SNe Ia, Implications, Interpretations, Lambda-CDM...

[modest]

No one really knows if dark energy exists or not. Astronomers do not "know it is there."

 

If you subscribe to quantum field theory, the Casimir effect is direct evidence that vacuum energy is real or that the vacuum expectation value is not necessarily zero. Just like everything quantum there are 'infinite' problems in applying this to cosmology. I don't understand the particulars of those problems or how the value predicted is tens of orders of magnitude too large. Will could no doubt explain in detail - but my point being: We would have a hard time saying it doesn't exist.

 

We also know the effect of vacuum energy would be to add value to the cosmological constant. So it seems so odd to me that you keep referring to lambda as trash, a curse, kooky, and the like. Isn't it something that needs to be studied, measured, and better understood?

 

-modest

[coldcreation]

If you subscribe to quantum field theory, the Casimir effect is direct evidence that vacuum energy is real or that the vacuum expectation value is not necessarily zero. [...] my point being: We would have a hard time saying it doesn't exist.

 

There is a huge difference, both conceptually and physically, between energy (zero-point energy, ground state energy, or energy in general) and "dark" energy. You seem to be implying that they are one and the same thing. This is obviously not the case.

 

Ground state energy is the lowest possible energy state of a system. Energy cannot be decreased indefinitely. Sometimes referred to as the ground-energy state; also associated to a ground state mass (see zero-point energy ZPE and zero-point fluctuation ZPF)

 

 

We also know the effect of vacuum energy would be to add value to the cosmological constant. So it seems so odd to me that you keep referring to lambda as trash, a curse, kooky, and the like. Isn't it something that needs to be studied, measured, and better understood?

 

 

 

• “This is a name without any meaning' date=' which was only conferred upon it because it was thought appropriate that it should have a name, and because it appeared to have something to do with the constitution of the universe; but it must not be inferred that, since we have given it a name, we know what it means. We have, in fact, not the slightest inkling of what it means.” ([b']de Sitter, Kosmos, 1932[/b])

 

 

 

Actually, "kooky" came from an article: Revolution in Cosmology …something is amiss. At the very least, the expansion is not decelerating as rapidly as once though. Either scientists must reconcile themselves to kooky energy, or they must modify or abandon inflation. (Scientific American, Jan. 1999 Vol. 280, 1).

 

 

I am, by the way, a fervent believer in Einstein's cosmological term. I believe that its value is not just close to zero, but is precisely zero. And for good reasons lambda should not be confused with dark energy. In order to understand this assertion, which goes against the grain of common practice, one must first understand what is lambda. In order to understand lambda (and the physical mechanism behind it), we must first elucidate the physical mechanism responsible for the gravitational interaction (or visa versa).

 

The cosmological constant is thus, as you correctly point out in your question, something that needs to be studied, measured, and better understood. Good point.

 

 

CC

[modest]

There is a huge difference, both conceptually and physically, between energy (zero-point energy, ground state energy, or energy in general) and "dark" energy. You seem to be implying that they are one and the same thing. This is obviously not the case.

 

I could see how I have implied that. I would not intentionally mean to. I'd prefer to leave open the possibility that lambda is influenced by more than just vacuum energy. My quote:

 

We also know the effect of vacuum energy would be to add value to the cosmological constant.

 

explicitly leaves open the possibility that other factors may or may not also add value or take value from lambda.

 

My point is that we know vacuum energy would be a factor of negative pressure in general relativity. Therefore if it exists (evidence speaks loudly that it does) it is most natural to consider necessary the addition of lambda to omega as both positive and significant. This is touched on slightly in wikipedia's article on vacuum energy:

 

The vacuum energy also has important consequences for Physical cosmology. General relativity predicts that energy is equivalent to mass, and therefore if the vacuum energy is "really there" it should exert a gravitational force. Essentially, a non-zero vacuum energy is expected to contribute to the cosmological constant, which affects the expansion of the universe.

 

I would agree with this as well as the other wikipedia articles you referenced.

 

In order to understand this assertion, which goes against the grain of common practice, one must first understand what is lambda. In order to understand lambda (and the physical mechanism behind it), we must first elucidate the physical mechanism responsible for the gravitational interaction (or visa versa).

 

Indeed, lambda is negative pressure and vacuum energy is the mechanism that gives that negative pressure. The difference does need to be understood even if they are only implied in the conversation. One can relate the cosmological constant to the pressure of the vacuum by:

 

[math]\lambda=8{\pi}{G}{P_{vac}}[/math]

 

I would be interested to hear how lambda could be real and zero while vacuum energy is real and not zero as you claim. I don't see how that would be possible without breaking some rules of relativity.

 

-modest

[Erasmus00]

There is a huge difference, both conceptually and physically, between energy (zero-point energy, ground state energy, or energy in general) and "dark" energy. You seem to be implying that they are one and the same thing. This is obviously not the case.

 

They are very, very related. Any "zero point energy" should be a source of gravity- hence a source of "dark energy." It may not be the ONLY source of dark energy but it certainly is one source that should exist.

 

I am, by the way, a fervent believer in Einstein's cosmological term. I believe that its value is not just close to zero, but is precisely zero.

 

This implies that the vacuum energy should be exactly 0 as well. I know of no way to do this except unbroken super-symmetry which is experimentally ruled out.

 

And for good reasons lambda should not be confused with dark energy.

 

A non-zero lambda is the most straightforward way to understand dark energy.

 

In order to understand this assertion, which goes against the grain of common practice, one must first understand what is lambda.

 

I think this is usually what is done. Move Einstein's constant to the other side (the stress energy tensor side), and we can recognize it as the energy density of empty space, i.e. what you called "zero-point energy."

-Will

[coldcreation]

... I'd prefer to leave open the possibility that lambda is influenced by more than just vacuum energy.

 

I would think, rather, that vacuum energy (ground energy or ZPE) is influenced by lambda as well as gravity. The difference with what you wrote above is that lambda remains the same. It is thus a true constant of nature, a fundamental one (the value of which is fixed for all times, again, in my opinion (based on empirical data), equal to zero).

 

 

explicitly leaves open the possibility that other factors may or may not also add value or take value from lambda.

 

This hypothesis has been developed extensively, but I remain reticent.

 

 

My point is that we know vacuum energy would be a factor of negative pressure in general relativity. Therefore if it exists (evidence speaks loudly that it does) it is most natural to consider necessary the addition of lambda to omega as both positive and significant. This is touched on slightly in wikipedia's article on vacuum energy:

 

The interpretation of "negative pressure" to describe lambda is untenable, for a variety of reasons. I argue that there is no such thing as negative pressure. All pressure must be positive. There is therefore the need for an absolute scale (similar to the Kelvin temperature scale, where absolute zero is the starting point, the ultimate limit of coldness, beyond which, even in principle, temperature cannot drop). Lambda would thus be defined as the ultimate limit of pressure equal to zero pressure. The implications of this interpretation are profound and far-reaching, since it requires the identification of a new law of nature which would explain a fundamental constant of nature: lambda.

 

Unfortunately, a full review of this concept is beyond the scope of this thread. I will begin a new thread on the subject of lambda within the coming week. In the new thread it will be shown that the current problems not just cosmology, but physics in general (the problem of unification between gravity and the other forces of nature, between gravity and QM, the problem of equilibrium, both locally and globally, etc.) can be reconciled -- once the physical mechanism of both lambda and gravity are elucidated. It will be shown, too, that it is the same physical mechanism responsible for both phenomena.

 

Too ambitious, or even too pretentious? Perhaps. But in light of the risk to reward ratio, for science generally, I would think it is a solution worth considering. If this interpretation lambda is wrong then the only thing wasted is time and a little money (time = money), but if it is correct -- and I will argue on empirical grounds that it is indeed -- then the time ($) will have been put to good use. :)

 

 

Indeed, lambda is negative pressure and vacuum energy is the mechanism that gives that negative pressure. The difference does need to be understood even if they are only implied in the conversation. One can relate the cosmological constant to the pressure of the vacuum by:

[math]lambda=8{pi}{G}{P_{vac}}[/math]

 

In my opinion, this explanation of negative pressure is untenable. So is this one. And these definitions do not apply to lambda.

 

"It's weird negative pressure" (Dr. Krauss).

 

Yes, it can be related to pressure just as gravity can be related to pressure. But does not mean that it is pressure at all (let alone with a negative sign).

 

Two problems with this hypothetical state (negative pressure) are that it can never be detected empirically, thus the term ‘dark’ energy, and it always requires new physics (something that is not physics).

 

For Einstein to have excluded the cosmological term for reasons of ‘aesthetic’ simplicity, before ever having spelled out a fully persuasive and unambiguous elucidation of its meaning, is as understandable as it is forgivable. However, for cosmologists to have reinvented and savored the principle (despite Einstein’s original motivations and ambitions for having introduced lambdda, i.e., to secure a stationary universe) and exploit it as the propulsion mechanism, the driving force, the ‘tantamount’ negative pressure, that produced the cosmic repulsion or the acceleration of expansion, bestows real physical meaning to the expression paradoxical.

 

 

I would be interested to hear how lambda could be real and zero while vacuum energy is real and not zero as you claim. I don't see how that would be possible without breaking some rules of relativity.

 

Lambda could be equal to zero if it turns out that lambda is not vacuum energy. That is what I will argue. Vacuum energy is simply vacuum energy (usually in the form of ZPE or ground state energy). The rules of GR would not be broken. However, an extension of GR would be required, yet would not take away any of its beauty, quite the contrary.

 

Lambda should no longer be considered a parameter that is either positive or negative in relation to zero. That is almost as arbitrary as zero degrees on the Celsius temperature scale. However Celsius was justified in his use of zero degrees. In the case of lambda, the zero (flanked by a positive and negative) value is not justified, since there is absolutely no guarantee that negative pressure exists. Indeed, no vacuum experiment can demonstrate the existence of pressure with a minus sign. What vacuum experiments do demonstrate is that zero pressure is the ultimate limit inherent in nature. No amount of work (energy, if you will) is capable of producing a vacuum with less than absolute zero pressure since an infinite amount of energy would be required: something that is not available here on earth or anywhere else in the universe.

 

Thus my conclusion: there is no such thing as negative pressure, and hence, the SNe Ia data is not evidence for the existence or dark energy.

 

 

 

CC

[PhysBang]

It is thus a true constant of nature, a fundamental one (the value of which is fixed for all times, again, in my opinion (based on empirical data), equal to zero).

Perhaps you can explain how something can be both a constant of nature and equal to zero everywhere. I think I'll develop an "angel constant" and claim that it is a true constant of nature that is zero everywhere.

The interpretation of "negative pressure" to describe lambda is untenable, for a variety of reasons. I argue that there is no such thing as negative pressure. All pressure must be positive. There is therefore the need for an absolute scale (similar to the Kelvin temperature scale, where absolute zero is the starting point, the ultimate limit of coldness, beyond which, even in principle, temperature cannot drop).

Indeed, it is very similar, since there are applications for temperature below absolute zero.

Lambda would thus be defined as the ultimate limit of pressure equal to zero pressure. The implications of this interpretation are profound and far-reaching, since it requires the identification of a new law of nature which would explain a fundamental constant of nature: lambda.

So what you are saying is that you want to introduce a totally new concept, give it the same name as an existing constant (or the purposes of confusion?) ? A concept that goes against the existing well established laws of physics that use terms like "negative pressure" and has no conceptual or empirical support behind it?

In my opinion, this explanation of negative pressure is untenable. So is this one. And these definitions do not apply to lambda.

They aren't very good entries, but what can one expect from Wikipedia? The negative pressure of the cosmological constant is associated with the basic mathematics of general relativity.

"It's weird negative pressure" (Dr. Krauss).

Yes, it's very weird if one does not address it in the actual scientific terms but instead dresses it up for a pop audience.

Yes, it can be related to pressure just as gravity can be related to pressure. But does not mean that it is pressure at all (let alone with a negative sign).

Sure. But what does the actual physics say?

Two problems with this hypothetical state (negative pressure) are that it can never be detected empirically, thus the term ‘dark’ energy, and it always requires new physics (something that is not physics).

The term "dark energy" arises because it's a new cosmological idea to popular science journalism. That this cosmological behaviour is related to negative pressure is something that can be measured. You even linked to a study that was all about trying to determine the equation of state of this energy density, and that determines the pressure!

For Einstein to have excluded the cosmological term for reasons of ‘aesthetic’ simplicity, before ever having spelled out a fully persuasive and unambiguous elucidation of its meaning, is as understandable as it is forgivable.

It is forgivable in the sense that we can forgive him for removing a part of the mathematics of his theory without good grounds. That doesn't mean that every scientist should ignore the empirical results regarding this part of the theory.

However, for cosmologists to have reinvented and savored the principle (despite Einstein’s original motivations and ambitions for having introduced lambdda, i.e., to secure a stationary universe) and exploit it as the propulsion mechanism, the driving force, the ‘tantamount’ negative pressure, that produced the cosmic repulsion or the acceleration of expansion, bestows real physical meaning to the expression paradoxical.

If you would read through the mathematics of the theory, you would see that there is nothing to negative pressure in this case that isn't forced by Einstein's mathematical theory.

What vacuum experiments do demonstrate is that zero pressure is the ultimate limit inherent in nature.

What about the applications of negative pressure listed in the wikipedia article that you linked to? Are the technologies based on these principles not actually operating?

[Mike C]

What does this have to do with SNe Ia observations? What are the distances and redshifts involved?

 

My answer to the type of units involved in the error ranges for the SN 1a's that I gave on #47 was not correct.

I said the units for these error ranges for the SN 1a's was +/- 5 and that I thought the units represented just 'parsecs', but these error bars for the

SN 1a's is a 'mega' parsec. So this is much larger because mega means a million.

So one error unit should be 1 megaparsec. That transulates to 3.26 million light years.

 

The current distance that involved the 'dark' energy observations are a considerable distance further.

The Virgo Cluster is at a redshift distance of .0023-.004.

The latest obsevations of these SN's is at distances of RS z=2,

So these DE observations are aproximately 560 times further away than the VC.

 

What does this have to do with SNe Ia observations? What are the distances and redshifts involved?

 

I answered that above. The comparison of the VC to these DE observations are compared because the same objects were involved in these comparisons.

 

Do you have any actual physical theory to back up this opinion? Can we see this physical behaviour in a toy model? Can we produce any guess as to its magnitude?

 

The nature of these 'light curves' used to compare to the local observed SN 1a's was apparently done to improve the Hubble Constant parameter.

So this DE anamoly was not expected.

But, I do not give much credibility to this latest interpretation and also do not consider the SN 1a's as reliable candles.

My interpretation of possible errors being added to these latest observations is just my own possibilities for added errors.

You have to use your visualizations of what I say.

Although the SN1a's are considered to be very large spherical explosins, I presumed that they could be somewhat linear and directional to have these light curves depart from the standard model.

 

Mike C

 

 

 

Mike C

[modest]

The interpretation of "negative pressure" to describe lambda is untenable, for a variety of reasons. I argue that there is no such thing as negative pressure. All pressure must be positive.

 

PhysBang is right. "negative pressure" "cosmological constant" "vacuum energy" are all verbal descriptions to something that has only one mathematical meaning in GR. As Will pointed out, if you rearrange the field equations with lambda on the stress-energy tensor side it shows clearly its effect. The stress energy tensor of the vacuum equals lambda over eight pi times the metric tensor. So, when you say lambda is not a negative pressure of the vacuum - there would appear to be no discernible mathematical meaning behind that. When you say new physics has to be invented to cope with new observations - I honestly don't know what new physics you are referring to. The physics has been there since GR was envisioned and would seem to work to describe the SNe 1a observations. If lambda is the 'new physics' then I am thoroughly confused.

 

I think we should investigate deeper lambda in the field equations and in their metric solutions particularly the FLRW metric or perhaps a vacuum solution, because it feels like some key ingredient is missing in our conversation. It feels like we think we are discussing the same thing while perhaps we are not.

 

-modest

[coldcreation]

They are very, very related. Any "zero point energy" should be a source of gravity- hence a source of "dark energy." It may not be the ONLY source of dark energy but it certainly is one source that should exist.

 

This implies that the vacuum energy should be exactly 0 as well. I know of no way to do this except unbroken super-symmetry which is experimentally ruled out.

 

A non-zero lambda is the most straightforward way to understand dark energy.

 

I think this is usually what is done. Move Einstein's constant to the other side (the stress energy tensor side), and we can recognize it as the energy density of empty space, i.e. what you called "zero-point energy."

-Will

 

See response below.

 

 

CC

[modest]

The response to this post by PhysBang, as well as this post by modest, will appear in the Cosmological Constant thread

 

CC

 

I'm sorry CC but this is not good. It would be beneficial to explore lambda in the context of this discussion. Indeed, I don't see how lambda could be off topic in a discussion about lambda's influence on the accelerating expansion of the universe. Notice the title of this thread.

 

I sincerely hope this is not an attempt to segregate lambda from its observational effects such as SN 1a data. Would discussion of that data be out of the scope of the other thread while lambda's implication in GR is out of scope here? Do you see the problem with that? As far as the standard model is concerned, lambda, SN 1a observations, and GR are all inexorably linked. It serves no beneficial purpose to have 2 different discussions about the same thing.

 

-modest

[coldcreation]

I'm sorry CC but this is not good. It would be beneficial to explore lambda in the context of this discussion. Indeed, I don't see how lambda could be off topic in a discussion about lambda's influence on the accelerating expansion of the universe. Notice the title of this thread.

 

I sincerely hope this is not an attempt to segregate lambda from its observational effects such as SN 1a data. Would discussion of that data be out of the scope of the other thread while lambda's implication in GR is out of scope here? Do you see the problem with that? As far as the standard model is concerned, lambda, SN 1a observations, and GR are all inexorably linked. It serves no beneficial purpose to have 2 different discussions about the same thing.

 

-modest

 

 

You have good point. Let's continue the discussion here. I place the other thread on hold. Below is a continuation of the discussion...(the same that I posted in the Cosmological Constant thread)

 

 

 

 

 

 

No one really knows if dark energy exists or not. Astronomers do not "know it is there."

 

You can take lambda out of the trash, but you can't take the trash out of lambda!

 

 

If you subscribe to quantum field theory, the Casimir effect is direct evidence that vacuum energy is real or that the vacuum expectation value is not necessarily zero. [...] my point being: We would have a hard time saying it doesn't exist.

 

 

There is a huge difference, both conceptually and physically, between energy (zero-point energy, ground state energy, or energy in general) and "dark" energy. You seem to be implying that they are one and the same thing. This is obviously not the case.

 

 

They are very, very related. Any "zero point energy" should be a source of gravity- hence a source of "dark energy." It may not be the ONLY source of dark energy but it certainly is one source that should exist.

 

 

That ZPE gravitates is not the problem. The problem occurs when dark energy is treaded as if it were negative energy (or negative pressure). ZPE is not negative energy, nor is it a negative absolute pressure, or negative gauge pressure). It is non-zero and positive. Though ZPE gravitates, it does not follow that ZPE is a source of dark energy. Zero point energy is the lowest possible energy state of a system. It cannot be removed from the system. Nor could it be a zero-point field; the lowest energy state of a field (also called the ground state).

 

 

 

I am, by the way, a fervent believer in Einstein's cosmological term. I believe that its value is not just close to zero, but is precisely zero.

 

This implies that the vacuum energy should be exactly 0 as well. I know of no way to do this except unbroken super-symmetry which is experimentally ruled out.

 

That would be the case if (and only if) the cosmological constant was in fact vacuum energy. Unfortunately that is not fact. I argue that it is possible to have lambda equal to zero and vacuum energy non-zero, i.e., positive. So, as energy tends to zero, the vacuum state described by lambda is approached, but not attained (since there will always remain a residual ground energy).

 

The stress-energy tensor of the vacuum does not obligatorily (or, at all) lead to a negative energy state, as long as lambda is thought of as a vacuum state that induces a 'tension' (rather than a kind of energy with a plus or minus sign). It can then be shown that lambda acts as a repulsive force without actually being one.

 

It follows that because we live in a universe with matter (as opposed to one that is empty), the gravitational field curvature is implicitly and explicitly a result of the tension associated with lambda in the presence of matter. There is no fine-tunning problem since lambda and gravity are not opposite forces (energies or pressures). They are simply part of the same field, where lambda represents the ultra-high vacuum minima.

 

In geometrical terms, lambda describes the special relativistic gravity-free vacuum state with a Minkowski spacetime signature, while the field equations of general relativity describe the deviation-from-linearity (the curvature) of the manifold obtained by measurements of the metric properties internal to the manifold.

 

 

A non-zero lambda is the most straightforward way to understand dark energy.

 

How does treating 'something' as non-zero provide a clue as to the nature of 'something.'

 

With the description above, a "non-zero" lambda is simply called gravity.

 

This may appear, at first glance, to be a non-conventional precept of spacetime, or at least a non-conventional interpretation of lambda. But it actually is not, since there is no new physics involved, and since lambda still represents (or describes) the state of empty space in relation that which gravitates, i.e., in interaction with the gravitational field (in semi-accord with Einstein's initial version of lambda). However it is no longer a parameter that can be tweaked, since its value must remain constant and equal to zero at all times. And so it does not increase with distance opposite to the inverse square reduction of the gravitational potential with distance. Curvature varies, lambda would not.

 

The good news: we rid ourselves of the "tendentious tenebrous speculation that the cosmological constant is different from zero" (see Sandage 1993).

 

 

... Move Einstein's constant to the other side (the stress energy tensor side), and we can recognize it as the energy density of empty space, i.e. what you called "zero-point energy."

 

The difference here is that you describe lambda (in accord with the standard contemporary interpretation) as the energy density of empty space, or ZPE as you wrote above, whereas I describe it as the minima of curvature upon which (or within which) ZPE and other forms of mass-energy; galaxies, stars, planets, people, etc., subsist.

 

The explosion of 1998 seemed capable of blowing-up the bureaucratic shell of expansionists. But the regenerative capacity of the cosmological constant has once again played its role. In the long run, the only good deed introduced by the resurrected trepidation could be that it may unwittingly have set in motion the forces that will end the Great Cosmological Slump of the twentieth century. But that is a distant threat, for now. There are no reasons yet (or, perhaps there is one) to shrug off the disturbing evidence of gravity’s weakness (failure) to slow down the runaway universe.

 

We humans naturally reach for transcendence (not transhumance), seeking symbols with which to make it real. Science and religion have always worked that way. So, for that matter, has art. But transcendence, by definition, transcends. We should be reticent, consequently, in the claims we make on the unlimited—the existence of a force above and apart from the material world. And equally reticent, yes, in claims we make on absolutes.

 

 

 

 

CC

[Erasmus00]

I apologize for double posting. This was by request

 

That ZPE gravitates is not the problem. The problem occurs when dark energy is treaded as if it were negative energy (or negative pressure). ZPE is not negative energy, nor is it a negative absolute pressure, or negative gauge pressure). It is non-zero and positive. Though ZPE gravitates, it does not follow that ZPE is a source of dark energy. Zero point energy is the lowest possible energy state of a system. It cannot be removed from the system. Nor could it be a zero-point field; the lowest energy state of a field (also called the ground state).

 

A brief example of how gravitating zero point energy causes "dark energy." Consider a universe that has real scalar particles in it, described by a field [imath]\phi[/imath] with action

 

[math] S = \int \sqrt{-g} d^4x \frac{1}{2}g^{\mu\nu}\partial_{\mu}\phi\partial_{\nu}\phi - V\left({\phi}\right) [/math]

 

This has a stress energy tensor

 

[math] T_{\mu\nu} = \frac{1}{2}\partial_{\mu}\phi\partial_{\nu}\phi +\frac{1}{2}g^{\rho\sigma}\partial_{\rho}\phi\partial_{\sigma}\phi g_{\nu\mu} -V\left(\phi\right)g_{\mu\nu} [/math]

 

Now, lets assume that we have a vacuum, the state of lowest energy of our system.

 

[math] T_{\mu\nu} = -V\left(\phi_o\right)g_{\mu\nu} = -\rho_{vac}g_{\mu\nu}[/math]

 

Here I identified the lowest value of V as the energy density of the vacuum. Lets go to a local lorentz frame and look at this.

 

[math] T_{\mu\nu} = \rho_{vac} \left(\begin{array}{cccc} 1&0&0&0\\ 0&-1&0&0\\0&0&-1&0\\0&0&0&-1 \end{array}\right) [/math]

 

Now compare this to the stress energy tensor of a perfect fluid with energy [imath] \rho[/imath] and pressure P.

 

[math] T_{\mu\nu} = \left(\begin{array}{cccc} \rho&0&0&0\\ 0&P&0&0\\0&0&P&0\\0&0&0&P \end{array}\right) [/math]

 

We see right away that the energy of a vacuum (the positive energy density) can be thought of as a perfect fluid with [imath] P = -\rho_{vac} [/imath]. While I have shown this for one specific case, it is a general result. Vacuum energy behaves as a fluid WITH NEGATIVE PRESSURE.

 

Now, can we identify this with a cosmological constant? Consider Einstein's equations with cosmological constant (as Einstein wrote it)

 

[math] G_{\mu\nu} +\Lambda g_{\mu\nu} = 8\pi T^{matter}_{\mu\nu}[/math]

 

If we move lambda to the other side, we see that the right side can be written

 

[math] 8\pi\left(T^{matter}_{\mu\nu} -\frac{\Lambda}{8\pi} g_{\mu\nu}\right)[/math]

 

Comparing this to our above expression for the stress energy tensor, we see that

 

[math] \frac{\Lambda}{8\pi} = \rho_{vac}[/math]

 

Hence, the cosmological constant is completely equivalent to vacuum energy!

 

So, to recap- I have demonstrated that

1. Vacuum energy (what you call zero point energy) gravitates as a fluid with negative pressure.

2. This vacuum energy/pressure whatever you want to call it is exactly equivalent to a cosmological constant as Einstein introduced it.

 

Care to comment?

-Will

[PhysBang]

Bra - f'n - vo!

[modest]

Will, I was just writing a reply that shows that exactly including this link:

 

http://www.astro.ucla.edu/~wright/Pvac_details.gif

 

You so beat me to it :)

 

Yours is 100 times more elegant and well-written than anything I was saying.

 

-modest

[PhysBang]

My answer to the type of units involved in the error ranges for the SN 1a's that I gave on #47 was not correct.

I said the units for these error ranges for the SN 1a's was +/- 5 and that I thought the units represented just 'parsecs', but these error bars for the

SN 1a's is a 'mega' parsec. So this is much larger because mega means a million.

So one error unit should be 1 megaparsec. That transulates to 3.26 million light years.

 

The current distance that involved the 'dark' energy observations are a considerable distance further.

The Virgo Cluster is at a redshift distance of .0023-.004.

The latest obsevations of these SN's is at distances of RS z=2,

So these DE observations are aproximately 560 times further away than the VC.

This doesn't tell me anything about the degree of error in these observations or the effect of this error.

I answered that above. The comparison of the VC to these DE observations are compared because the same objects were involved in these comparisons.

I really do not understand. Surely not all the SNe Ia observed were in the Virgo Cluster. What is the relationship between this cluster and the sample of supernovae observed?

The nature of these 'light curves' used to compare to the local observed SN 1a's was apparently done to improve the Hubble Constant parameter.

So this DE anamoly was not expected.

It was not expected, but it was one of the things that the observation was able to measure. It influences the second derivative of the scale factor, which was the target of the observations.

But, I do not give much credibility to this latest interpretation and also do not consider the SN 1a's as reliable candles.

Sure, but is this based on the actual evidence about these events?

My interpretation of possible errors being added to these latest observations is just my own possibilities for added errors.

You have to use your visualizations of what I say.

Although the SN1a's are considered to be very large spherical explosins, I presumed that they could be somewhat linear and directional to have these light curves depart from the standard model.

Is that a long way of saying that you don't have a physical theory upon which to base your criticisms?

[modest]

To make sure we're on the same page about lambda, some basics:

 

Einstein's field equations:

[math]G_{\mu\nu}=\frac{8{\pi}G}{c^4}T_{\mu\nu} [/math]

 

with [imath]8{\pi}G/c^4[/imath] as [imath]{\kappa}[/imath] and an expanded [imath]G_{\mu\nu}[/imath] is:

 

[math]R_{\mu\nu}-\frac{1}{2}g_{\mu\nu}R=-{\kappa}T_{\mu\nu}[/math]

 

where [imath]R_{\mu\nu}[/imath] is the Ricci tensor, [imath]g_{\mu\nu}[/imath] is the metric tensor and [imath]T_{\mu\nu}[/imath] is the stress-energy tensor. In deriving this equation a constant has been left out - or assumed to be zero. That constant is [imath]\Lambda[/imath] and when included makes the term [imath]\Lambda{g_{\mu\nu}}[/imath] (lambda-g-mu-nu) The term follows the rules for the left side of Einsteins field equations.

 

1) Not higher than linear in the second-order derivitive of the metric

 

2) Symmetric to match the right side

 

When included we have:

 

[math]R_{\mu\nu}-\frac{1}{2}g_{\mu\nu}R+\Lambda{g_{\mu\nu}}=-{\kappa}T_{\mu\nu}[/math]

 

[imath]\Lambda[/imath] is now a constant that can be positive, negative, or zero. The term is called the cosmological constant probably because it's implications are cosmological. It has dimensions of [imath](length)^{-2}[/imath] like R. Speaking of R, if we substitute [imath]R=\kappa{T}+4{\Lambda}[/imath] and rearrange we get the usual form that includes the cosmological constant:

 

[math]R_{\mu\nu}=-{\kappa}(T_{\mu\nu}-\frac{1}{2}T{g_{\mu\nu}})+\Lambda{g_{\mu\nu}}[/math]

 

And so the curvature of space is a function of lambda as well as the usual stress and metric tensors. If you follow the steps on wikipedia's Einstein's Field Equations page to derive newton-like gravity from this (noting we have one more term than they do) in a weak field you get:

 

[math]{\nabla}^2{\Phi}=4{\pi}G{\rho}-{\Lambda}c^2[/math]

 

so that the force in a weak field with mass M is:

 

[math]{\Phi}\vec{\nabla}=-{\frac{GM}{r^2}}{\vec{r}}+\frac{c^2{\Lambda}r}{3}{\vec{r}}

[/math]

 

we see the cosmological constant is a repulsive effect when it is positive. We also see it is linear (it's force increases linearly with distance) unlike the force of gravity.

 

I'd like to work out lambda in the FLRW metric and show some of the cosmological consequences - I'll pick up on it tomorrow - very tired.

 

- modest

[modest]

CC,

 

De Sitter's Model and Luminosity-Distance in Cosmology

RC Barnes; 1981; Ro. Astro. Soc. 195, 959;

 

Seems to discuss exactly what you've been discussing. I just skimmed over it, but I'm sure I can read it in detail soon. It discusses apparent vs. intrinsic brightness at redshift in de Sitter's model vs. other models. It was obviously written before SNe 1a data.

 

-modest