Is Dark Energy Consistent with a Cosmological Constant?

[Chronos]

I was reading about this on Arxiv over the weekend and was about to start a thread here when I notice alexsok got the scoop on me in the 'Beyond the Standard Model' forum. So give him credit for 'catch of the day' for the link to
http://physicsweb.org/articles/news/10/11/16/1

Here is the Arxiv release:

http://www.arxiv.org/abs/astro-ph/0611572
New Hubble Space Telescope Discoveries of Type Ia Supernovae at z > 1: Narrowing Constraints on the Early Behavior of Dark Energy

"We have discovered 21 new Type Ia supernovae (SNe Ia) with the Hubble Space Telescope (HST) and have used them to trace the history of cosmic expansion over the last 10 billion years. These objects, which include 13 spectroscopically confirmed SNe Ia at z > 1, were discovered during 14 epochs of reimaging of the GOODS fields North and South over two years with the Advanced Camera for Surveys on HST. Together with a recalibration of our previous HST-discovered SNe Ia, the full sample of 23 SNe Ia at z > 1 provides the highest-redshift sample known. Combined with previous SN Ia datasets, we measured H(z) at discrete, uncorrelated epochs, reducing the uncertainty of H(z>1) from 50% to under 20%, strengthening the evidence for a cosmic jerk--the transition from deceleration in the past to acceleration in the present. The unique leverage of the HST high-redshift SNe Ia provides the first meaningful constraint on the dark energy equation-of-state parameter at z >1.
The result remains consistent with a cosmological constant (w(z)=-1), and rules out rapidly evolving dark energy (dw/dz >>1). The defining property of dark energy, its negative pressure, appears to be present at z>1, in the epoch preceding acceleration, with ~98% confidence in our primary fit. Moreover, the z>1 sample-averaged spectral energy distribution is consistent with that of the typical SN Ia over the last 10 Gyr, indicating that any spectral evolution of the properties of SNe Ia with redshift is still below our detection threshold."

This firms up the work done by Perlmutter, et. al., putting accelerated expansion and dark energy on the cosmological modeling table. The timing is interesting given some of the recent dissent on the legitimacy of SN Ia as standard candles.

 

[Garth]

If cosmic acceleration is due to the cosmological constant then that raises two questions:

1. "How constant is constant? - Does it go all the way back to the BB, and if so what would that do to BBN?" Note that if truly a cosmological constant $\Lambda$ in the Einsteinian sense then it cannot vary at all, it would have to apply even to the earliest stages of the universe but AFAIK that would distrupt the BBN element abundances.

2.. "The coincidence problem: why should the energy density associated with the cosmological constant be approximately equal to the density of DM and matter in the present epoch?"

Garth

 

[Chronos]

Good questions, Garth. A possible partial explanation:

http://arxiv.org/abs/gr-qc/0611090
Cosmology as a search for overall equilibrium
Authors: Carlos Barcelo
Comments: 9 pages, 1 figure

In this letter we will revise the steps followed by A. Einstein when he first wrote on cosmology from the point of view of the general theory of relativity. We will argue that his insightful line of thought leading to the introduction of the cosmological constant in the equations of motion has only one weakness: The constancy of the cosmological term, or what is the same, its independence of the matter content of the universe. Eliminating this feature, I will propose what I see as a simple and reasonable modification of the cosmological equations of motion. The solutions of the new cosmological equations give place to a cosmological model that tries to approach the Einstein static solution. This model shows very appealing features in terms of fitting current observations.

 

[SpaceTiger]

1. "How constant is constant? - Does it go all the way back to the BB, and if so what would that do to BBN?" Note that if truly a cosmological constant $\Lambda$ in the Einsteinian sense then it cannot vary at all, it would have to apply even to the earliest stages of the universe but AFAIK that would distrupt the BBN element abundances.

The energy density of the cosmological constant would be negligible at the time of nucleosynthesis. Remember that the matter and radiation energy densities decrease with time.

 

[Garth]

Thank you ST - of course!

That just leaves the coincidence problem...

Garth

 

[EL]

That just leaves the coincidence problem...

Yes, and this is imo indeed a serious problem. The recent Riess et al paper (although which I've heard is a bit unclear, they seem to be using a lot of priors) claim:

http://www.arxiv.org/abs/astro-ph/0611572]The[/PLAIN] result remains consistent with a cosmological constant (w(z)=-1), and rules out rapidly evolving dark energy (dw/dz >>1).

It still leaves room for a slowly varying w though. I'd have a hard time accepting a true cosmological constant.

 

[George Jones]

Yes, and this is imo indeed a serious problem.

Why is this a problem?

 

[EL]

Why is this a problem?

In short: The energy density of dark energy comming from a true cosmological constant, is constant in time.
The matter density goes like a^-3, where "a" is the scale factor of the FLRW metric.
Only during a relatively short period of the history of the universe the two densities (dark energy and matter) will be of equal magnitudes. At all other times either the matter or the dark energy will totally dominate.
How does it come we are so "lucky" we live at exactly the right time so that they are of the same size (omega_matter=0.3, omega_lambda=0.7) now? This seems like a too big coinsidence to be true for me. I find it much more probable they have been of comparable size during a long period of time, something which can't be true for a true cosmological constant type of dark energy.

 

[Garth]

Especially when you realize that a has increased in scale by something like a factor of 10⁶⁰ since the Planck era.

Garth

 

[Kea]

If one were willing to consider the QG zero-CC solution, such as via a varying c cosmology, the problem goes away.

 

[George Jones]

To me, it sounds a lot like the Feynman license plate story.

 

[Mike2]

How does it come we are so "lucky" we live at exactly the right time so that they are of the same size (omega_matter=0.3, omega_lambda=0.7) now? This seems like a too big coinsidence to be true for me.

As I understand it, the universe started accelerating in its expansion when the dark energy density became larger than all other energy densities combined. So when the expansion started accelerating, the cosmolgocial event horizon began to shrink. With faster expansion, there is now a shorter distance to where space is receding faster than light. Beyond this cosmological event horizon we lose information about the universe further away than that.

Some propose that the cosmological event horizon acts like the event horizon of a black hole in that the entropy associated with the surface area of the horizon constrains the entropy inside it. So as the cosmological event horizon shrinks, this acts like a force to reduce the entropy inside the horizon. And a reduction of entropy is equivalent to an increase in improbable, complex structures, such as life perhaps.

So perhaps it is no accident that we live in a time when dark energy has begun to dominate. This might be more strongly correlated if it happens to be the case that the time when the dark energy density was equal to the other densities was when life started to appear on earth. As I understand it, the universe started accelerating about 4 billion years ago which is when life first appeared on earth.

 

[EL]

To me, it sounds a lot like the Feynman license plate story.

No no. It's not at all the same thing. Feynman could have said the same about any car.

 

[Mike2]

1. "How constant is constant? - Does it go all the way back to the BB, ?"

During Inflation the universe expanded very much more rapidly than today. So the vacuum energy was much, much greater than now. If vacuum energy is the same as the cosmological constant, then it was not constant all the way to the BB.

One question I have about Inflation is whether a much larger vacuum energy mean that h-bar was much larger during that time. If a vacuum energy is due to particles popping in and out of existence so that the average time of there existence allows an average energy density to exist according to Heisenberg's Uncertainty Principle, then does that mean a greater vacuum energy allows more uncertainty so that the average energy density is larger for that same average duration of time?

 

[Kea]

One question I have about Inflation is whether a much larger vacuum energy mean that h-bar was much larger during that time.

Mike

If you allow $\hbar$ to vary (which is good) you will at least have to go with varying c also, to avoid some pretty basic inconsistency problems.

 

[EL]

Mike2, not sure I got everything in your post #12, but as I think you'd like to point out, if we could find evidence for that the existence of life is strongly correlated to the equality of matter and dark energy densities, then there wouldn't be a coincidense problem anymore.
However I have a hard time making such a (in my eyes quite far-fetched) connection, but rather find a time dependent equation of state more appealing.

 

[selfAdjoint]

One question I have about Inflation is whether a much larger vacuum energy mean that h-bar was much larger during that time. If a vacuum energy is due to particles popping in and out of existence so that the average time of there existence allows an average energy density to exist according to Heisenberg's Uncertainty Principle, then does that mean a greater vacuum energy allows more uncertainty so that the average energy density is larger for that same average duration of time?

I think this is mixing apples and oranges. The "vacuum energy" that is suggested as the expansion cause is a feature of the Einstein equations of the diffeomeorphic theory GR; the virtual particle picture is due to (one formulation of) Quantum Field Theory. One is "classical all the way down", the other assumes that quantumness is the unversal law of nature.The big problem for theorists today, as has been stated over and over again, is that these theories have nothing whatsoever to do with one another. And although popular books (not the better ones) do things such as you suggest here, real physicists doing real physics don't.

And just remember, many particle physicsts do not believe that virtual particles are physical; they consider them just intermediate terms in a calculation, like indices you sum over or variables of integration.

 

[EL]

During Inflation the universe expanded very much more rapidly than today. So the vacuum energy was much, much greater than now. If vacuum energy is the same as the cosmological constant, then it was not constant all the way to the BB.

First of all, that's Garth you're quoting, not me!
Secondly, SpaceTiger gave the correct explanation why a cosmological constant doesn't affect BB nucleosynthesis. Contrary to what you said, the dark energy density was at that time completely negligeble compared to radiation and matter densities.

 

[SpaceTiger]

During Inflation the universe expanded very much more rapidly than today. So the vacuum energy was much, much greater than now. If vacuum energy is the same as the cosmological constant, then it was not constant all the way to the BB.

The "vacuum energy" that led to inflation is thought to have been due to a scalar field (dubbed the "inflaton field") that then decayed at the time of reheating. This isn't the same as the cosmological constant, though it behaves identically throughout most of inflation. The current accelerated expansion could also be due to a scalar field (such as a "quintessence field") which would be time variable, but the standard $\Lambda CDM$ cosmology just assumes a cosmological constant.

 

[hellfire]

As I understand it, the universe started accelerating in its expansion when the dark energy density became larger than all other energy densities combined. So when the expansion started accelerating, the cosmolgocial event horizon began to shrink.

The cosmological event horizon does not shrink, as we discussed here based on Figure 1 of this reference.

 

[CosmologyHobbyist]

Hello everyone!
I am absolutely delighted by this turn of events!
I have played with the idea that dark matter is a product of quantum particle pair (perhaps neutrino) creation; and dark energy is a space-time expansion in response to the creation of matter.
Assuming quantum particle pair output to be constant, this puts dark energy & matter to always be proportional to the volume of the universe, as the universe doubles in size, the dark energy/matter proportion goes up by 2 cubed (8). Therefore dark matter exceeded matter about halfway through the life of the universe, which should show up in galactic disk rotation spectra.
The beauty of this line of thinking is the inflationary moment (its too quick to call an epoch), becomes the spacetime response to a huge amount of energy conversion into nuclear strong force. This means spacetime is volatile, expanding and contracting according to creation and annhilation of matter. This should be measurable by atomic clocks near nuclear reactors, which might detect the conversion of a gram of mass into energy over 20 years as a clock slowing equivalent to the gravity emitted by 3 grams of matter. I get mired in the maths at this point, but its only a toy idea, really not worth a mention among people who can probably name 10 reasons why it doesn't work.
But I still find it exciting that evidence is going in this direction, and spacetime may yet become as dynamic a player in physics as the 4 forces.

 

[SpaceTiger]

To me, it sounds a lot like the Feynman license plate story.

Perhaps, though I think this lies in an uncomfortable gray area. The reasoning being used is very similar to that used with the flatness problem (a motivator for inflation), but the apparent coincidence is a bit less striking. Unfortunately, it's difficult to quantify the "Feynman license plate" bias, so I think we should just keep this "coincidence" in mind as we try to understand dark energy.

 

[Mike2]

The "vacuum energy" that led to inflation is thought to have been due to a scalar field (dubbed the "inflaton field") that then decayed at the time of reheating. This isn't the same as the cosmological constant, though it behaves identically throughout most of inflation. The current accelerated expansion could also be due to a scalar field (such as a "quintessence field") which would be time variable, but the standard $\Lambda CDM$ cosmology just assumes a cosmological constant.

A rose by any other name... This all leads me back to a question I asked earlier, wouldn't ANY kind of energy density proprotional to a changing volume of space have to be defined as a zero point energy?

 

[SpaceTiger]

A rose by any other name... This all leads me back to a question I asked earlier, wouldn't ANY kind of energy density proprotional to a changing volume of space have to be defined as a zero point energy?

Well, no, since a scalar field has kinetic energy (meaning that w isn't exactly -1, even when it's slowly rolling) and can decay. The inflaton field is associated with a specific spin-0 particle (the inflaton), while the zero-point energy is an intrinsic property of space derived from all QFTs in a particular GUT.

 

[Mike2]

Well, no, since a scalar field has kinetic energy (meaning that w isn't exactly -1, even when it's slowly rolling) and can decay. The inflaton field is associated with a specific spin-0 particle (the inflaton), while the zero-point energy is an intrinsic property of space derived from all QFTs in a particular GUT.

I guess asked differently, if there were an energy density that was an "intrinsic property" of space, then wouldn't that be a zero pont energy - zero point in the since that it is the lowest density possible for space? I'm using "zero point energy" differently than that used in quantum mechanics, but it would still be zero point in that it is the lowest possible. I'm trying to mark a distinction between a zero point energy density calculated by QFT and a zero point energy density used separately, say in Einstein's cosmological constant. I'm suggesting that perhaps we have confirmed a zero point energy density independent from QFT calculations. We would then have to discover the quntum field responsible for this observed ZPE. Perhaps it awaits a quantum gravity theory in order to calculate it.

 

[SpaceTiger]

I guess asked differently, if there were an energy density that was an "intrinsic property" of space, then wouldn't that be a zero pont energy - zero point in the since that it is the lowest density possible for space? I'm using "zero point energy" differently than that used in quantum mechanics, but it would still be zero point in that it is the lowest possible. I'm trying to mark a distinction between a zero point energy density calculated by QFT and a zero point energy density used separately, say in Einstein's cosmological constant. I'm suggesting that perhaps we have confirmed a zero point energy density independent from QFT calculations. We would then have to discover the quntum field responsible for this observed ZPE. Perhaps it awaits a quantum gravity theory in order to calculate it.

You can include a non-zero cosmological constant into a theory of gravity without a QFT-related ZPE, but this has nothing to do with inflation.

 

[Mike2]

You can include a non-zero cosmological constant into a theory of gravity without a QFT-related ZPE, but this has nothing to do with inflation.

I'm under the impression that inflation does not obey GR but is something entirely different, probably having more to do with quantum gravity. Is this correct?

 

[SpaceTiger]

I'm under the impression that inflation does not obey GR but is something entirely different, probably having more to do with quantum gravity. Is this correct?

I don't think anyone could say at this point, though AFAIK, most theories of inflation work with general relativity.

 

[Mike2]

You can include a non-zero cosmological constant into a theory of gravity without a QFT-related ZPE, but this has nothing to do with inflation.

I'm not so sure. I'm reading Scott Dodelson's book Modern Cosmology about Inflation, section 6.3.3.

He assumes a scalar quantum field for the mechaism of inflation (Not the Higss field); he calculates the energy-momentum tensor, then proves that the expansion pressure can be negative if the potential energy is creater than the kinetic energy of the field. He's using the same relation between pressure and energy density as is used for a cosmological constant of today. And he is calling that potential a vacuum energy - a "false" vacuum energy.

I don't see where he is making any essential difference between cosmological constant, QFT, and Einsteins' Field Equation when he uses them before and after Inflation. I think the only difference is that he is not using the QFT of the Standard Model. But I think it is assumed that this scalar quantum field of Inflation breaks down to become the SM after Inflation.

So it seems to me that the cosmological constant is being just as much associated with a vacuum energy of a quantum field both before and after inflation. If so, then the question remains if the vacuum energy was much greater during inflation, does that mean that h-bar was greater during inflation? Or is h-bar only relevant to particle properties which may not have existed during Inflation when space was still tightly curved?

 

[SpaceTiger]

I don't see where he is making any essential difference between cosmological constant, QFT, and Einsteins' Field Equation when he uses them before and after Inflation. I think the only difference is that he is not using the QFT of the Standard Model. But I think it is assumed that this scalar quantum field of Inflation breaks down to become the SM after Inflation.

But this is precisely why a false vacuum energy and a zero-point energy are not the same thing. A false vacuum energy is not the true zero point -- it is due to a scalar field that has kinetic energy and can decay. The difference between this and the cosmological constant is that the energy density is not constant. It is approximately constant throughout most of inflation, so during this time, the behavior of the universe will be nearly identical to that under a pure cosmological constant.

If the current acceleration were due to a false vacuum state (still a possibility), then we would expect it too to eventually decay, in contrast to the standard $\Lambda CDM$ model. As I said before, the cosmological constant can be due to a non-zero ZPE (the true vacuum state), or it could simply be an extra integration constant in GR. Since GR still obeys the equivalence principle with the inclusion of the cosmological constant, it's just as good a theory of gravity as one with zero CC. This latter possibility is what I was referring to in the post you quoted and it really has nothing to do with inflation.

 

[Sariaht]

So since it decay, it is constant, ie. if vacuum has energy, it is constant since the original state 1 of the universe, is derived from its original properties k1, k2, k3...

If these properties of something that did not yet exist, were true for that which the universe was defined as being that which does not exist, the decay of that which does exist will cause the original properties. Hence cc.

Is there something I'm missing. SpaceTiger, what are the actual facts in the matter?

 

[SpaceTiger]

Is there something I'm missing. SpaceTiger, what are the actual facts in the matter?

I'm sorry, Sariaht, I don't know what you're trying to say. I suggest studying up on GR a bit...Gokul's link https://www.physicsforums.com/showthread.php?p=1169553#post1169553" wouldn't be a bad place to start.

 

[Mike2]

But this is precisely why a false vacuum energy and a zero-point energy are not the same thing. A false vacuum energy is not the true zero point -- it is due to a scalar field that has kinetic energy and can decay. The difference between this and the cosmological constant is that the energy density is not constant. It is approximately constant throughout most of inflation, so during this time, the behavior of the universe will be nearly identical to that under a pure cosmological constant.

If the current acceleration were due to a false vacuum state (still a possibility), then we would expect it too to eventually decay, in contrast to the standard $\Lambda CDM$ model. As I said before, the cosmological constant can be due to a non-zero ZPE (the true vacuum state), or it could simply be an extra integration constant in GR. Since GR still obeys the equivalence principle with the inclusion of the cosmological constant, it's just as good a theory of gravity as one with zero CC. This latter possibility is what I was referring to in the post you quoted and it really has nothing to do with inflation.

Actually, I'm not sure that whether the vacuum energy is the zero point of a quantum field or not is relevant to the question. I think all that is relevant is what is the vacuum energy at a particular time. Isn't the vacuum energy (whether false, true, or whatever) equivalent to the average energy density that exists for a given amount of time? Doesn't the vacuum energy define the amount of uncertainty in Heisenberg's uncertainty principle? If so, then doesn't a higher vacuum energy mean that h-bar was higher than otherwise? Thanks.

 

[SpaceTiger]

Actually, I'm not sure that whether the vacuum energy is the zero point of a quantum field or not is relevant to the question.

I wasn't responding to your question, I was responding to the passage I quoted.

I think all that is relevant is what is the vacuum energy at a particular time. Isn't the vacuum energy (whether false, true, or whatever) equivalent to the average energy density that exists for a given amount of time? Doesn't the vacuum energy define the amount of uncertainty in Heisenberg's uncertainty principle? If so, then doesn't a higher vacuum energy mean that h-bar was higher than otherwise?

It's not clear to me what that would mean, since h-bar has units. We generally only consider the time-variation of unitless quantities, like the fine structure constant.

 

[Mike2]

It's not clear to me what that would mean, since h-bar has units. We generally only consider the time-variation of unitless quantities, like the fine structure constant.

We 'are talking about the priod of Inflation before the Standard Model was in effect, right? So I suppose anything's possible there, including a different speed of light, etc.