Big Bang 2 and a new beginning of space/time

An interesting idea and one dealt with in the scientific literature.

First of all I assume that you do not mean matter expanding into a pre-existing space. This can be easily distinguished from our current universe as the motion of matter is not driving the expansion between the galaxies (easily seen to be true as the galaxies show no effects of acceleration).

So I will take you to mean to the following scenario. That there was already space and in a small region of that space some ball of matter began to cause the space in which it existed to expand rapidly (i.e. its section of the larger universe began to expand).

The problem with this is very simple. You simply can't have that amount of matter compressed in a pre-existing universe and then have it expand. Einstein's General Relativity (or even alternate theories of gravity like Brans-Dicke) just don't predict that a ball of matter would evolve like that in pre-existing spacetime. Rather it would collapse in on itself.

ramoss writes: Well, wouldn't it be a highly compact amount of energy, rather than matter? Didn't it take a certain period of time for even sub atomic particles to form?

Energy is just a property of matter, not a thing itself. Early in the universe matter wouldn't have been organised into states that we'd recognise as particles, but it was still matter, highly compressed matter.

Could you point me to an essay or article on it??

On what specifically?

And I thought that the far galaxies DID show effects of acceleration.. as measured by the Ia supernovae in them.

They show effects due to the acceleration of the expansion of the universe, but they are not really moving themselves, rather the space they exist in is expanding.

I am beginning to see, through a glass darkly. However , if gravity causes space to bend, why didn't the matter cause the space to bend rather than 'inflate'??

Matter doesn't really cause space to bend. Rather matter determines what the geometry of spacetime will be.

More specifically the energy density of matter at a point added to the flow of momentum caused by the matter at that point determines the part of the curvature of spacetime which causes balls of particles to shrink over time (The volume shrinking curvature). More detail in this post: Einstein's Equations

Although you can mathematically calculate the spacetime geometry which results from a piece of matter, there isn't really an intuitive way to guess at what it would be like.

For a spherical ball of matter like the Sun the result is something you could call a bending of spacetime (mostly time in this case).

For a homogeneous gas (like the universe on the largest scales) the result is a spacetime where space expands as time passes.

Is that one of the things that 'dark energy' is responsible for, since the expansion of space is accelerating?

In the post I link to above I give the Einstein's equations as:

The term on the right is completely fixed, it is the energy and momentum flow density of matter. On the left-hand side you have a term related to the geometry of space. In this case , called the Einstein Tensor. The Einstein Tensor measures the volume shrinking part of curvature.

You can't just put any geometric term on the left hand side, as Einstein realised, since most geometric quantities "diverge". This basically means that they can grow in value at a given point without being compensated by a decrease at another point.

which measures the matter, never diverges (new matter can not just "appear" without a compensating loss of matter elsewhere). So only divergence-less geometric terms can be used, since only they will match the behaviour of .

This really restricts the choice of what can be on the left-hand side, down to pretty much just:

In this equation is just a number and is the metric, a geometric term describing how distances work in the spacetime.

Einstein, and most people after him had no idea what value should have. So in most textbooks on general relativity and in research up until the late 90s it was largely ignored and instead we used the equation given above:

This is because the results in most cases aren't really that different. For instance the shape of the spacetime around the sun is virtually identical under the two equations (unless is unrealistically large).

However for a homogenous cloud of gas (like the universe on the largest scales), the two equations give quite different results. The simpler equations give an expanding universe, however the equations with a positive give an accelerating expanding universe.

Then basically in 1998 we found that observations of distant stars in our universe match the universe described by the equations with a very small positive .

Now the question is: why does have the value it has?

There are several different proposals, we just call all of them "Dark Energy", because has units of "joules per volume", i.e. units of energy density.

Edited by Son Goku, : Small typo

I should follow up on the previous approach and attempt to say what exactly is Dark Energy, or rather the two most popular ideas. There is some very bad information out there on this, so I want to carefully explain the two ideas.

Vacuum Energy:
This is probably the most basic, least exotic guess at what Dark Energy is. In the previous post I wrote the Einstein's equations as:

However the matter here is classical, but we know matter is quantum mechanical. We don't know if spacetime is quantum mechanical (and if it is we don't know how to describe it, that's the problem of quantum gravity). So, to improve this equation in a way consistent with what we know already we make matter quantum mechanical, but keep gravity classical.
Since matter is now quantum mechanical it is probabilistic. Hence, has no definite value and fluctuates. However, gravity is still classical and deterministic, so it cannot interact directly with something fluctuating like this. We need it to interact with a deterministic quantity. Fortunately the average stress-energy is deterministic.
(Averages are always deterministic in quantum mechanics and behave classically. Also by average I mean that the quantum matter will have a stress-energy that jumps all over the place, but is the central value about which it fluctuates.)

This leads to the naive semi-classical gravity equations:

These are naive, since if you try to solve the equations you get infinities.
This is the problem known as renormalisation. Quantum theories often have infinities if you use the exact same equations as the classical theory. Generally these infinities only disappear when you add new terms to the equation. Basically the quantum theory requires new terms.

It turns out the infinities only vanish if you add two new terms to the equation:

Two interesting things here:

1. Even if I'd started with no cosmological constant, like:
   
   I would still have ended up with:
   
   in order to remove the infinities. Even if I start off with no , it's automatically generated when I try to get rid of the infinities. That is Quantum matter requires the cosmological constant. So we at least know why it isn't zero.

2. The new terms:
   
   are geometric terms describing how curvature changes as you move through spacetime. ( are just numbers) At first people found them a bit odd. They make the equations much harder to solve and they're not "natural" quantities by which I mean, aside from removing infinities, they don't seem to have a physical explanation. However they were later discovered to have a very important effect, they make spacetimes containing time-machines impossible. The old classical equations:
   
   can give rise to time machines with the right on the right-hand side.
   This can never happen under the new equations:
   
   Quantum matter does not allow time machines.
   

There are a lot of things making up :

1. The first is the part coming from when you try to remove infinities that the theory would have even if there was no matter, i.e. infinities that are there even in a vacuum. This is .

2. The second part is called (ind=induced). This part comes from infinities relating to:
   The masses of the W and Z weak bosons
   The strength of the Higgs field
   The energy where left-spinning and right-spinning quarks behave the same
   The energy where the electroweak force separates into the electromagnetic force and the weak force.
   

I'll stop here and continue in the next post because it looks a bit less cluttered.

Now, and are very large quantities, corresponding to a huge amount of energy. However they have opposite signs and cancel to incredible precision.

The total is tiny compared with either of them. Both and are times larger than .

Now to handle an often repeated myth. Many critics of current cosmology say we cannot explain the value of and that when we tried to do it we get an answer far larger than we should.
This myth is based on early papers that calculated only and found it was far larger than . The reason this was done is because is related to vacuum infinities, you don't need to go into the details of particle physics when there is no matter around, so it's an easier quantity to calculate and you would hope that is unimportant. Unfortunately of course it turns out we need to look at as well. The first papers handling go back to 1975, so anybody still peddling this myth that the cosmological constant is "billions of times larger" than physicists thought is nearly forty years out of date.

So the actual problem we have today is:
Why do the two sources for the cosmological constant cancel so precisely?

At the moment we know the source of most of the cancellation (quite technical, but it can be explained if anybody wishes), however we still need to understand the remainder, which currently looks quite difficult.

This is the most widely accepted idea for Dark Energy, let me sum up the facts:

1. Quantum Mechanical matter automatically introduces a new term to Einstein's equations:
   
   in order to remove infinities.
   
2. This term gives rise to an accelerating expanding universe, as explained in my first post on this thread. This matches our universe provided is small and positive.
   
3. The Standard Model does seem to predict that is small and positive, due to precise cancellations between the two terms that contribute to it.
   
4. The problem is we don't understand this cancellation as much as we would like.
   

Quintessence
This is another idea for Dark Energy, but observations are making it increasingly unlikely. Basically quintessence is a field filling the universe. It naturally interacts with gravity in such a way as to act like the term:

It also sets the real to zero, so no need to worry about cancellations. It also means Dark Energy is an actual substance, the quintessence field. However observations of the universe have caused serious problems for this. The Quintom scenario/problem (found in 2004), means that to match the behaviour of the universe you need at least two of the these fields. Nobody can really think of a convincing way of having two of these fields without us having already noticed them.

Other ideas
All other ideas for Dark Energy are just different things which act like:

Such as a larger extra-dimensional universe "pressing" on ours or "Cracks/Defects" in spacetime. All these ideas are really cool, but I must emphasis that theoretical calculations and experimental evidence are increasingly favouring Vacuum energy.

Summary
The Cosmological constant(Dark Energy) increasingly seems to be, not a substance, but rather a natural quantity arising from precise cancellations that occur when removing infinities from quantum matter.

About Einstein’s equations, I believe you left out the gravitational constant.

No, I was just using relativistic units where it is equal to 1. In human units (meters, seconds, e.t.c) the equation is:

My first problem with your treatment of and what side of the equation you are placing it. Lawrence M. Krauss and Michael S. Turner would have us place it on the other side with the Stress energy tensor as follows:

Well things can be placed on any side of the equation you want, fundamental part of algebra.

This would be consistent with a Quantum energy flux added to the total momentum energy flux.

It isn't, as I said only is not enough, you need the other terms I listed, namely:

otherwise there are infinities. on its own is not consistent with quantum mechanical matter. (This is a mathematical theorem, reference for proof available on request)

I see you can accept the balancing of the universe on the head of a pin. Your equation faces the same shortcomings as when Einstein first proposed the cosmological constant. In other words, to maintain an observable flat universe over time (as time goes by, continuous adjustments must be made to your alpha and beta), simply because an expanding universe alters the state of flatness.

and , the terms in front of:

Do not need to be adjusted at all. Where did you get that idea from? You solve the equations and you get an expanding universe, nothing needs to be tuned. Can you explain your thinking behind this? and have very little effect on cosmological scales and aren't really relevant for the Big Bang or inflation.

Without this imperative then the terms still make sense. You can make up all kinds of terms to reduce the calculated quantum flux to match the observed dark energy effect but that is again just fantasy.

The terms are not introduced to match Dark Energy. As I said, they are naturally introduced by quantum mechanics. The values given to the parameters (by quantum mechanics) then match the observed evolution of the universe.

Personally, I believe dark energy is just fantasy.

Well, it is predicted by quantum mechanics and produces an evolution of the universe that matches all observations of WMAP data and distant supernovae. Very strong evidence, but believe what you wish.

The key term here is small and positive and I would add unlikely.

Is there something wrong with it being small and positive, I mean that's what matches the observed universe.

zaius137 writes: Son Goku writes: 3. The Standard Model does seem to predict that is small and positive, due to precise cancellations between the two terms that contribute to it. Too precise, as Einstein lamented over this fact.

The prediction is too precise? The cancellation too accurate? I actually don't understand what the problem is. How can a result be too precise?

Hawking may have folded on the two-channel gamma/gamma and the 4-lepton excess, but the obtained 5 sigma was still from the combination of two separate experiments. Not the independent discovery from two independent experiments. Science spent the money and must receive a return, maybe real, maybe false. I still do not believe in all pervasive fields.

ATLAS obtained its five sigma result independently. CMS is currently at 4.9 sigma. Where are you getting this information from?

I still do not believe in all pervasive fields.

Again, same as Dark Energy, the idea of quantum fields matches all the information that has come out of every collider ever built. What is your belief based on?

zaius137 writes: I would wonder since you inexplicitly used geometrized units why you did not include also.

Why does it matter?

Does it look like I preformed an algebraic operation? Just start by showing your conversion from: () to ()

They can't be converted into each other. is a separate term to .

I was saying it doesn't matter which side is put on.

Really, my point of the position of vacuum energy with the stress energy tensor is to express the current view that dark energy is a form of “energy” not a property of space itself. Did you catch that?

has units of energy no matter which side of the equation it's on. It really doesn't matter which side of the equation it appears on.

Please proceed and include some citation for me the hopeless layman..

A proof that the terms I listed above are necessary in the presence of quantum mechanical matter is given in:

S. A. Fulling, Aspects of Quantum Field Theory in
Curved Space-Time (Cambridge University Press, Cambridge,
1989).

The original paper is:
R. M. Wald, Commun. Math. Phys. 54, 1 (1977).

First off, your terms are complete contrivances, they do not relate to any known observed phenomenon.

They do, they contribute to anisotropies in the Cosmic Microwave background.

They are known in physics as hidden values and are nothing more than mathematical convinces that facilitate a current solution. I emphasize current as the expansion rate of the universe has varied over time according to the BB paradigm. You do not get these values, as you put it, then “solve the equations and you get the expanding universe”.

Yes, you do. Again I can give you a paper proving it. With those terms the solution is an entire four-dimensional history of a universe which has accelerating expansion. Can you show me a paper with detailed mathematical calculations showing this does not occur.

Specifically, what are these natural introduced quantum values? I do not know of any parameter values from quantum mechanics that could match the observed evolution of the universe… that is the point.

I've described them in the posts above. Quantum Mechanics naturally induces a small positive value of through renormalisation. The value it predicts matches the observational value obtained from studies of distant supernovae.

To my mind it is now clear that you aren't even following your own points, most of what you have written doesn't directly connect with the context in which it is being discussed.

Let me deal with your points:

Because you need to hold to some kind of expositional consistency, so the reader can sort out your points… my opinion.

General Relativity is usually written in units where G(Newton's constant) and c(the speed of light) are set to 1. This is because their presence just clutters up intermediate calculations. They can always be restored at the end of a calculation when you want to compare results to experiment.
is a geometric factor and is usually kept since it cancels out factors coming from areas of circles. One could work in "circle units" where the equations wouldn't have this factor, but there isn't a need to, unlike the case with G and c.

Further more, which units one uses are irrelevant to this discussion as we are not talking about units.

I am trying to find this paper but only get the abstract. I believe I see what the problem is here, the paper was written prior to the discovery of the accelerating universe (about 1998).

This point is irrelevant. Let me remind you what has been said.

I claimed that quantum mechanical matter requires the addition of three extra terms to Einstein's field equations. You doubted this and said the terms were invented for no reason. In response to this I provided you with references containing proofs that these terms are required. (If you would prefer freely accessible course notes containing the proofs I can supply those as well.)

Whether one observes the universe to be undergoing an accelerating expansion or not is independent of the mathematical fact that quantum mechanics requires this terms. It is this requirement that I have provided references for.

Of course, the interesting thing is that one of the terms introduced predicts an accelerating universe, which we then saw in 1998. Hence these papers from the 1970s contain predictions we saw later. There is nothing wrong with a piece of theory being written before observation of its predictions (in fact it's better isn't it?, a genuine prediction). Some people were expecting the accelerating universe observations before 1998 for this reason.

I believe that the terms you are using are outdated in there relation to the stress energy tensor.

They most certainly are not. All modern work on cosmology takes them into account.

Type "The Cosmological Constant Problem and Renormalization Group" into google. A talk by Il Shapiro is the first result. Page 7 of the talk contains the statements I'm making and provides more references. Note the sentence:
"Higher derivative terms are necessary in quantum theory."

Other returns from the search will give other papers which include these terms. As Shapiro's talk is from 2011, I hope you can see these terms are not out of date.

The CMB is another conversation altogether… Try goggling “Cosmic Background fails the shadow test”.

Again you are ignoring the context of the discussion.

You said the new terms had no physical effects. I said they do, they effect the anisotropies of the CMB. Hence the terms predict physical consequences, refuting your claim.

Whether those consequences are observed is a separate issue.

They actually are observed in case you are wondering. Look at any papers dealing with the data from the WMAP studies of the Cosmic Microwave background to see this.

Theory is one thing… proof is another.

Okay, once more I shall explain the discussion.

You claimed that the values of the parameters need to be adjusted constantly or tuned.

I said they are not, their values are explicitly predicted by quantum field theory. So not only are the not tuned or adjusted, they cannot be tuned. The have a value fixed by the Standard Model. I then said that if you take the values which are predicted by the Standard Model for these parameters and solve the equations, you get an accelerating expanding universe..

So quantum matter has fixed values for these parameters and even with these modifications (the extra terms coming from quantum mechanics) the field equations still give a solution which is an accelerating expanding universe.

As you can see this is a purely mathematical claim. That theory has fixed values for the parameters and gives an accelerating expanding universe as a solution.

The full proof that this is true is given in the 2007 paper by the General Relativity group at Barcelona (Guillem Perez-Nadal, Albert Roura, Enric Verdaguer) in their paper:
"Stability of de Sitter spacetime under isotropic perturbations in semiclassical gravity"

de Sitter spacetime = the accelerating expanding universe solution

stability = still a solution

under isotropic perturbations in semiclassical gravity = the effects of quantum matter, specifically the extra terms introduced by quantum matter

Hence my statement has a mathematical proof. Unless you know of some error in the paper above, then my claim is correct.

In your response "Theory is one thing… proof is another.", although it is vague, I assume you are alluding to this result being purely mathematical and not experimentally supported.

However:

1. As I explained, your claim that the theory needs to have its parameters fixed and doesn't give an accelerating expanding universe solution without this fixing is a mathematical statement about the properties of the theory. It is also a provably incorrect statement.

2. Experiment comes after we have proven that the new quantum-mechanically modified theory predicts an accelerating expanding universe solution. We then check if that solution is what we actually observe in the universe.
   One good check is to see does it predict the right multiploe moment contributions to the CMB.
   

The l-th multipole moments measure how much the CMB looks like it is the temperature distribution of a set of l objects.

So the 2nd multipole moment would be a measure of how much the CMB looks like the temperature profile of two hot objects.

If the 2nd multipole moment was very large the CMB would look mostly like two hot objects.

The power spectrum is how much each multipole moment contributes to the CMB.

So do we see the right power spectrum? Well, one of the authors of the paper I gave above, Albert Roura, gave a nice talk at Los Alamos. Just search for "Semiclassical stability of de Sitter spacetime & RG running cosmological constant".

On page four of the talk you'll see a picture of the Cosmic Microwave Background and a smaller picture on the bottom right of the power spectrum. The line is the spectrum predicted by the solution he and his colleagues have shown is still a solution when quantum mechanical matter is added. The points are the observed multipole moments.

Let me include that diagram here:

The error on the observed values around the 700th multipole is because our telescopes were not yet good enough to resolve them at the time.

ACBAR has since gone up to l = 2,000. For these more accurate measurements please see the paper:
"Small Angular Scale Measurements of the Cosmic Microwave Background Temperature Power Spectrum From QUaD", available for free from arxiv.org

On the fourth page you will a graph of the power spectrum with results from telescopes all over the world agreeing precisely with the CMB power spectrum predicted by the deSitter (accelerating and expanding) solution.

Edited by Son Goku, : Editing

zaius137 writes: I understand you could not present the field equation in a reasonable way because of all the deep calculations you are performing. I view your equivocations as an avoidance of omission. That is an assumption on your part.

This is silly. If somebody wrote down the Euler equations (which describe fluids) in meters or feet it would still give the same predictions. The units don't matter. I wrote down the field equations in geometric units where G = 1 and c = 1, because that is the way they are commonly written down. What are you trying to prove here, how am I "equivocating"? Units don't matter.

I mean I can say Alpha Centauri is 1.34 parsecs or 4.37 light years away, it doesn't affect any predictions of any theory one might use. How could it?

Yes one of the term predicts an accelerating universe, it also predicts an expanding version a static version and if stretched predicts a contracting version.

Not with the matter density of the observed universe. Of course if you put in matter far more dense than the matter that really exists then the equations will predict the wrong thing. However this is no different to any other area of physics. If you put in incorrect details about the distribution of charges into Maxwell's equations, then they will predict an incorrect electric field.

The CMB only shows what the value of the cosmological constant must take. It is interesting that NO values can be presented from Quantum field theory to match the prediction. If you us the contributions of say those found in the Casimir Effect the following value for the cosmological constant is infinity.

You are repeating the lie I pointed out in message 16. The pure vacuum part of the cosmological constant is times too large (not infinitely large however, I don't know where you got that from).

However this ignores effects from , contributions to the vacuum energy density coming from particle physics effects. With them added in, one gets a realistic value for .

Also the CMB experiments measure far more than the value must take. They measure hundreds of parameters.

The values of alpha and beta are renormalization parameters.

No. are finite parameters induced by renormalisation. Renormalisation (the prescription for removing infinities from quantum field theories) generates them.

In your citation there is reference to solutions by the Bunch-Davis vacuum which some claim is not even relevant to the primordial universe. My point being that any solution you wish to examine is dependent on the evolutionary era of the Big Bang. Making matters even worse is that if the universe is non-local what can be said about these parameters, them being fixed as you claim.

You didn't understand the paper I'm afraid. The Bunch-Davies vacuum is a possible quantum state of matter in DeSitter spacetime, the spacetime that describes an expanding accelerating universe.

If the spacetime with matter in the Bunch-Davies vacuum is stable, then it will be stable in other states. So all somebody needs to do to prove stability is prove stability with the Bunch-Davies vacuum. They're not saying it is the real state.

You miss the whole point… these values fine tune the cosmological constant, the value of the constant is what is in question.

The values of do not affect the value of , they are separate parameters. Naturally affects the value of . However there is no fine tuning because the parameters are given a single predicted value by quantum field theory.

I believe I have found the document and cannot deem it as support to your claims. If you have the exact URL please provide it.

The exact url is:
http://arxiv.org/abs/0712.2282
I would be very interested to hear how you think this paper doesn't support my claim, which was:
That the quantum theory, has and requires the parameters and that it predicts an expanding accelerating universe.

This was a response to your claim that you weren't aware of any value from quantum theory which could match the observed evolution of the universe.

Considering that the paper is a mathematical proof of my claim, I would be interested to know how you consider it not to support that claim.

zaius137 writes: The rest of your response is a nice little bloviation on CMB. Thanks for that….

I wanted to deal with this point separately as it is an important one.

What I presented you with was a paper with a meta-study of the observations of telescope arrays across the world, as well as satellites in space. These are carefully designed to be sensitive to the frequencies of the CMB.

When the measurements of all these probes are put together we get a graph of the power spectrum of the CMB, a detailed description of how the CMB looks, up to the l = 2,500 mode. An impressive feat of engineering.

The predictions of the Big Bang model is straight line going directly through all of these observed values. It is one of the most accurate agreements between observation and theory in scientific history. It shows that the Big Bang model directly matches observation.

Instead of dealing with this evidence you sidestep it, calling my presentation of it a "bloviation".

However this evidence is the most important fact of all.

How do you respond to the fact that the Big Bang model matches the power spectrum of the CMB so well?