Initial value for hubble parameter

[apeiron]

Simple question hopefully. What was the initial value for the Hubble parameter immediately following the big bang (or ending of inflationary epoch)? I presume the initial velocity of expansion was lightspeed and started slowing from there.

 

[apeiron]

Simple question hopefully. What was the initial value for the Hubble parameter immediately following the big bang (or ending of inflationary epoch)? I presume the initial velocity of expansion was lightspeed and started slowing from there.

Bump...what no answers yet on such a basic question?

I did have a good go googling for the answer before asking and was surprised not to be able to find a clear statement. So either this is a hard one to answer for reasons I don't appreciate, or it is just not something people often think about.

 

[marcus]

Simple question hopefully. What was the initial value for the Hubble parameter immediately following the big bang (or ending of inflationary epoch)? I presume the initial velocity of expansion was lightspeed and started slowing from there.

I probably won't be able to answer the question--at least as formulated now!

But I can help you clarify the statement of the question.

First, what do you mean by "the velocity of expansion"?

As a warm-up to asking about THEN, what would you say the "velocity of expansion" is today? If it is a velocity I assume you want it expressed in km/second or the equivalent.

 

[apeiron]

I probably won't be able to answer the question--at least as formulated now!

But I can help you clarify the statement of the question.

First, what do you mean by "the velocity of expansion"?

As a warm-up to asking about THEN, what would you say the "velocity of expansion" is today? If it is a velocity I assume you want it expressed in km/second or the equivalent.

Sure, I understand how the Hubble parameter works. So go out to the current visible event horizon and you will find recession speed looks to be light speed. Which is why there is an event horizon .

So extrapolating that principle backwards in time, to the big bang, the event horizon would have been "no distance at all" from any point in the universe at that stage. The velocity of space expansion on the most local possible scale would have been "lightspeed" by that reasoning (and not faster, nor slower).

I agree if you say it is hard to attribute physical meaning to any of this at around the Planck scale, or even at the EW scale if inflation was just breaking then. But still the reasoning seemed sound to me, yet when I came to check for a positive statement to this effect, I couldn't find it.

You could talk about the same issues from the perspective of average energy density or local temperature of the universe - extrapolate back and say that the initial conditions were Planck scale (as opposed to infinite, or for some reason less dense, less hot). It would be the same reasoning?

What I am actually trying to do is make that necessary distinction between event horizon and the underlying expansion of the metric (one being communication across the metric, the other being ground-up expansion of the metric, which thus can go supraluminal in effect. Well, which in fact started supralumimal everywhere, and will steadily come back within the global event horizon if the universe goes to heat death).

But roll things back the other way to the very beginning, and it would seem the two views would have to start at the same scale. The event horizon and the rate of expansion would have been the same "speed". But then event horizon speed of growth remained at c, while metric expansion has been slowing due to gravitational braking/generalised cooling.

 

[BillSaltLake]

The Hubble parameter was the inverse of the age give or take a factor of 2, so it was very large.

 

[marcus]

Sure, I understand how the Hubble parameter works. So go out to the current visible event horizon and you will find recession speed looks to be light speed. Which is why there is an event horizon .

That is not correct, but you are only about 10 or 15 percent off so it doesn't matter.

If you go out to the Hubble radius, distances there are increasing at rate c.

However that is not our visible event horizon, which IIRC is between 15 and 16 lightyears, substantially more than the Hubble radius.

Distances there are increasing substantially faster than c, but a signal sent from that far, today, could still reach us.

Most of the galaxies which we currently observe are out beyond the Hubble radius and are receding faster than c---I think you know this, being quite knowledgeable, but mention it in case others are reading the thread.

So what do you want to call the "velocity of expansion"? Astronomers do not talk in those terms. The "velocity of expansion" is not part of any mathematical model of the cosmos that I am familiar with. But let's not allow that to worry us!

Let's give it a precise meaning! What meaning would you like? Let's see if we can get a useful definition that we can work with.

 

[apeiron]

So what do you want to call the "velocity of expansion"? Astronomers do not talk in those terms. The "velocity of expansion" is not part of any mathematical model of the cosmos that I am familiar with. But let's not allow that to worry us!

OK, I am talking about the metric expansion of space. Measuring the "velocity" of that metric expansion at any time is a tricky concept. And I am familiar with different kinds of horizon effects like Hubble spheres and particle horizons.

So the intuitive view I am trying to confirm is that at the beginning, the rate of metric expansion would be everywhere effectively lightspeed. Any two definable points arbitrarily close to each other would have had that recessional velocity. And then things slowed down very fast. With that, you move into a world where the Hubble parametre can function as a pratical measure. Locally, recession speeds are slow looking, rising towards an event horizon, and unbounded even beyond.

So at the beginning, recession is supraluminal over any distance larger than a pair of adjacent points. Afterwards, cooling allows space to become organised with a lightcone coherence. Space is expanding slow enough that there is an ever growing opportunity for radiative interactions across the metric.

A big rip scenario, for example, could take us back again to a realm where local recession velocities are again such as to shrink effective event horizons to zero.

So it is key that the two things - lightspeed interaction and metric expansion are both "sources of velocity". And it is the gap that develops between the two rates that makes things what they are. And as rates, it would seem they were also once necessarily unified.

But this is the question. Is there some reason to believe that two arbitrarily close points would have had a recessional velocity due to metric expansion of either much greater, or much less, than the then effective rate of light? Of lightspeed interaction?

I am thinking that even inflation mechanics assumes this - that inflation is an exponential period doubling growth, yet still the recessional velocity of adjacent points would not be more than lightspeed during inflation? I will have to check some ancient notes on this, but you will probably have the ready answer.

 

[apeiron]

The Hubble parameter was the inverse of the age give or take a factor of 2, so it was very large.

Yes, but I am presuming that the inverse has a cut-off at the Planck scale. So a cut-off at lightspeed recessional velocities for adjacent points. This is the question I'm asking.

 

[bapowell]

Yes, but I am presuming that the inverse has a cut-off at the Planck scale. So a cut-off at lightspeed recessional velocities for adjacent points. This is the question I'm asking.

If you impose a cutoff on the age of the universe, then you will correspondingly impose a cutoff on the Hubble parameter. This will give you a minimal effective Hubble radius beyond which recession velocities become superluminal.

 

[marcus]

I'm beginning get a notion of what you might mean by "initial value".

You are talking about ADJACENT POINTS. You are talking about PLANCK SCALE geometry and probably you want to know, timewise, about things within say 100 Planck time units of the start of expansion.

That makes it simpler in a sense, because the ordinary GR model quits long before that. It simply does not apply. You are into the precincts of QUANTUM COSMOLOGY. So you need to use QC models to get answers.

At the very very beginning classic GR just does not say anything meaningful. Work is beginning on testing the QC models---phenomenologists are telling us how they can be tested and falsified if wrong, by among other methods, polarization CMB observation.

You can read about the current QC models here, and there are some phenom. papers mixed in:
http://www-library.desy.de/cgi-bin/spiface/find/hep/www?rawcmd=dk+quantum+cosmology+and+date+%3E+2008&FORMAT=WWW&SEQUENCE=citecount%28d%29
This is ranked by citecount so it gives an idea of what the currently most-studied models are that the desy librarians classify as QC.

The short answer is this: if the most-studied QC models are true then we can say that at the start of expansion the value of the Hubble parameter was zero.

(quantum effects at high density were reversing gravity so it was repellent instead of attractive, so expansion was speeding up. the model automatically triggers inflation without being fine-tuned)

Also however you define "velocity" of expansion, at the beginning of expansion it was zero.
"Adjacent points" however you define that, were neither getting closer nor getting farther apart, at that moment (the moment expansion began.)

 

[apeiron]

If you impose a cutoff on the age of the universe, then you will correspondingly impose a cutoff on the Hubble parameter. This will give you a minimal effective Hubble radius beyond which recession velocities become superluminal.

So far I'm not hearing that my reasoning is fundamentally wrong, just that notions about the rate of expansion are not an elegant way to phrase the issues. I don't disagree, but I still wanted to make sure I had the right mental picture when it comes to a cooling and expanding universe.

 

[apeiron]

I'm beginning get a notion of what you might mean by "initial value".

You are talking about ADJACENT POINTS. You are talking about PLANCK SCALE geometry and probably you want to know, timewise, about things within say 100 Planck time units of the start of expansion.

That makes it simpler in a sense, because the ordinary GR model quits long before that. It simply does not apply. You are into the precincts of QUANTUM COSMOLOGY. So you need to use QC models to get answers.

I don't want to get bogged down in the different opinions of various models. I am just sticking to a simple extrapolation of GR as much as possible. Of course QM makes a difference ultimately, but near enough approximations are good enough here.

It still seems to me that the expansion rate did not start at a minimum (zero) but at the maximum (lightspeed). Every point of space had the maximum density of kinetic energy. And expansion then cooled this action exponentially.

You could be saying that every point had instead just a maximum density of potential energy at the first moment of expansion. And this would be right in the sense that if you have not yet started going anywhere, there is nothing kinetic going on, just potential.

But that is simply repeating the point that expansion had to start from a maximum energy density that was Planck scale (or thereabouts?) rather than some value either much more (infinite?) or much less. And extrapolating backwards from our current view, as I am, it still seems right to talk about kinetics - the first instant when things were moving, when metric expansion and so cooling were first actually happening.

 

[bapowell]

It still seems to me that the expansion rate did not start at a minimum (zero) but at the maximum (lightspeed).

OK, but this sentence does not make sense. The expansion rate is not a speed. What I think you mean to say, is that there was some maximal effective Hubble parameter which has subsequently decreased as the universe has expanded and cooled. As the Hubble parameter decreases, the Hubble radius increases -- the distance at which recession velocities satisfy $v = c$ grows in time. But there's nothing special about the speed of light here...there is always a Hubble radius and corresponding distance at which recession velocities become superluminal, be it the early universe or right now. The only difference between now and then is that then this distance was much smaller. In the limit that $H \rightarrow \infty$, this separation $\rightarrow 0$. This is just the big bang singularity.

 

[marcus]

I don't want to get bogged down in the different opinions of various models. I am just sticking to a simple extrapolation of GR as much as possible. Of course QM makes a difference ultimately, but near enough approximations are good enough here...

Then I'm off the hook. Classically there is no "simple extrapolation" that removes the singularity and allows one to talk about the beginning of expansion.

The simplest extrapolation I know is basically just a quantization of the Friedmann eqn model that everybody uses. It goes one step better than the Wheeler-DeWitt quantization, which didn't quite succeed in curing the breakdown, kind of a minimal improvement that works.

QM makes a huge difference, it turns out, at very high densities. High energies packed into small volumes. You'd expect that. Small scale is where QM normally applies, close together is small scale. It's obvious.

You are not going to get "near enough approximations" of around the beginning of expansion (within a few Planck time units) if you do not go to some QC. It will not be "good enough" it will make no sense.

QC models getting a lot of attention currently blend seamlessly into the semiclassical and classical by about 70-100 Planck time units after the start of expansion. So they recover classical cosmology, Friedmann equation stuff, very quickly after the bounce. They also produce a natural inflation episode for free, no extra charge

Think about it Ap. 100 Planck time is a very small amount of time. If you want to get within that time interval of the start of expansion, you need to shift to QC. And it will be indistinguishable from classical by about 100 ticks. If you reject QC and insist classical, whatever your "simple extrapolation" of classical says will be meaningless.

http://www-library.desy.de/cgi-bin/spiface/find/hep/www?rawcmd=dk+quantum+cosmology+and+date+%3E+2008&FORMAT=WWW&SEQUENCE=citecount%28d%29

 

[apeiron]

OK, but this sentence does not make sense. The expansion rate is not a speed. What I think you mean to say, is that there was some maximal effective Hubble parameter which has subsequently decreased as the universe has expanded and cooled.

That is certainly what I am saying - the Hubble parameter has evolved over time. It has fallen from some maximal (yet not infinite!) level and will fall towards some minimal (but not actually zero) level at the heat death (barring all the alternative complications to cosmological models like big rips, bounces, etc).

Yet I still want to be able to say what can be said about the expansion component, and to tie it in with the cooling component. So yes "speed" or "velocity" is loose terminology. But it also seems easy to see what I really mean.

Another way of looking at this is how would you describe the recessional velocity of two adjacent points at the current general temperature of the universe? Ignoring gravitational attraction - just take two points of arbitrary closeness in a deep space vacuum.

OK dark energy is one of the new complications that contribute to any velocity. But still, there will be a recessional speed that is greater than zero even in the current very cold state of the universe won't there? Even if QM would again swamp any such notion of an actual movement if you try to measure points "too close", there would still be a predicted recessional velocity in the metric at least from theory. You need some expansion locally to get the big expansion over cosmological distances. Multiples of zero would just give you zero, so local recession cannot be zero from classical observation.

Now extrapolate back to the big bang and that most local scale of recession would be of a far greater energy scale. Enough I am presuming to be fairly called "lightspeed". But not infinite. or 50 times lightspeed. And not quarter lightspeed or some other lesser fraction.

You have argued that if you extrapolate GR all the way back to a singularity, you get H at infinity and separation of zero.

Well I am arguing I guess for a Planck scale cut-off so that you can't get to infinity nor to zero. The universe is born with already a minimal size and maximal energy density as QM would argue.

Probably Marcus is saying that I am right to introduce Planck scale as an effective cut-off, but wrong in how QM now models the early history of things for the first 100 ticks. GR is dissolved long before you get down to the Planckscale.

I'm still dubious about inflation and positively against bounce cosmologies (we all have our prejudices ) but even so, I think the naive approach here makes a reasonable starting point. Extrapolate GR until you hit the Planck limit, and then introduce the Planck cut-off. Speed of light then would be your finite recession velocity between two notional points at the earliest moment. It may be a cartoon view, but it is the start that can then be modified.

It is just the same justification people give for the finite Planck energy density - determined by the frequency of a single wavelength spanning the Planck radius (spanning it at the speed of light in a Planck instant)?

But if someone here is arguing that recessional velocities would be for some reason higher or lower than the "usual Planck deal", that's what I'd like to hear about.

 

[Chalnoth]

Simple question hopefully. What was the initial value for the Hubble parameter immediately following the big bang (or ending of inflationary epoch)? I presume the initial velocity of expansion was lightspeed and started slowing from there.

1. Nobody knows the precise energy at which inflation ended, so we can't say for sure yet. It had to be warm enough to produce the matter/anti-matter imbalance as well as dark matter, but we only have lower limits on how hot that has to be (basically, it has to be hotter than we've ever tested in the lab).
2. There is no such thing as lightspeed expansion. Expansion is a rate with units of inverse time. It is not a speed. Not being a speed, it cannot be compared to the speed of light, period.