# Questions Concerning The Planck Epoch

1. Jan 19, 2015

### Stan Stuchinski

Questions Concerning The Planck Epoch​

I must begin this thread with an apology.

I am NOT a physicist nor astronomer; in fact, my degree is in biology. However, for decades I have had a deep interest in what is commonly referred to as Big Bang Cosmology and have an “educated layman’s” knowledge and appreciation for this field.

My eventual goal is to establish a “best-guess” or “theoretically-acceptable” step-by-step chronology of the Big Bang. I have found WikiPedia’s Chronology of the Universe to be an extremely useful starting point. However, a number of areas in their Chronology are in need of clarification for my humble intellect. In addition, in cross referencing WikiPedia’s information with other sources, both on and off the Internet, I have found that there exists no concensus of opinion regarding certain data and concepts. I am hoping that the intellect and benevolence of the members of this forum will see fit to display a little patience and assist me in my understanding.

So allow me to begin at the beginning… with the Planck Epoch:

Five Basic Parameters of the Planck Epoch (Time 0 to 10^-43 second)

PARAMETER ONE: Time
Time at BEGINNING of Epoch: 0
Time at END of Epoch: 10^-43 second (1 Planck Time)

PARAMETER TWO: DIAMETER
Diameter of Universe at BEGINNING of Epoch: 0
Diameter of Universe at END of Epoch: 10^-35 m (1 Planck Length)

PARAMETER THREE: TEMPERATURE
Temperature at BEGINNING of Epoch: ∞
Temperature at END of Epoch: 10^32 K (Planck Temperature)

PARAMETER FOUR: MASS
Mass at BEGINNING of Epoch: ∞
Mass at END of Epoch: 10^19 GeV (Planck Mass)

PARAMETER FIVE: DENSITY
Density at BEGINNING of Epoch: ∞
Density at END of Epoch: 10^97 g/m3 (Planck Density)

Now I DO understand that (to quote http://www.whillyard.com/science-pages/planck-epoch.html): “The equations of General Relativity suggest that the Universe started as a singularity; that is, infinite density in an infinitely small space. Scientifically, this is not acceptable, and most scientists agree that General Relativity breaks down below the Planck Length due to random quantum mechanical fluctuations. Quantum physics places limits on size and density, and suggests that the expansion started with the entire Universe in a space with the diameter of the Planck length, and with the density at around 10^94 grams per cubic centimeter.”

(Please understand that I am using time=0 (the “singularity”) solely as a metaphorical starting point.)

Now for my for my humble (and no doubt naïve) questions regarding this initial Epoch:

Question # 1: Are my (rounded to the nearest factor of 10) numbers for the Planck Epoch even remotely accurate and theoretically acceptable?

Question # 2: During the Planck Epoch all four of the forces observable in the present-day Universe were combined into a single, unified force, sometimes referred to as the Superforce, Supergravity, or Mother-Force. Am I correct in stating that eventually (at t = 10^-43 second after the beginning) the gravitational force condensed out from the Superforce, and this symmetry-breaking event marked the END of the Planck Epoch and initiated the BEGINNING of the next epoch, the GUT Epoch?

Stan

2. Jan 19, 2015

### Staff: Mentor

This only applies if the universe is closed, which according to our best current model it isn't. If the universe isn't closed, its diameter is always infinite.

What is this supposed to be the mass of?

Given the assumption of an initial singularity and a classical GR model of expansion from that beginning, the numbers are obvious: they're just the Planck numbers (Planck time/length/density). Those numbers mark the Planck epoch by definition.

The problem, of course, is that assumption. As you note, it's not really considered scientifically acceptable. We actually don't know if the classical GR model you're using is even close to what actually happened in this regime; basically, we don't really have good knowledge of anything prior to the end of the inflationary epoch. We don't even know if there was a Planck epoch; there are models being investigated in which the universe "bounces" from a previous contracting phase into its current expanding phase, without ever getting down to Planck dimensions.

This is all speculative too, because we don't have a good theory of a single "superforce"--we know how to unify the three non-gravitational interactions (strong, weak, and electromagnetic), but we don't know how to unify gravity with the others--and because we don't know, even if there was a single superforce at one time, exactly when the symmetry between gravity and the others would have been broken; it seems plausible that it would have been at around Planck dimensions, but without any evidence and without any theory all we're really doing is guessing.

3. Jan 20, 2015

### Stan Stuchinski

Good morning, Pete, and thanks for your prompt and courteous response to my initial post.

In reading your answers, it occurs to me that I may have been wise to add to the preface to my post that I am trying to develop a reasonably cogent and systematic Big Bang timeline that is intellectually accessible and logical to the scientifically passionate LAYMAN (myself included). I feel that, for the first time in history, we are currently on the cusp of developing a true Theory of Everything, and I want to display this information in a way that it can be at least somewhat understood and APPRECIATED by the non-scientist. I fully realize that to accomplish this it is necessary to “bend the rules” to a degree (i.e. “no analogy can be 100% accurate”)

For example:

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(1)
PARAMETER TWO: DIAMETER
Diameter of Universe at BEGINNING of Epoch: 0
Diameter of Universe at END of Epoch: 10^-35 m (1 Planck Length)

Your reply: “This only applies if the universe is closed, which according to our best current model it isn't. If the universe isn't closed, its diameter is always infinite.”

Now, I DO understand that… “According to the FLRW model, observational data best fit with the conclusion that the shape of the Universe is infinite and flat.”

However… Although I realize that the concept of “infinity” is a mathematical necessity, quite frankly, I have trouble “wrapping my mind around” ANY physical quantity (the Universe included) that is “infinite.” Perhaps I should have used the term OBSERVABLE Universe, the current diameter of which is, if I’m not mistaken, generally given as 92 billion light years. Using this definition, the size of the Universe at the end of the Inflationary Epoch (for example) is POPULARLY given as “approximately 10 centimeters in diameter (the size of a grapefruit).”

-Stan

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Likewise…

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(2)
PARAMETER FOUR: MASS
Mass at BEGINNING of Epoch: ∞
Mass at END of Epoch: 10^19 GeV (Planck Mass)

Quote: “Unlike all other Planck based units and most Planck derived units, the Planck mass has a scale more or less CONCEIVABLE TO HUMANS.” And this, after all, is what I’m after… a conceptual picture of the evolution of the Universe that is CONCEIVABLE (and able to be appreciated) by the non-scientist. Thus, I am using the Planck mass as the mass of the nascent Universe at this point; in fact, I am using ALL of the Planck-derived units as applying to the Universe as a whole at this time. (Planck particle? Planckon?)

-Stan

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(3)
Are my (rounded to the nearest factor of 10) numbers for the Planck Epoch even remotely accurate and theoretically acceptable?

Your reply: “Given the assumption of an initial singularity and a classical GR model of expansion from that beginning, the numbers are obvious: they're just the Planck numbers (Planck time/length/density). Those numbers mark the Planck epoch by definition.”

“The problem, of course, is that assumption. As you note, it's not really considered scientifically acceptable. We actually don't know if the classical GR model you're using is even close to what actually happened in this regime; basically, we don't really have good knowledge of anything prior to the end of the inflationary epoch. We don't even know if there was a Planck epoch; there are models being investigated in which the universe "bounces" from a previous contracting phase into its current expanding phase, without ever getting down to Planck dimensions.”

Yep! Again, my friend, you are 100% accurate in your appraisal of my poor attempts at explanation. It is true that we don’t even know if there WAS a Planck Epoch; it is certainly not a “carved-in-stone-empirically-tested-and-proven” fact. But I feel that when dealing with a concept as speculative as the beginning and evolution of the Universe certain assumptions HAVE to be made, as an explanatory model ONLY. I look at it merely as a “conjecturally convenient” way to express a beginning of the Universe to a person who would otherwise yawn at the truly accurate explanation. It goes without saying that I also look at it as a way that I, myself, can grasp (at least to a degree) this era.

-Stan

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(4)
Am I correct in stating that eventually (at t = 10^-43 second after the beginning) the gravitational force condensed out from the Superforce, and this symmetry-breaking event marked the END of the Planck Epoch and initiated the BEGINNING of the next epoch, the GUT Epoch?

Your reply: “This is all speculative too, because we don't have a good theory of a single "superforce"--we know how to unify the three non-gravitational interactions (strong, weak, and electromagnetic), but we don't know how to unify gravity with the others--and because we don't know, even if there was a single superforce at one time, exactly when the symmetry between gravity and the others would have been broken; it seems plausible that it would have been at around Planck dimensions, but without any evidence and without any theory all we're really doing is guessing.”

Absolutely! It IS all “speculative!” And I agree that “all we’re really doing is guessing.” But I just feel that we have to start somewhere and proceed to further, LESS speculative eras of cosmic evolution.

As you state, Pete… “it seems plausible…” Well, “plausible” is ALL I’m after – a best-guess scenario that has at least a MODICUM of hard scientific theory behind it.

-Stan

At this point it might pay to further state:

1. I am NOT a proponent of any of the theories that incorporate a “bounce” from a previous universal contraction. In my opinion, such theories necessarily incorporate “infinities” of one kind or another. I am more intellectually comfortable with a defined beginning.

2. Conversely, I AM a proponent of a (limited) Multiverse theory, simply because it neatly solves the Anthropic Problem and eliminates the need for a “universe custom designed for intelligent life.”

3. Although I favor a specific beginning of the Universe, my aim is NOT to use it as evidence for a so-called Prime Mover; I am NOT a theist. I consider myself ambivalent on the subject; while a comprehensive theory of cosmic evolution with a definite beginning cannot definitively rule out a Prime Mover, it neither “proves” the necessity for one.

4. I consider myself to be a Big Bang “semi-conservative.” By that I mean that while I do not yet give a great deal of credence to such ideas as String Theory (M-theory), I DO ascribe to concepts like Super Symmetry (I am hoping that the next run of the LHC this spring will give concrete evidence of super symmetric partners.)

In closing this reply, Peter, I would once again like to thank you for your thoughts regarding my initial post.

-Stan

4. Jan 20, 2015

### Staff: Mentor

Then I think focusing on the Planck epoch is a mistake, because that epoch is the least likely to be included in any theory of everything we come up with.

You are not the only one. However, that's what our current best-fit model says. So any model that does not include infinite spatial extent for the universe is not consistent with our current best-fit model, and hence doesn't seem to me to be a step in the right direction given your stated goal of describing the best model we have in layman's terms.

It's about 47 billion light years. I'm not sure where you got the 92 billion figure from.

I think you must mean the observable universe, correct? If the universe as a whole is spatially infinite, as above, it has an infinite amount of mass.

Sure, but it helps to make assumptions that are less likely to turn out wrong as our models improve. The assumptions you are using for the Planck epoch are, as I said above, probably the most likely to turn out wrong as our models improve.

How does the Planck epoch qualify as "less" speculative? It's the most speculative of all the epochs that anyone has proposed, because it's the part of the "naive" classical model (starting with a singularity of infinite density) that is most likely to be overridden by a theory of quantum gravity when we have it--"overridden" in the sense that it won't even survive as an approximation, but will simply no longer be there at all once quantum effects are taken into account.

Then, once again, I think you are making a mistake to focus on the Planck epoch, because it has practically no "hard scientific theory" behind it. It is a "naive" extrapolation of the pure classical GR model back to the initial singularity, but that is the one regime where we are practically certain that the pure classical GR model is wrong--not just an approximation, but wrong period, because quantum effects completely change the dynamics.

Again, you are not alone, but all such theories are purely speculative at this point, like all theories of the pre-inflation era that don't incorporate a "bounce".

Again, you are not alone, but this theory is purely speculative at this point.

Basically, you are trying to put together a layman's summary of what our "best guess" at a theory of everything will say about what happened before the earliest time we have any real evidence of--the end of the inflationary epoch. The problem is that right now there is no "best guess". We do not have a theory in this regime; all we have are speculations, and there simply isn't enough evidence to choose between them, or even to know if our current speculations cover all the possibilities. So, while I sympathize with what you are trying to do, I think it's premature. The only really correct thing to say to a lay person at this point is that we don't know.

5. Jan 21, 2015

### Stan Stuchinski

I think that, once again, Peter, my friend, that I must beg your forgiveness for not expressing myself clearly.

For example:

You state: “Then I think focusing on the Planck epoch is a mistake, because that epoch is the least likely to be included in any theory of everything we come up with.”

You are absolutely, 100% correct! Anything that we can state regarding the Planck Epoch borders on science fiction. What I obviously did not make clear is that I am not FOCUSING on the Planck Epoch; I am merely using it as a necessary (but evil?) starting point. I currently feel that, with your assistance, I have been able to “smooth off (some of) the rough edges” of my admittedly meager understanding of this highly speculative Epoch. I now plan to move on to increasingly LESS speculative epochs, beginning with, of course, Epoch # 2 – the GUT Epoch. (Hoo, boy, THIS is gonna be fun!)

-Stan

You state (in referring to my figure for diameter of the Observable Universe): “It's about 47 billion light years. I'm not sure where you got the 92 billion figure from.”

Note that I am talking about DIAMETER, which, if I’m not mistaken, IS generally given as approximately 92 billion light years; your figure of 47 billion light years is (again, if I’m not mistaken) the RADIUS. Wikipedia gives an excellent discussion of this topic at: http://en.wikipedia.org/wiki/Observable_universe. I’ve also researched this figure on a number of other sites, and the accepted wisdom is generally that the DIAMETER of the (observable) Universe is 96 billion light years. (or am I misinterpreting something?)

-Stan

You state: “How does the Planck epoch qualify as "less" speculative? It's the most speculative of all the epochs that anyone has proposed, because it's the part of the "naive" classical model (starting with a singularity of infinite density) that is most likely to be overridden by a theory of quantum gravity when we have it--"overridden" in the sense that it won't even survive as an approximation, but will simply no longer be there at all once quantum effects are taken into account.”

Again, I apologize for not being clear enough, but if you reread my statement… “I just feel that we have to start somewhere and proceed to further, LESS speculative eras of cosmic evolution…” I am attempting to AGREE that the Planck Epoch IS the most speculative epoch, and that I will continue to move toward more current, LESS speculative eras.

-Stan

You state: “…So, while I sympathize with what you are trying to do, I think it's premature. The only really correct thing to say to a lay person at this point is that we don't know.”

Again, you are accurate…We don’t know! However, what I am trying to do is to make the case that, although ALL conjectures about the very early Universe are ‘premature’ at this point, that we are at least on our way TOWARD developing a conceptual framework of the genesis of the Universe from nothing (creation ex nihilo/vacuum genesis) to the complexity we observe around us today, WITHOUT resorting to a Prime Mover.

-Stan

In closing, I would again like to thank you for your time and input and (most importantly) your infinite patience.

Stan

6. Jan 21, 2015

### Staff: Mentor

Why is it necessary? Why can't we just say that, before a certain point, we simply don't know enough to give even a "best guess" model?

Ah, sorry, I was thinking of radius, yes.

I think this is going beyond what the science can actually justify at this point.

7. Jan 21, 2015

### bapowell

Until we know whether the universe itself is infinite or finite in extent, we really cannot be making such claims.

8. Jan 21, 2015

### nikkkom

It is not a "necessary" (what that even means) starting point.

If you want to understand Big Bang in layman terms, it may be better to go backwards in time, and along with forming a picture of the Universe at every epoch, you also need to memorize how well is our knowledge about it. For example:

200..400 thousand years after BB - recombination epoch:
What was happening: read-hot (~4000K) ionized hydrogen and helium gas cools, recombines into neutral gas.
How sure are we: 100% - we have definitive evidence of it

3 minutes..200 thousand years - nucleosynthesis:
What was happening: when temperature fell to 10 MeV, previously free neutrons merged with protons and form deuterium and He4 nuclei
How sure are we: 100%

10–6 second...1 second
What was happening: The quark–gluon plasma that composes the Universe cools. Quarks can no longer be created by gammas. Hadrons, including baryons such as protons and neutrons, form.
How sure are we: 99% (not giving it 100% yet since quark–gluon plasma is not fully understood theoretically yet, and only recently was observed in experiments)

10–12 second...10–6 second, or more usefully, temperature ~150 GeV - electroweak symmetry breaking.
What was happening: Higgs field oscillations (density of Higgs particles) become smaller that the size of the "Mexican hat" central bump of potential of Higgs field's energy, and Higgs field settled into its energy minimum with nonzero value: IOW, the vacuum as we know it has formed, electromagnetism and weak force began to look the way we see them now.
How sure are we: 95% (Higgs particle was only recently seen, confirming the model)

At temperature somewhere above 10 TeV: baryogenesis
What was happening: somehow, number of quarks become larger that the number of antiquarks.
How sure are we: we almost certain this did happen (unless there are large volumes of Universe filled with antimatter - very unlikely), but we don't know how it happened. We know a few processes which can produce excess of matter, but calculations say these specific processes couldn't do it.

And so on.

As you go deeper, you'll notice that theories are becoming more and more speculative, and less supported by facts or even calculations. As a layman, you should choose a point where you say to yourself: "ok, at this point these guys seem to be just guessing and throwing wild ideas around. Science did not crack this nut yet."

Popular articles usually fail to convey this point.

9. Jan 21, 2015

### Stan Stuchinski

Stan>>> Again, my friend, you ARE right. This IS going beyond what science CAN justify at this point. Perhaps you feel that I'm being intellectually dishonest in my approach, but I'm going for a "grand scheme comprehensibility" and NOT a "proven-beyond-all-reasonable-doubt" chronology. You may understand my point of view a little better by reading my reply to "nikkkom," below.

All-in-all, the Planck Epoch DOES, quite frankly, leave very little to discuss by it's very speculative nature. I appreciate the feedback I've received from other members, and the answers I've received HAVE helped me a great deal; it's been VERY instructive!

I think that I'll now move on to epoch #2, the GUT Epoch (or, using the term I prefer, the ElectroNuclear Epoch). It's just a little less speculative, and there's a lot more going on. And I DO have questions.....

-Stan

10. Jan 21, 2015

### Stan Stuchinski

Stan>>> Holy cow! In looking at your avatar, I can only surmise that you ARE "The Dude!" In that case I must inevitably bow to superior knowledge and intellect!

Take care and have a terrific evening, my friend.

-Stan

11. Jan 22, 2015

### Stan Stuchinski

Let me begin, Nikkkom, by saying that I deeply appreciate the time you took to generate your reply to my post. I found it to be extremely enlightening and, of course, it engendered questions. Please understand also that, when I throw out a question or make a comment, it is NOT meant to be argumentative; it is merely my weak attempt to clarify certain aspects.

-Stan

(nikkkom says): “If you want to understand Big Bang in layman terms, it may be better to go backwards in time…”

(Stan says): I take your point, Nikkkom. Many, if not most, of the early universe chronologies I’ve seen DO go ‘backwards in time.’ In fact, when I started my personal education of Big Bang Theory (‘way back when the Big Bang and the Steady State were still equally competitive theories), going ‘backward in time,’ going from the LESS speculative to the (far more) speculative eras WAS the way that I learned it. I’m just taking a different approach.

(nikkkom says): “…and along with forming a picture of the Universe at every epoch, you also need to memorize how well is our knowledge about it. For example:”
“200..400 thousand years after BB - recombination epoch:
What was happening: read-hot (~4000K) ionized hydrogen and helium gas cools, recombines into neutral gas.
How sure are we: 100% - we have definitive evidence of it”

(Stan says): Yep! We DO have definitive evidence of it (although I prefer the term ‘Decoupling Epoch’). However, the physical parameters of this epoch are not as clearly defined. For example, the time at which decoupling occurred I’ve seen (in a number of sources) as more closely confined to right AT 377,000 years. Likewise, I’ve seen the temperature given as 3,000K.

And here, I have a question: Why do we continue to retain the term “RE-combination” for this period? Is the term a misnomer, considering that it represents the first time that electrically neutral hydrogen formed. Hydrogen and helium ions are combining to form electrically neutral atoms; they are not REcombining. Or is my limited understanding leading me astray?

(nikkkom says): “3 minutes..200 thousand years - nucleosynthesis:
What was happening: when temperature fell to 10 MeV, previously free neutrons merged with protons and form deuterium and He4 nuclei
How sure are we: 100%”

(Stan says): Most of the sources I’ve consulted most recently give the period of nucleosynthesis as lasting just 17 minutes - from T=+3 minutes to T=+20 minutes. Again, though, I must defer to superior knowledge….. am I laboring under a misunderstanding and/or misinterpretation?

nikkkom says): “10–6 second...1 second
What was happening: The quark–gluon plasma that composes the Universe cools. Quarks can no longer be created by gammas. Hadrons, including baryons such as protons and neutrons, form.
How sure are we: 99% (not giving it 100% yet since quark–gluon plasma is not fully understood theoretically yet, and only recently was observed in experiments)”

(Stan says): We’re REALLY on the same page here, Nikkkom; as far as I’ve been able to cross-reference, the Hadron Epoch DID last from 10^-6 to 1 second, and it WAS during this epoch that hadrons formed. I don’t THINK I have any questions at this point.

(nikkkom says): “10–12 second...10–6 second, or more usefully, temperature ~150 GeV - electroweak symmetry breaking.
What was happening: Higgs field oscillations (density of Higgs particles) become smaller that the size of the "Mexican hat" central bump of potential of Higgs field's energy, and Higgs field settled into its energy minimum with nonzero value: IOW, the vacuum as we know it has formed, electromagnetism and weak force began to look the way we see them now.
How sure are we: 95% (Higgs particle was only recently seen, confirming the model)”

(Stan says): Once again, I concur wholeheartedly. Multiple sources give the Quark Epoch as lasting from 10^-12 second to 10^-6 second

(nikkkom says): “At temperature somewhere above 10 TeV: baryogenesis
What was happening: somehow, number of quarks become larger that the number of antiquarks.
How sure are we: we almost certain this did happen (unless there are large volumes of Universe filled with antimatter - very unlikely), but we don't know how it happened. We know a few processes which can produce excess of matter, but calculations say these specific processes couldn't do it.”

(Stan says): I was under the impression that baryogenesis (satisfying the Sakharov conditions) occurred during the Hadron Epoch and was complete when the Hadron Epoch ended, at T=+ 1 second. I was also under the impression that neutrinos decoupled at this time (T=+ 1 second), resulting in the (hypothetical) CNB, similar to the CMB. Finally, I was also under the impression that there was alsoa period of Leptogensis (similar to Baryogenesis), during the Lepton Epoch. Am I again laboring under misinterpretations?

(nikkkom says): “And so on.

As you go deeper, you'll notice that theories are becoming more and more speculative, and less supported by facts or even calculations. As a layman, you should choose a point where you say to yourself: "ok, at this point these guys seem to be just guessing and throwing wild ideas around. Science did not crack this nut yet."

Popular articles usually fail to convey this point.”

(Stan says): I couldn’t agree more with your statement that… “As you go deeper, you'll notice that theories are becoming more and more speculative, and less supported by facts or even calculations.” However, I see nothing wrong with…” these guys seem to be just guessing and throwing wild ideas around…” Such “wild ideas” enable lowly laymen like me to wrap our minds around times and events that can NEVER be experienced directly.

Thanks again, my friend, for your input and patience,

Stan

12. Jan 22, 2015

### nikkkom

Yes, "recombination" is just a misnomer in this case.

13. Jan 22, 2015

### Amaterasu21

My understanding is that "recombination" is a general physics term for the change of state from plasma to gas, in the same way that "condensation" is the change from gas to liquid and "freezing" is the change from liquid to solid. The term comes from the fact that to observe that change of state under essentially all terrestrial, everyday circumstances we'd first have to heat up and ionise a gas to produce a plasma, before letting that plasma cool again and become a gas - so the electrons and nuclei would indeed be "recombining" in everyday experiments.

In the circumstance of the Big Bang though the nuclei and electrons were never combined in the first place, but "recombination" is still the term we use for that change of state, and "the recombination epoch/era/time" is the name we give to the time period where the Universe underwent this change of state. It's a little like the term "black body," I suppose - literally true under some circumstances, but that limited case name has become a label for a more general concept.

(I'm not a plasma physicist though, so someone correct me if I'm wrong!)

14. Jan 22, 2015

### ChrisVer

I will try to be the devil's advocate in this case, and just point out that "combination" of electrons and protons was occuring in the primodial plasma, but it was in thermodynamical equilibrium with the ionization process due to the presence of highly energetic and abundant photons . What happened in the recombination epoch is not just the formation of bound states, but those bound states were actually "stable" (they wouldn't get ionized again - went out of equilibrium), and so photons started travelling "freely" making the recombination epoch universe transparent and the one we can actually observe...

A naive idea for example, is to think that the recombination happened when Hydrogen was formed, and Hydrogen cannot be ionized with photons of energy $E_\gamma \sim T_\gamma < T_\gamma^* =13.6 ~eV$. So end up saying "recombination happened when photons' temperature reached 13.6eV...Of course that is not the case, because the photons' energies had some distribution (of the black body), and because they were abundant, the recombination happened at later times/lower temperatures than $T^*_\gamma$ ... A better calculation gives an answer of around 0.3eV...So even when most of your photons had energies around 1eV, you would still have a large fraction of "ionization" going on...

Last edited: Jan 22, 2015
15. Feb 13, 2015

### wabbit

Regarding diameter at epoch 0: My understanding is that in LQC there is a maximum density of order Planck mass divided by Planck volume. As a result the universe can't squeeze down to diameter 1, rather to something of order "cubic root of the total mass of the universe" in Planck units, or about 10^20 Planck lengths or 10^-15 m. Modulo egregious mistakes that should about the size of a proton.
Also one might expect the duration of that QG epoch where compression is maximal to be of order c*its diameter, ie 10^-24 s.
Presumably "t=0", which could be the birth of spacetime as we know it, happens at the end of this phase.

16. Feb 13, 2015

### Chronos

The era of recombination is rather more complicated than suggested by the usual popular explanation. The universe did not suddenly become transparent at z=1089 [~374,000 years after the BB]. That is the age when about half of the neutral hydrogen gas in the observable universe had 'frozen' out of the hot 'soup' from the BB. The neutral hydrogen freeze out began around z = 1587 (based on the Saha equation) and was essentially [99%] complete by z = 820 (based on the Peebles equation) - re:http://folk.uio.no/hke/AST5220/v10/AST5220_recombination_2010.pdf . These figures correspond to a time after the big bang ranging from about 196,000 years to 600,000 years based on Jorrie's cosmo calculator - re:http://www.einsteins-theory-of-relativity-4engineers.com/cosmocalc_2013.htm.