# Hubble parameter in early universe

1. Nov 30, 2007

### zankaon

If the Hubble parameter is always decreasing for very early stages of Big Expansion of manifold (i.e. Big Bang), then what was it decreasing from?

2. Nov 30, 2007

### marcus

unbounded as you go back in time

to take a simpler example---consider not the Hubble parameter but simply the function 1/x defined for x>0.
It is always decreasing. Can you ask what is it decreasing FROM?
No. It is not decreasing from any definite value. It is is just decreasing----not FROM anything.

But one can get some values, just as a sample, of what it has been in the past.
Let's find out what it was at z = 1000, and at z = 10,000.

Morgan's calculator should give this----maybe inaccurately but at least you get some idea.

Last edited: Nov 30, 2007
3. Nov 30, 2007

### jonmtkisco

Hi zankaon

The Hubble parameter is defined to be equal to the scaled expansion rate, that is, the change in scale factor divided by the scale factor a(t). According to inflation theory, at the end of inflation, the scaled expansion rate was equal to the peak rate of inflation -- which is faster than the expansion rate is believed to have been at any other time after the big bang. One estimate of the Hubble parameter at the end of inflation at t=E-33 seconds (after the big bang) is about E+52. By 3.6 seconds after the end of inflation, the Hubble factor had decreased dramatically to about E+20.

Jon

4. Nov 30, 2007

### jonmtkisco

At z=1000, the Hubble factor was around 1.3E+6. At z=10000 it was around 1.1E+7.

Jon

5. Nov 30, 2007

### marcus

Good work!
Let me compare what Morgan's cosmos calculator says

http://www.uni.edu/morgans/ajjar/Cosmology/cosmos.html

putting in parameters 0.27 for matter 0.73 for lambda and 71 for current Hubble

at z = 1000 it says 1.2 million km/s per Mpc

Ok you said 1.3 million, close enough.

Now I will try 10,000-------the calculator says 37 million km/s per Mpc.
But you say 11 million, Jon.

I don't know which is right. I don't trust Morgan calculator at such high redshift. Could well be that your figure is better.

BTW what is your source? I told you mine, just using this online calculator I gave the link to

Last edited: Nov 30, 2007
6. Nov 30, 2007

### jonmtkisco

Hi Wallace,

Actually I made a boo boo. At redshift z=10000, I have H around 85-90 million km/s per Mpc.

My source is Jorrie's spreadsheet which integrates critical densities backwards from the present.

Jon

7. Nov 30, 2007

### marcus

how do I get, or how does someone get, Jorrie's spreadsheet?

8. Nov 30, 2007

### jonmtkisco

Marcus,

I'll be happy send it to you. Can I send it through the forum?

I'll ask Jorrie if it's ok to distribute it.

Jon

9. Nov 30, 2007

### marcus

is Jorrie a PF member? I will try to PM jorrie direct.

10. Nov 30, 2007

### zankaon

Hubble Hubble toil and trouble...

Quote:
Originally Posted by zankaon
If the Hubble parameter is always decreasing for very early stages of Big Expansion of manifold (i.e. Big Bang), then what was it decreasing from?
unbounded as you go back in time

marcus quote
Posts: 10,836
Recognitions:
[PF Contributor] PF Contributor

to take a simpler example---consider not the Hubble parameter but simply the function 1/x defined for x>0.
It is always decreasing. Can you ask what is it decreasing FROM?
No. It is not decreasing from any definite value. It is is just decreasing----not FROM anything.

But one can get some values, just as a sample, of what it has been in the past.
Let's find out what it was at z = 1000, and at z = 10,000.

Morgan's calculator should give this----maybe inaccurately but at least you get some idea.
========

If one had a Big Crunch leading into a Big Expansion (Big Bang), for consideration of a model with curvilinear motion, then a previous increasing Hubble parameter (acceleration of contraction rate) could change into our decreasing Hubble parameter (deceleration of expansion rate). Of course, how would a model incorporate such curvilinear motion? Any such model would seem to have to include at least 1 more manifold (i.e. continuum); hence two manifolds revolving around a common center of energy, which could be outside of the 2 manifolds (like for center of mass/energy outside of a torus/donut).

Last edited: Dec 1, 2007
11. Dec 1, 2007

### Jorrie

My spreadsheet was not designed to be accurate at such high redshifts; as a matter of fact, I originally worked back reasonably accurately to around the last scattering time. The version that you refer to was done to get an OOM feeling for densities at earlier epochs.

I think it will give the OOM of the Hubble parameter as well, but not very accurately. Anyone drawing conclusions from it at high redshift does so at her/his own risk...

Jorrie

Last edited: Dec 1, 2007
12. Dec 1, 2007

### marcus

Hi Jorrie, thanks for showing up. We were talking about things related to your spreadsheet. I think you are right about just aspiring to OOM (rough order of magnitude) estimates for these things at high redshift.
It is sort of ridiculous of me to put Morgan's calculator to that extent.

It is probably really for use with redshift z < 10.
But i want SOME idea of the rough magnitudes.
Here's what I was using, if you want to try it for comparison.

13. Dec 1, 2007

### Jorrie

According to my spreadsheet, Jon is roughly correct with his last post (some 80 - 90 million km/s per Mpc at z ~ 10,000). I have tried a slightly more accurate integration as follows: start at z ~ 1,000 and t ~ 380,000 years after inflation and numerically integrate the Friedmann initial conditions backwards to z ~ 10,000, using:

$$dt = \frac{da}{H_0\sqrt{\Omega_m/a^3+\Omega_r/a^4 + \Omega_v}}$$

With the usual values of the parameters and constants and at z ~ 10,000, I've got the following values: t ~ 9,000 years, H ~ 74 million km/s per Mpc, which is about double what the Morgan calculator gives. Maybe that's good enough for a ROM? (Edit: The
t ~ 9,000 years seems highly uncertain and very sensitive to starting assumptions. H ~ 74 million km/s per Mpc seems fairly insensitive to starting assumptions)

It looks like the Morgan calculator ignores radiation energy density (as it should at 0 <= z <= 6, it's specified regime). When I set Omega_r = 0 in my spreadsheet, I get H ~ 37,000 million km/s per Mpc at z ~ 10,000.

Jorrie

Last edited: Dec 1, 2007
14. Dec 1, 2007

### marcus

Nice! Neat inference. Thanks. I see you have an ebook at your website that you wrote, Relativity 4 Engineers. Could be a very enlightening book 4 anybody, if this is a fair sample.

15. Dec 1, 2007

### jonmtkisco

Jorrie,

You have mentioned in several posts that the Friedmann equations may not be accurate within about the first 1 second after the end of inflation, due to a potential difference in the equation of state of radiation, (or a more significant degree of energy exchange between radiation and matter, whatever that means) during the first second.

Do you have any sense as to whether the universe was likely to have been expanding more quickly, or less quickly, than the Friedmann equations calculate, during that first second?

Is perhaps the potential cause of this variation a relatively high level of transformation back and forth between free radiation and the initial quark-gluon plasma? Something perhaps roughly analagous to the dynamic pair-generation and -anihiliation during the subsequent baryongenesis era?

Jon

Jon

16. Dec 1, 2007

### jonmtkisco

Here is Wikipedia's concise take (from "Timeline of the Big Bang" and referenced articles) on the period of the first few seconds after the end of inflation (at around E-32 seconds):

Electroweak Epoch: "... the electroweak epoch was the period in the evolution of the early universe when the temperature of the universe was high enough to merge electromagnetism and the weak interaction into a single electroweak interaction (> 100 GeV). The electroweak epoch began approximately [E-32] seconds after the Big Bang, when the potential energy of the inflaton field that had driven the inflation of the universe during the previous inflationary epoch was released, filling the universe with a dense, hot quark-gluon plasma. Particle interactions in this phase were energetic enough to create large numbers of exotic particles, including W and Z bosons and Higgs bosons. As the universe expanded and cooled, interactions became less energetic and when the universe was about [E-12] seconds old, W and Z bosons ceased to be created. The remaining W and Z bosons decayed quickly, and the weak interaction became a short-range force in the following quark epoch."

Quark Epoch: "... the quark epoch was the period in the evolution of the early universe when the fundamental interactions of gravitation, electromagnetism, the strong interaction and the weak interaction had taken their present forms, but the temperature of the universe was still too high to allow quarks to bind together to form hadrons. The quark epoch began approximately [E-12] seconds after the Big Bang... During the quark epoch the universe was filled with a dense, hot quark-gluon plasma, containing quarks, leptons and their antiparticles. Collisions between particles were too energetic to allow quarks to combine into mesons or baryons. The quark epoch ended when the universe was about [E-6] seconds old, when the average energy of particle interactions had fallen below the binding energy of hadrons."

Lepton Epoch: "...the lepton epoch was the period in the evolution of the early universe in which the leptons dominated the mass of the universe. It started roughly 1 second after the Big Bang, after the majority of hadrons and anti-hadrons annihilated each other at the end of the hadron epoch. During the lepton epoch the temperature of the universe was still high enough to create lepton/anti-lepton pairs, so leptons and anti-leptons were in thermal equilibrium. Approximately 3 seconds after the Big Bang the temperature of the universe had fallen to the point where lepton/anti-lepton pairs were no longer created. Most leptons and anti-leptons were then eliminated in annihilation reactions, leaving a small residue of leptons. The mass of the universe was then dominated by photons as it entered the following photon epoch."

Considering all of this together, it sounds like there was a lot of particle production and anihilation going on during the first 3 seconds, which probably would make it impossible to calculate any stable independent densities of radiation and matter. It suggests that the radiation/matter ratio was tipped further towards matter during the hadron and lepton epochs, before most of the pair-antipairs were anihilated (converted to radiation).

So one might guess that the universe was less radiation-dominated (or maybe even matter-dominated) during much of the first 3 seconds. That would in turn result in a lower (less negative) deceleration rate during this period than predicted by the historical Friedmann equations, if the equations of state of matter and radiation were not also different.

A lower deceleration rate means that the scale size of the universe would have been larger at the end of inflation, and less dense, which in turn would require a lower initial expansion rate (in order to preserve flatness). Which means that the peak expansion rate of inflation would have been equally lower.

But these extrapolations may well be too speculative.

Jon

Last edited: Dec 1, 2007
17. Dec 1, 2007

### Jorrie

Thanks Marcus. People are welcome to take a peek, but no advertising here...

Jorrie

18. Dec 1, 2007

### Jorrie

Hi Jon, quite frankly, I haven't got a clue. Pervect provided some ideas in:

My feeling is that if we could know the conditions at the end of inflation from the 'other side', one could work back from the 'Friedmann side' and try to find a match...

Jorrie

19. Dec 1, 2007

### jonmtkisco

Jorrie,

I agree that if we could start from inflation and calculate forward, and start from the present and calculate the Friedmann equations backward, we could squeeze out a solution between the two.

On another point, I don't see why the equations of state must necessarily have been different during the first 3 seconds. If one is looking for uncertainty in the expansion rate, the uncertain and unstable radiation/matter ratio during that time seems like enough grist for the mill...

Jon