Size of Universe: Planck Time to Inflation

[clinden]

What do we know or speculate as to the size of the visible and entire universe between the Planck time and the beginning of explosive inflation?

 

[marcus]

Not much of any substance. Not much is known. And different people speculate different things.

We do not know that an inflation episode occurred--it used to be considered the simplest way to explain observed features like near flatness and isotropy. "Necessary" in some sense to get a good fit. But now it seems there may be simpler ways---alternatives to inflation that don't involve postulating an exotic "inflation" field, fine-tuning its potential, quantum fluctuations to start or to stop, elaborate bubble universes etc etc.

There seem to be simpler more straightforward less "made-up" alternatives that get the same match to reality, so inflation no longer seems as "necessary".

 

[marcus]

So a simpler version of your question might be to forget about the size at the "beginning of explosive inflation" and just ask for a function of time that estimates the scale factor as it evolves during a time interval spanning shortly before and shortly after the start of expansion. That is the kind of thing that for example Yi-Fu Cai and Edward Wilson-Ewing plot in their inflation-free scenario they proposed in December 2014, called "LambdaCDM bounce"

If you google "LambdaCDM bounce" the first hit will be a preprint PDF of their paper at the preprint arXiv.org. As I recall it was almost immediately accepted for publication and came in peer-review journal form in March 2015. But the preprint is free to download. Lots of diagrams.

That is just one of a growing body of literature about a no-singularity no-inflation start of the observed expansion. I like it in particular because it uses the actual standard cosmic model LambdaCDM with fairly standard parameters, and because it has a bunch of figures, and because it has some parts that are comparatively easy to understand and assimilate.

 

[clinden]

Thank you Marcus. I will study the paper.
I asked my question as I had found estimates ranging between the Planck length (observable universe) and about 100 kilometers.

 

[marcus]

Some parts you will be able to get the idea, some parts will seem opaque and impossible---too technical. As long as you think it can help, ask questions about the paper here---I don't understand as much as some of the others but I can try, and others may try, to answer.
they have a convenient timescale called conformal time which they write with an "eta" η. And their formula (8) shows how to convert back and forth between that and the real time.
|η| is just the size of a generic distance so as distances increase this "time" parameter increases proportionally. It's just a convenient device for simplifying the formulas and you can always convert back to real time t, in (incredibly tiny) fractions of a second.

So you see in their Figure 2a on page 5---the extremely simple relation between distance size as it evolves over conformal time. Linear. really obvious. the graph looks like a letter Vee.
Like a letter Vee except rounded at the very corner where the bounce happens.
Quantum mechanics takes over and refuses to allow the density of matter/energy to exceed a certain critical density, gravity briefly repels and the bounce happens.
Except for that tiny blunt rounded corner at the bottom of the Vee, the relation is linear. Straight line contraction and expansion of distances, in conformal time.

Figure 2b shows how the Hubble expansion rate evolves over conformal time
from slowly declining negative in the contraction phase, to extreme negative, then a rebound to extreme positive and then slowing to nearly steady slightly declining positive.

 

[Chronos]

It depends on your model and preference. The classical BB model assumes the observable universe begins as a point particle [not unlike an electron]. The quantum version smears it out across a region that could, mathematically, be regarded as infinite, or undefined.

 

[clinden]

Some parts you will be able to get the idea, some parts will seem opaque and impossible---too technical. As long as you think it can help, ask questions about the paper here---I don't understand as much as some of the others but I can try, and others may try, to answer.

Well Marcus, you are right. Much of it is too technical for me. But, 2 questions;
1 There was no discussion of entropy pre/post bounce. Any comment on this?
2 How has the paper been received by both bounce and non-bounce mavens?

 

[marcus]

... 2 questions;
1 There was no discussion of entropy pre/post bounce. Any comment on this?
2 How has the paper been received by both bounce and non-bounce mavens?

Too early to judge reception. Edward Wilson-Ewing was just awarded the Bronstein Prize. That is a prize given to some up-and-coming young quantum gravity researcher every two years. But it is a loop-community thing. I'm not sure who would qualify as a "non-bounce maven" but they most likely would never have heard of the young Russian researcher Lev Bronstein, a key figure at the very beginning of quantum gravity research, or of the prize named after him. Anyway I'd say there's favorable reception and strong approval in a limited circle.

In a GR context we should be prepared for surprises. As you may know there is no global energy conservation law. Also entropy is observer-dependent.
The second law only applies as long as you stay with one given observer. There was a paper by Robert Wald in the 1990s about the subtleties of defining entropy in GR. That seems to carry over to quantized GR.