How big was the Universe 13 billion years ago?

[marcus]

...
In the example I suggest above, the figure in Col 6 =5.4 and the figure in Col 4 = 3.5.

5.4/3.5 = (roughly) 1.543. Would this mean that at the time of emission the recession rate was above c? In which case the light would not reach Earth?...

You are asking just the right question! In fact it would eventually reach earth! this is a surprising thing that most people do not realize.

As you point out it would at first LOSE GROUND. It would be swept back at the rate of about 0.5c as you calculate. But if it hangs in there and keeps trying it will eventually make it.

It starts in year 2.3 billion and in fact in the next 0.5 billion years it will only be swept back a total of 0.2 billion ly, and it will be at a distance of 5.6 billion ly from us. Look at the next row of the table.
in year 2.3 billion the ratio you calculated before is now 1.3333 (5.6/4.2) and if you average those recession speeds (1.5 and 1.3) you get 1.4. So for the first 0.5 billion years he is losing ground at an average rate of 0.4c, therefore he has lost 0.2. therefore he is at 5.6!

But that is also on track. If a galaxy is at distance 5.6 in year 2.8 and emits some light, that light will also get here today. Even though the distance to the galaxy is increasing at 1.333 c and the light initially gets swept back at 0.333c.

In the next 0.7 billion years he will only get swept back, again, by 0.2 . So in year 3.5 he will be only a little worse off---at distance 5.8 from us. You see these numbers in the next row?

Now he's essentially safe! because that distance is only increasing at about the speed of light, so he is not making headway but at least he is not getting swept back. He is "breaking even" so to speak.

For the next 0.7 billion years (from 3.5 to 4.2) the average recession speed is about the average of 5.8/5 and 5.8/6 which is 1.06 so he is only losing 0.7 times 0.6 or 0.04 billion lightyears. At year 4.2 billion he is still essentially at distance 5.8!
And then he starts gaining ground!

Any photon of light that, in year 4.2 billion is only at distance 5.8 from us, you can see from the table is making HEADWAY!
The distance is only increasing at 5.8/6 c, that is less than the speed of light. And he is proceeding towards us at the speed of light. So he is gaining. And it gets better and better as he gets nearer.

In a universe with expansion like ours, the real light cone is PEAR SHAPE. Photons at the bottom get swept outwards away from us at first but they hang in there and keep trying and eventually come up the rounded side of the pear and start to come in towards us. The D_then column of the table outlines the teardrop or pear shape of the light cone. (it would only be a cone in a static non-expanding universe). the basic reason is the fact that the Hubble radius is increasing.

I hope you are feeling better and making a full recovery from the pneumonia! Don't worry about doing this stuff. I am learning how to use the table to help explain basic cosmology stuff so I'm satisfied to have the practice. Just do the amount that is right for you.

 

[Endervhar]

Suppose a galaxy emits some light in year 1.6 billion, and the galaxy is 4.8 billion lightyears from here. Then the light will be just arriving now (the table indicates) and it will have traveled for 12.2 billion years. (Subtract 13.8 - 1.6)
However the distance to the galaxy NOW is 23.9 billion lightyears.

OK with that, except; how do you discover from the table that the light will be just arriving now?

 

[marcus]

==quote==
Suppose a galaxy emits some light in year 1.6 billion, and the galaxy is 4.8 billion lightyears from here. Then the light will be just arriving now (the table indicates) and it will have traveled for 12.2 billion years. (Subtract 13.8 - 1.6)
However the distance to the galaxy NOW is 23.9 billion lightyears.

Distance then = 4.8
Distance now = 23.9
Travel time = 12.2 billion years (the time has no simple practical relation with either distance)

{\begin{array}{|r|r|r|r|r|r|r|} \hline S=z+1&a=1/S&T (Gy)&T_{Hub}(Gy)&D (Gly)&D_{then}(Gly)&D_{hor}(Gly)&D_{par}(Gly)\\ \hline5.0&0.20&1.6&2.3&23.9&4.8&7.9&4.5\\ \hline4.4&0.23&1.9&2.8&22.3&5.1&8.7&5.6\\ \hline3.8&0.26&2.3&3.5&20.6&5.4&9.5&6.8\\ \hline3.3&0.30&2.8&4.2&18.8&5.6&10.3&8.3\\ \hline2.9&0.34&3.5&5.0&16.8&5.8&11.2&10.2\\ \hline2.6&0.39&4.2&6.0&14.8&5.8&12.0&12.5\\ \hline2.2&0.45&5.1&7.1&12.7&5.7&12.8&15.2\\ \hline2.0&0.51&6.1&8.3&10.5&5.4&13.5&18.5\\ \hline1.7&0.58&7.3&9.6&8.3&4.9&14.1&22.4\\ \hline1.5&0.67&8.7&10.9&6.2&4.1&14.7&27.1\\ \hline1.3&0.76&10.2&12.1&4.0&3.1&15.1&32.6\\ \hline1.1&0.87&11.9&13.1&1.9&1.7&15.5&39.1\\ \hline1.0&1.00&13.8&14.0&0.0&0.0&15.8&46.7\\ \hline\end{array}}Time now (at S=1) or present age in billion years: 13.8
http://www.einsteins-theory-of-relativity-4engineers.com/TabCosmo7.html
==endquote==

OK with that, except; how do you discover from the table that the light will be just arriving now?

I may have to try several answers. Bear with me. One answer is that THIS IS WHAT THE TABLE IS ABOUT. It is about light that is arriving just now. If we examine the light and discover it has been stretched by a factor of 5, then we figure out, from the model, that it was emitted in year 1.6 by something that was distance 4.8 from here at that time.

the equations have been worked out, the equations constitute the model universe, in which everything adds up right and it fits the data. what the table does is make the model more visible in a way. It is like a window into the equation model.

 

[Endervhar]

Makes sense, thanks.

Lots more thinking to do!

 

[Endervhar]

Just an update. My friend visited and was quite happy with what I could tell him. I have to say there is still quite a lot more I want to sort out. However, I'm awaiting a date for admission to Hosp. in London, so things will be a bit disrupted for a while.

I wanted to say thanks for the patient support, and "I'll be back".

 

[Endervhar]

This may seem a little off topic, but its a question that arose from my thinking about the subject matter of this thread.At the time of the BB the Universe was smaller than an atomic nucleus. It is sometimes described as being "infinitely small".

Unless, at t = 10^-43s, the Universe had a diameter greater than 10^-35m, every part should have been in contact.

If this is the case, why is inflation necessary in order to explain the uniformity of the CMB, which, presumably, reflects the uniformity of the temperature of the Universe at the period of last scattering?

 

[marcus]

This may seem a little off topic, but its a question that arose from my thinking about the subject matter of this thread.


At the time of the BB the Universe was smaller than an atomic nucleus. It is sometimes described as being "infinitely small".

Unless, at t = 10^-43s, the Universe had a diameter greater than 10^-35m, every part should have been in contact.

If this is the case, why is inflation necessary in order to explain the uniformity of the CMB, which, presumably, reflects the uniformity of the temperature of the Universe at the period of last scattering?

Ender, I'm sure you realize this: you have to be very cautious about believing whatever you get from the popular media.
When they talk about the "universe" being at one time amazingly small, they are talking about the currently OBSERVABLE portion, not the whole universe. We don't know if the entire universe is infinite in size (in which case it would have been infinite at the start of expansion) or finite in size. If it is finite then its size could still be many times larger than the observable portion---we don't know!
So it is useless to talk about the size or the "diameter" of the universe at the start of expansion.

To make it mean something definite you have to specify that you are talking about the currently observable portion of it. We have a pretty good idea how big that is at present.

That's just a minor point, but it needs to be made to avoid unnecessary confusion.

 

[Endervhar]

I generally regard anything in the popular media with extreme suspicion, unless you include popular science books in this, in which case I might drop the "extreme".

John Gribbin suggests using Universe (higher case U) for the detectable universe, universe (lower case) for any other proposed universe and cosmos for everything there is or could be.

Obviously I should have been more specific, but it was the Universe sensu Gribbin I meant.

 

[marcus]

... why is inflation necessary in order to explain the uniformity of the CMB, which, presumably, reflects the uniformity of the temperature of the Universe at the period of last scattering?

That's a good question. People have different views on that. Some experts challenge the necessity of inflation to explain uniformity of CMB. They argue that the uniformity could have other explanations.What makes the whole discussion so interesting is that the answers depend on how you model the start of expansion. The usual consensus cosmology DOES NOT COVER the exact beginning of expansion---the old conventional math model breaks down there. So there are various rival ways to fix that which different people are working on. And some of these can explain uniformity without inflation. But they may still involve some episode of inflation for other reasons.

Inflation is really great, it helps explain several different things. Even if you don't need it to explain uniform CMB temperature (because your model has uniformity already without it) you might still want to include some form of inflation in your model for other reasons.

I'd like to recommend a video lecture to you, because I admire the guy as a critic of inflation even though I don't accept what he is offering in its place.

Google "steinhardt pirsa" and see what you get. Princeton's Paul Steinhardt recently gave a talk at Perimeter Institute saying what he sees wrong with the usual inflation ideas. PIRSA stands for perimeter institute recorded seminar archive. An intelligent contrarian can be someone good to listen to, a bit, even if you don't buy the whole message. I think the first 25 or 30 minutes is probably all you need to watch.

 

[marcus]

...
John Gribbin suggests using Universe (higher case U) for the detectable universe, universe (lower case) for any other proposed universe and cosmos for everything there is or could be.
...

I'd never seen that suggested! Most people here seem to say "observable universe". That's what my prof at UC berkeley taught us to say. And then universe for the whole thing, and what you mean by that depends somewhat on your model.

Gribbin's books are supposed to be very well written and quite popular, but I'm sorry to say I haven't read one.

He's on the right track there in the sense that we really must make the distinction in our nomenclature. But his particular notational device (upper/lower case) has yet to be widely adopted.

 

[marcus]

As you probably know, one bunch of people doing Quantum Cosmology are working on the "bounce" idea that at very high density quantum effects make gravity repellent, so collapsing geometry rebounds.
With that, one can go back in time past the start of expansion. No mathematical breakdown ("singularity") occurs.

So then, in that line of research, the question is not "how big?" but "what density?" at the start of expansion.

You don't have to address the question of overall size.

A calculation about 5 years back, in LQC (socalled Loop quantum cosmology) came up with a figure of 41% of Planck density. that was the point where the rebound occurred. It started at around 1% of Planck density, when repellent quantum corrections to gravity began to appear. So that picture prevailed in Lqc for a while.
But just this past year a young researcher named Edward Wilson-Ewing has challenged that. According to him if you include the temperature or kinetic energy of matter in the calculation the quantum bounce occurs earlier, at a lower density. I forget the exact figure, my impression is that he was talking about something on the order of a billionth of Planck density instead of 41%
It's confusing to get inconsistent signals like this, I know. But I just wanted to mention it. It's a complicated subject, involving work in progress, and frequent surprises.

I doubt you'd want to read Wilson-Ewing paper but just in case you want to glance at the abstract or introduction to it I will get the link.
http://arxiv.org/abs/1211.6269
Smart young guy, well respected. we should probably pay more attention to what he says about the critical bounce density being much lower than previously calculated.

 

[Chronos]

My objection to Wilson-Ewing is they suggest black holes could achieve a critical bounce density. I realize that possibility has been previously suggested, but, strikes me as implausible. We have no evidence to suggest our universe is an inverted black hole.