omegas requires that there is no solution of the equation that permits recollapsing of the universe. I now see that I was mistaken about the possibility that some combination of four Omegas with the sum of 1 could be a solution with recollapsing.

Regards,
Buzz

 

[Orodruin]

Only $\Omega_m$ and $\Omega_\Lambda$ have appreciable size. The radiation component is pretty negligible today - around 1e-4.

I would like to see a curve (of several) which expands and then contracts, like the orange curve, but one in which the Omegas sum to 1.

You will not find this, as indicated above. However this

1 is the critical density, which by definition separates the recollapsing group of curves from the forever expanding ones.

is not entirely accurate. It separates spatially closed universes from open ones. While this also separates recollapse from eternal expansion in a matter only universe, it is no longer true when dark energy is included.

 

[Bandersnatch]

is not entirely accurate. It separates spatially closed universes from open ones. While this also separates recollapse from eternal expansion in a matter only universe, it is no longer true when dark energy is included.

But it is. In the sense that you can't have any combination of matter and lambda summing up to 1 that results in recollapse.

 

[Orodruin]

But it is. In the sense that you can't have any combination of matter and lambda summing up to 1 that results in recollapse.

It really isn’t though as you can have combinations with Omegas summing up to more than one that expand forever.

 

[Orodruin]

To illustrate:

The divisor between eternal expansion and recollapse in a universe with only matter and a cosmological constant goes along the $\Lambda = 0$ line until it reaches flatness. It them deviates upwards as matter closes the universe and dominates to a large enough extent that the cosmological constant never starts to dominate. This divisor is clearly different from the flatness line and they only coincidence when there is no cosmological constant.

Edit: As pertains to this thread, it is also pretty clear from this that to have a collapsing flat universe, you would require a negative cosmological constant.

 

[Bandersnatch]

You're right. That was sloppy.

 

[Ibix]

To illustrate:

Slightly off topic - the contour lines represent bounds on our universe's values from different lines of evidence, I presume?

 

[Orodruin]

Slightly off topic - the contour lines represent bounds on our universe's values from different lines of evidence, I presume?

Yes, those noted in the figure: CMB, SNe, clusters

 

[Cerenkov]

Hello Orodruin.

Re the graphic you posted...

With my Basic level of understanding I seem to see three data sets (Supernovae, Clusters and CMB) appearing to overlap at a value of about 0.7 on the vertical axis. Is that correct? And this is the value of what is generally taken to be the cosmological constant? I hope that this is so, because that would mean I've read and understood something about your graphic. That would mean a lot to me.

What I don't currently understand is what is meant by the Omega M along the horizontal axis. Also, the line marked 'Flat' slices right through this overlap, telling me that these three lines of evidence all point to our universe being Flat. Is that correct, too?

Finally, could you please provide a link to where you sourced this graphic from please? So that I can see and appreciate it in it's original context? Thank you.

I do thank you for posting this graphic here because rank amateurs like me need to rely heavily on visual aids to help us understand these interesting (but complex) issues.

All the best,

Cerenkov.

 

[Orodruin]

With my Basic level of understanding I seem to see three data sets (Supernovae, Clusters and CMB) appearing to overlap at a value of about 0.7 on the vertical axis. Is that correct?

Yes, this is correct. Or, well, it is the relative energy density of the cosmological constant relative to the critical density required for a spatially flat universe. It is in essence telling you that ca 70% of the energy content of the Universe is cosmological constant.

What I don't currently understand is what is meant by the Omega M along the horizontal axis.

The same thing as above, but for matter. Ca 30% of the energy content is in the form of matter.

Also, the line marked 'Flat' slices right through this overlap, telling me that these three lines of evidence all point to our universe being Flat. Is that correct, too?

The strongest contributor to that is CMB data, which essentially lies along the flat line. If you only had the other two you would need to combine them to see that tgey intersect on flat.

Finally, could you please provide a link to where you sourced this graphic from please?

I took it from a Google search because I know it since before. The original source is the supernova cosmology project and the data sources are shown in the figure.

 

[Cerenkov]

Ok, that's great Orodruin.

Thanks for the clarification about the relative energy density of the cosmological constant relative to the critical density. That's very helpful. I can now follow up on Knop, Spergel and Allen and the Supernova Cosmology Project too. Which is good too.

But there's just one last thing, if you please. Ca 30% and Ca 70% ? What does Ca refer to please?

Thank you.

Cerenkov.

 

[Ibix]

What does Ca refer to please?

It's a standard abbreviation for circa, Latin for "near".

 

[Cerenkov]

Thanks Ibix.

I wondered about circa, but wasn't sure if that term was applied in scientific circles.

Now I know.

Thanks again,

Cerenkov.