Standing in nothingness before the Big Bang

[marcus]

I am sceptical regarding this conclusion, as the matter density today is about 25% of the total energy density. The universe will approach an exponential expansion ...

I'm not sure what conclusion you find dubious, Tim. I'm saying that right now we have almost exponential distance growth at around 1/144% per My
And eventually in future we will have exponential growth at 1/173% per My (according to standard cosmic model).

Maybe the the word "almost" is too vague for you. It is vague! I think you would like to see a TIMETABLE for the decline in percentage growth rate from 1/144 to 1/173 and that is easy to supply. Just google "lightcone cosmological calculator" and look at the column labeled "R" for Hubble radius.
As that increases from 14.4 to 17.3 the percentage rate declines accordingly.

You can compare that with the "T" column which gives the time since start of expansion, i.e. age.

To get better time resolution, first click "set sample chart range" and then "calculate"

that will give a longer table with more gradual increase from today's 14.4 to eventual 17.3.

It also gives a substantial chunk of the past. You can see for instance that the distance growth rate was approximately 1% per My back in the year 67 million. that is what the first row of the table says (if you have pressed "set sample chart range")

If googling does not work, here is the link:
http://www.einsteins-theory-of-relativity-4engineers.com/LightCone7/LightCone.html

I also keep the link in my signature, it's handy for a LOT of purposes. You get to set the parameters of the table.

 

[timmdeeg]

I'm not sure what conclusion you find dubious, Tim. I'm saying that right now we have almost exponential distance growth at around 1/144% per My
And eventually in future we will have exponential growth at 1/173% per My (according to standard cosmic model).

Maybe the the word "almost" is too vague for you. It is vague! I think you would like to see a TIMETABLE for the decline in percentage growth rate from 1/144 to 1/173 and that is easy to supply. Just google "lightcone cosmological calculator" and look at the column labeled "R" for Hubble radius.
As that increases from 14.4 to 17.3 the percentage rate declines accordingly.

Thanks marcus and congratulation to you and Mordred, this table is very helpful. I haven't realized it till now and for sure will be busy with it from now on. And I agree regarding the development of 1/R , we are now already relatively close to exponential expansion, though it will take another 78 Gy to reach R = 17.2999, corresponding to an almost exponential expansion. Hereby I use 'almost' only in the sense to not hide that the approach is asymptotic.

 

[timmdeeg]

Once the matter density goes to zero, the expansion will be exponential, no asymptotic about it.

What is asymptotic is the approach of the matter density to zero.

It seems curious. "Gegen Null gehen" translated into English means "approaching zero", so, seems different from "goes to zero", as I used it wrongly by translating directly. I appreciate your comment.