What is the most detailed analysis of the very early universe?

[ficodr]

Hello people! I’m an engineer, and i’ve received math training, but i assume not to the level necessary to understand the deepest laws of the nature. Since I’ve reading about the Large Hadron Collider, I’ve been more and more interested in the cosmology.

I’m interested in the VERY VERY EARLY universe (from t=zero to t=1 sec.), … I wonder which book (or books, or articles/publications) have the most detailed analysis of that period of time… and if there is any other book like “The first 3 minutes” by Steven Weinberg (I don’t know if its quite old, because I have the 1977 edition, I guess maybe there’s another more recent and updated book).

Thank you for all the answers, and I’m very lucky to have discovered this forum… I’ll post more often.

Greetings!

Ficodr

 

[edgepflow]

For times greater than the Planck time (10^-43 sec), General Relativity applies and you can model the expansion of the universe with the Friedmann equation. This is discussed on line and in any good introductory cosmology textbooks. You do not need to know General Relativity to manipulate the Freedmann equation.

For times greater than zero but less than 10^-43 seconds, you need quantum gravity which is not fully established. You could look into current research in String Theory and Loop Quantum gravity.

I would start with the Friedmann equation. You can do "desktop universe" style solutions without too much difficulty. I an an engineering graduate too and have learned some of this on my own time.

 

[marcus]

The keyword that gets you Loop cosmology on Spires is "quantum cosmology, loop space"

The literature contains some fairly detailed analysis/modeling of what replaces the singularity. They run numerical (computer) models of the bounce, with various different assumptions---types of matter field, inflation or not, different versions of the collapse phase.

If you want to glance at the literature here's a listing of recent papers ordered by cite-count (so you get the most cited papers first).

This is QC as a whole (not limited to Loop) after 2008 (papers from 2009 and later):
http://www-library.desy.de/cgi-bin/spiface/find/hep/www?rawcmd=FIND+DK+QUANTUM+COSMOLOGY+AND+DATE+%3E+2008&FORMAT=www&SEQUENCE=citecount%28d%29

You will see plenty of Loop papers among those highly cited on the list. What happened was that after people had been working on LQG for some 10-15 years it was applied to cosmology (basically to get a quantum version of the Friedmann equation) and seen to resolve the singularity into a bounce. The mathematical treatment was significantly improved by Ashtekar's group around 2006 and both analytical and numerical studies proliferated. Inflation was gradually included, and phenomenology (ways of testing with proposed space instruments). By 2009 this led more or less to what we see today.

I think the most meaningful way to approach the subject is not to try to visualize the universe when it was, say, at 40% of Planck density---I don't think we have the conceptual tools to do that yet. But rather to see what people are saying about the features of ancient CMB light which are the observable consequences of the Loop bounce model---if it is correct.

In other words, focus on what we ought to be able to observe in the CMB, if we put up instruments able to map the polarization (as well as what has been mapped so far: the temperature). One should be able to detect the imprint of gravitational waves in the CMB and determine their spectrum.

With that in mind, I will get a link to the Loop early universe phenomenology (i.e. testing) literature. this is what I think is the most interesting thing about it---the empirical side.
Here is the empirical-oriented stuff from 2008 and later:
http://www-library.desy.de/cgi-bin/spiface/find/hep/www?rawcmd=FIND+%28DK+QUANTUM+GRAVITY%2C+LOOP+SPACE+OR+DK+QUANTUM+COSMOLOGY%2C+LOOP+SPACE%29+AND+%28DK+PRIMORDIAL%2C+FLUCTUATION+OR+DK+INFLATION+OR+DK+COSMIC+BACKGROUND+RADIATION%29+AND+DATE+%3E+2007&FORMAT=www&SEQUENCE=citecount%28d%29
For a bit more up-to-date selection here is the same stuff but from 2009 and later (i.e. after 2008):
http://www-library.desy.de/cgi-bin/spiface/find/hep/www?rawcmd=FIND+%28DK+QUANTUM+GRAVITY%2C+LOOP+SPACE+OR+DK+QUANTUM+COSMOLOGY%2C+LOOP+SPACE%29+AND+%28DK+PRIMORDIAL%2C+FLUCTUATION+OR+DK+INFLATION+OR+DK+COSMIC+BACKGROUND+RADIATION%29+AND+DATE+%3E+2008&FORMAT=www&SEQUENCE=citecount%28d%29

 

[ficodr]

thank you for the answers, my friends... I'll keep trying to understand (as most as i can) that epoch of time.

 

[edgepflow]

Marcus, I tried to skim a few of this papers to get a gross overview of this "bounce."

Is the general idea as follows?

* Universe is at the minimum scale factor (amin) at Planck time.
* At t=0, the scale factor of the universe is some value larger than amin. It then decreases to amin at the Planck time.
* After the Planck time, GR and the Friedmann equation apply.

 

[lasm2000]

At what level you want to read? For popular level books try "The Inflationary Universe" by Alan H. Guth.

At undergrad level "An Introduction to Modern Cosmology" by Andrew Liddle only requires calculus and elementary physics. If you are getting serious then learn GR, a very accesible book is "Gravity" by James Hartle.

At grad level "The Primordial Density Perturbation: Cosmology, Inflation and the Origin of Structure" by David H. Lyth and Andrew R. Liddle deals exclusively with the early universe. If you know GR at the level of Hartle and some classical/quantum mechanics you should be ready for it. The classic reference is "The Early Universe" by Kolb and Turner, it is very terse but has a very extensive coverage.

 

[bapowell]

The classic reference is "The Early Universe" by Kolb and Turner, it is very terse but has a very extensive coverage.

Terse and extensive? That's confusing. But confusion aside, I disagree that Kolb and Turner is in any way terse. Dated, but not terse.

 

[twofish-quant]

I’m interested in the VERY VERY EARLY universe (from t=zero to t=1 sec.), … I wonder which book (or books, or articles/publications) have the most detailed analysis of that period of time…

In addition to the references above, here is a page from wikipedia that let's you organize the time scales...

http://en.wikipedia.org/wiki/Timeline_of_the_Big_Bang

Something to point out that anything that happens before 10^-43 second is *total* speculation. In that era we are in the "your guess is as good as mine era."

 

[twofish-quant]

* Universe is at the minimum scale factor (amin) at Planck time.
* At t=0, the scale factor of the universe is some value larger than amin. It then decreases to amin at the Planck time.
* After the Planck time, GR and the Friedmann equation apply.

After Planck time, GR and Friedman more or less apply. Before Planck's Time, we don't have enough information to do anything more than guess what applies, and things go dark so to speak.

 

[marcus]

Edgeflow, I'll try to say what my impression of it is in my own words. QG is about developing a quantum version of the law of gravity (the 1915 Einstein version of it). The Loop quantum version turns out to have quantum corrections that become important at very high density and make it impossible for time to stop.

The quantum corrections become important starting around 1% of Planck density and as the density rises they dominate and cause gravity to repel instead of attract. The actual bounce occurs at about 40% of Planck density.

You can google Planck units and get more about that. Wikipedia has an article. Planck length, Planck volume, Planck mass, Planck density = unit mass per unit volume. These units work better for some kinds of basic physics than the SI metric ones do. G, c, and hbar have the value one in these units and it makes equations simpler.

So the Loop gravity law let's you work back in time, and it almost exactly duplicates the old picture until you get to very high density. And then quantum effects tae over and you find that time does not stop.
You just find that it reaches 40% Planck density and then opens up again.

they run computer models using numerical version of the equations, and they also analytically solve, and it always happens. No matter what parameters you plug in, you get this bounce. So no "beginning of time and space".

Just a mundane contraction, rebound, and expansion.

That still leaves the mystery of existence (if you are philosophically minded) why does existence exist? It doesn't say anything about that. It just says that existence didn't "begin" at that particular moment. The contracting phase prior to bounce was a "classical universe" (according to this picture) which could have gone back billions of years. We don't have to speculate about that, we can just focus on the bounce---and see if we can test it with observations. Did it leave an imprint on the CMB? Can we disprove? Can we rule it out? Science proceeds by little steps, one thing at a time. So rather than try to answer the Big Question of where it all came from, these people are just confronting a simpler question: did a bounce, according to such and such dynamical model, occur, or didn't it?

That's my rough overview of the basic thrust of the list of papers you glanced at

Marcus, I tried to skim a few of this papers to get a gross overview of this "bounce."

Is the general idea as follows?

* Universe is at the minimum scale factor (amin) at Planck time.
* At t=0, the scale factor of the universe is some value larger than amin. It then decreases to amin at the Planck time.
* After the Planck time, GR and the Friedmann equation apply.

 

[edgepflow]

Thanks Marcus - good information. I want to learn more about this subject. I am totally open minded to this stuff.

You mentioned the contracting phase prior to the bounce was a "classical universe."

So if the universe was contracting, it must have been closed. Was it closed due to a negative cosmological constant?

 

[marcus]

Thanks Marcus - good information. I want to learn more about this subject. I am totally open minded to this stuff.

You mentioned the contracting phase prior to the bounce was a "classical universe."

So if the universe was contracting, it must have been closed. Was it closed due to a negative cosmological constant?

I can't speak as an expert, can only refer you to papers on this. Ashtekar is the main authority. When he refers to the prior contracting phase as "classical" he means governed by ordinary vintage 1915 GR (until the close to the bounce). Here is his most recent review for non-specialists.
http://arxiv.org/abs/1005.5491
The Big Bang and the Quantum
Abhay Ashtekar

There are collapsing solutions of classical GR that have zero cosmological constant (let's call it Lambda). You don't need a negative Lambda to get a crunch.

I'm not entirely sure what you mean by "closed". A classical universe solution can be spatially infinite and still collapse (it just does not collapse to a classical point singularity).

The term closed had a clear meaning before 1998 when there were just 3 cases considered (closed, flat, open). Closed meant both spatially closed and expanding now but destined to eventually stop expanding and collapse.

Now the term closed can really get people confused. Do you mean spatially closed? I.e. like a sphere, finite, closed in on itself?

Instead of "closed" it would be clearer just to say spatially finite.

If we lived in a collapsing universe that had been collapsing forever, (not exactly but) a little bit like a movie of this one run backwards, with perhaps 13.7 billion years left to go, then the mere fact that it was collapsing would not imply anything about space being finite.

In a collapsing universe, space can be finite or infinite.

And likewise Lambda can be slightly pos or zero or slightly neg.

It is still a mystery how the U could exist, I can only express wonder about that. And confess I am just a half-evolved ape descended from a fish. Should a fish expect to understand? There is still the basic mystery. But the mystery is just no longer concentrated at a particular instant.

So it has come time for us to study the big bang observationally and model it and test empirically, strange as it seems. But this is hardly the end of the journey, it is just one more step.

I don't have time to correct this post and make it more understandable. Have to go. Hope this is all right.

 

[edgepflow]

Thanks for the reference paper Marcus. I need to study this.

I will have to think some more about how a spatially infinite universe can collapse.

I guess I have the sphere (closed), flat sheet of paper (flat) and saddle (open) universe etched in my mind. In this model, for a universe to ever collapse, it must be finite and closed ?

For the universe to be closed:

omega (matter density) + omega (curvature) + omega (cosmological constant) > 1.

Like you said, the cosmological constant could be zero and still have a closed universe if the other terms add to greater than 1.

So if I understand the idea of a spatially infinity and collapsing universe is not part of the Friedmann GR model but based on loop quantum cosmololgy?

I will read up on this some more.

 

[marcus]

.

I will have to think some more about how a spatially infinite universe can collapse.

I guess I have the sphere (closed), flat sheet of paper (flat) and saddle (open) universe etched in my mind. In this model, for a universe to ever collapse, it must be finite and closed ?

...

I understand the puzzlement and I'd be happy if anyone wants to correct me on this. All I can do is tell you my take on it.

We all have that pre-1998 picture etched in our mind of the sphere, flat, and saddle. And we all have the "Truth" etched our mind that only the sphere case will eventually stop expanding and collapse. These pictures apply for Lambda = 0, which is OK. We should understand the Lambda = 0 case, so let us focus on that.

But you did not read the fine print! Those pictures were based on the assumption that the U was expanding now! They did not say that flat and saddle cases cannot collapse. They only said that flat and saddle can only do one or the other (expand or collapse) but not both.

The equation that those three cases come from is the Friedmann equation you see here:
http://en.wikipedia.org/wiki/Friedmann_equations (EDIT: you already know the model, I just realized.)
and it is TIME-SYMMETRIC.
If you have a solution in the flat case, for example, you can run the movie backwards and get another solution.

The true meaning of the pictures is that if, for example, it is the flat case then either
1. the universe has always been contracting and will eventually crunch, or
2. the universe is expanding and will continue indefinitely to do so.

You are an engineering graduate so you know how to change the time variable in that equation for H² in Wikipedia. replace t by -t
H becomes negative, but it does not change the square. The righthand side is unchanged.

All we do that is different now is that we don't believe in a singularity and we quantize the equations so matter and geometry resist infinite density, the model no longer blows up, we get a bounce instead of a crunch.

So there is a classical collapsing U followed by a classical expanding U, with a brief quantum bridge.

This picture is simplified in the same way that the classical Friedmann model is----uniformity: homogeneity and isotropy. The matter is pictured as evenly spread out, characterized only by a uniform density. So you can keep on investigating and ask questions in greater detail. Like what happens to the black holes in the collapsing phase? And so on. But this is a good picture to start with.
Just realize that it is not exactly the same movie played backwards, only approximately, at the level of the Friedmann model with its uniform structureless matter.

EDIT: I looked back and realized that you know the Friedmann equation model and were talking about it right form the start. So I wrote this all at the wrong level! Sorry for this clumsiness. I won't bother to rewrite it. Maybe someone who is NOT thinking with the math model will get something out of this.

 

[edgepflow]

Thanks Marcus, I see what you are saying. I needed to think outside the bang and notice that even a flat universe with no cosmological constant can always have been contracting and will eventually crunch.

So, this LQC model has now introduced the idea of this classical universe that has always been contracting. Now I am thinking about the other possibility: a flat universe with no cosmological constant that banged. This universe could, in theory, persist forever. Conversely, the LQC pre-bounce contracting universe could also have previously existed forever.

Are we now confronted with the possibility an infinitely old universe before the bounce?

 

[marcus]

...

Are we now confronted with the possibility an infinitely old universe before the bounce?

Yes that is one possible model, if you want to think about Big Questions. There are various pictures of eternity and various dynamical models.

But I think a number of people do not worry about the very long term but just want to understand the big bang better.

The basic idea of empirical science is theories are not meant to be believed, they are meant to be tested. The LQC bounce is something to test. I posted that link to a list of phenomenology papers (pheno people are professional theory-testers, they win either way it goes )

The idea is let's focus on did this kind of bounce happen, or not?

Thinking very long term, beyond that immediate question, can get awfully speculative---does the cosmo constant change? etc etc. Even philosophical. No real reason to go there when the immediate hypothesis has not even been tested yet!

I'll get that list of pheno papers relating to CMB-polarization observation and bounce (also the connection of bounce with inflation has come up, the two hypotheses tend to reinforce each other)

http://www-library.desy.de/cgi-bin/spiface/find/hep/www?rawcmd=FIND+%28DK+QUANTUM+GRAVITY%2C+LOOP+SPACE+OR+DK+QUANTUM+COSMOLOGY%2C+LOOP+SPACE%29+AND+%28DK+PRIMORDIAL%2C+FLUCTUATION+OR+DK+INFLATION+OR+DK+COSMIC+BACKGROUND+RADIATION%29+AND+DATE+%3E+2008&FORMAT=www&SEQUENCE=citecount%28d%29

With one or two exceptions these are bouce pheno papers from 2009 onwards, ranked by cite-count.
There are thirty some.

 

[Chronos]

I agree with the phenomenological approach, marcus. It is the only truly scientific approach, imo. At present, we can only affirm it appears to be at least 13.7 billion years of age in its present form. Prior states of the universe may be as different as we are from the fertilized ovum from which we emerged. The truth may be phenomenologically inaccessible.