The specifications of a positive cosmological constant parameter is the method used to account for the apparent acceleration of universal expansion in the LCDM 'concordance' cosmological model, but it is not the only potential cause of this phenomena: please see http://arxiv.org/abs/1109.2314. The acceleration of expansion corresponds to the development of 'large scale' structure in the universe... I would think that one should carefully consider reinterpreting what might be considered founding principals in order to accommodate a cosmological constant representing yet unknown physics.

No. The universe is infinite.

Yes, adding arbitrary additional constants to try to make the theory fit the data (instead of looking for possible physical mechanisms that might produce the observed effect) is, IMO, not a sign of good theory. It can be useful as a short-term measure to allow modelling, but the danger is that once one of these arbitrary constants gets established and named, it starts to be seen as a legitimate part of the landscape, rather than as a short-term "band-aid".

At least //Einstein's// Cosmological Constant had //some// sort of theoretical reasoning behind it - it was quite fudgey, but at least he was using it to try to produce a fixed, principle-based outcome, and his Constant had a non-negotiable value derived from other parts of the equations. Einstein's CC and the concept behind it was was wrong, but at least it was honorably wrong, in that his associated result was amenable to testing and to scientific falsification (which then happened, a few short years later with Hubble shift). If the modern counterpart has no obvious theoretical basis at all and its value is set by hand to agree with whatever data we've collected, then it's not really part of a scientifically falsifiable theory, because if the available data changes, we can just change the value to suit, on a whim.

At that point, the system arguably becomes less of a theory and more of an arbitrary parametric modelling exercise (IMO). Modelling is legitimate and useful, but I still like old-fashioned scientifically-disprovable theories that generate actual testable predictions. :)

If the universe is the existing, including the observers, then it is closed by definition. If the universe is what is actually observed, then we cannot say. If the universe is really born some time ago, then it can hardly be considered a closed system. If the universe is a multiverse, it is open. You see, it all depends on global boundary conditions. The only known case of a closed universe is the spatially compact case, but then Conservation laws are identities, as Landau Lifshitz observed, and so again it looks closed by definition, as nothing can escape.

Luciano,

It seems to me that if the universe includes all that can be detected, it may be considered as an open system. However, if the universe has physically determinable boundaries it most likely must be considered as a closed system... As I understand, there is yet no evidence of any physical boundaries to 'our' universe.

Dear Luciano,

Thank you very much for your well-argued response.

However I have the following questions to you:

1. When it is said that conservation laws are identities what does that mean exactly?

2. Why did Landau–Lifshitz assert that, if so, "the gravitational field cannot itself be included in a closed system"?

3. Can you argue why you say that our universe can hardly be considered a closed system if:

a) it was born some time ago? (e.g., it could have been born from quantic vacuum fluctuations)

b) it belongs to a multiverse? (i.e., it is usually assumed that the universes would have no connection between them in a multiverse)

4. By "spatially compact" universe do you mean a closed manifold (i.e. compact without boundary) universe?

5. You say nothing about the cosmological constant and the fact that with a positive cosmological constant heat death scenario can also occur in a closed universe: what do you think about it?

James,

the conventional meaning of "closed system" in physics is one that cannot exchange energy, momentum, charge, information of any sort, etc.., with something "external", so I do not understand your use of the term "open". Even in the presence of boundaries, these can exchange energy with the bulk interior, so it all depends on whether you are willing to include or not the boundaries as part of the system. This sort of ambiguities are always present in cosmology, which study the universe without knowing precisely how to define it scientifically (if it is possible at all!)

Gravitation is a univironmental interaction between microcosm and macrocosm—one of the reasons the universe must be infinite. It would be impossible without a macrocosm:

Borchardt, Glenn, and Puetz, Stephen J. , 2012, Neomechanical gravitation theory ( http://www.worldsci.org/pdf/abstracts/abstracts_6529.pdf ), in Volk, G., Proceedings of the Natural Philosophy Alliance, 19th Conference of the NPA, 25-28 July: Albuquerque, NM, Natural Philosophy Alliance, Mt. Airy, MD, v. 9, p. 53-58.

Marc,

wow! so many questions for me. Let me try point after point. (1) this question is related to the covariance of the field equation. It means that what we call "conservation laws" in gen relativity are valid whether or not the field equations are satisfied, they are identities indeed. As a result, one can define only global quantities (for example the total energy) as surface integrals at infinity. For this reason a closed universe must have all conserved charges equal to zero. Also, there are infinitely many of them, so probably you cannot specify a closed system in the statistical mechanical sense.

(2) I really don't know about the thinking of Landau, but i think statistical physics needs external parameters to make sense, so if you include gravitation the conserved quantities become fixed at infinity (for reasons given above) and cannot be varied. The alternative, an ensemble of universes doesn't make much sense to me.

(3) I had in mind that in the case (a), before the born out event one cannot say there was nothing, because since that event happened (perhaps) there was at least the possibility of it happening. I am not sure that quantum fluctuations should be included in forming a closed system. (b) it is true that if the multiverse is as you described, there is no point. But what interest cosmologists is whether or not they have interacted in the past. You probably know about the bizarre theory that the cold spot in the cmv spectrum was an event like this, a bifurcation of two universes....

(4) yes, (5) the cosmological constant cannot change the role of conservation laws in GR, which are due to general covariance. I agree the heat death scenario can occur, but i think it will not occur, since there are on the market some mechanisms to make Lambda decay. Perhaps we collide with some other inflating region, who knows? The universe is a strange place, to quote Wilczek.

Luciano,

Thanks again for your well-argued answers.

About gravity what do you think of the hypothesis that laws of gravity are not fundamental but that they emerge as an entropic force?

Actually, according to, for example, Erick Verlinde "if the gravity and space time can indeed be explained as emergent phenomena, this should have important implications for many areas in which gravity plays a central role. It would be especially interesting to investigate the consequences for cosmology. For instance, the way redshifts arise from entropy gradients could lead to many new insights" (Verlinde, 2010: see attached file).

Luciano,

My apologies for my confused response. I intended the term 'open' to be synonymous with 'not closed' - but you're right I'd momentarily confused a closed universe with one that was confined within a 'multiverse'. Like Marc, I was confused by your statements, especially "... If the universe is what is actually observed, then we cannot say. If the universe is really born some time ago, then it can hardly be considered a closed system..." Marc's response far more clearly expressed my concerns - especially that you did not seem to address the question regarding the cosmological constant. Thanks for your response to Marc's excellent questions!

Marc,

I think it may be most instructive to consider that the accretion of massive objects is initiated not by gravitation but by EM charge attraction. As accretion condenses material mass-energy, it also necessarily _extracts_ mass-energy from the vacuum. It may be only at this point that gravitation emerges as the interaction between the residual kinetic energy of the now contracted vacuum (which physically corresponds to the dimensional coordinates of spacetime) and the potential mass-energy of massive objects...

As can be seen clearly in my review paper "From clock synchronization to dark matter as a relativistic inertial effect" (arXiv 1205.2481) in standard Einstein general relativity

one has to make a choice of some family of spacetimes when trying to solve Einstein's equations. One possibility (the one producing the theory of gravitational waves after linearization) are spacetimes asymptotically Minkowskian at spatial infinity (with a conformal transformation they could be transformed in spatially compact spacetimes with boundary; instead loop quantum gravity uses spacetimes spatially compact without boundary). In these spacetimes at spatial infinity there is the SPI Group of Ashtekar asymptotic symmetries: the generators are constants defined by the coiche of boundary conditions for the metric tensor. Since there is no trace of super-translations

in astrophysical interpretations of the astronomical data, one restricts oneself to the special family of asymptotically Minkowskian, globally hyperbolic spacetimes: in them the SPI Group is reduced to the asymptotic ADM Poincare' Group. The ten ADM Poincare' generators are determined by the boundary conditions (in particular the two ADM Casimirs define spacetimes with fixed total mass and total spin) and in the limit in which one turns off Newton constant they become the Poincare' generators of the standard model of elementary particles. In these spacetimes there are asymptotic inertial observers whose axes are identified by the fixed stars of star catalogues. In my paper arXiv 1202.4667 there is a discussion of the relativistic microcanonical ensemble, the only well defined one in presence of the gravitational long range forces. This description fits with classical astrophysics after the recombination surface. Before one has quantum cosmology and no accepted explaination of the transition from quantum to classical physics.

Dear Lucia,

Thank you for your intervention.

However don't you realize that your speech is so technical and specialized that it is totally incomprehensible to non experts such as myself?

Could I ask you to adopt, if possible, Luciano's kind of speech which is as clear as possible and not too technical?

That the cosmological constant is non-zero doesn't have anything to do with conserved qantities in general relatvity, as such. The reason is that the cosmological constant is a term that is consistent with all symmetries of the Einstein-Hilbert action, as deduced from Noether's theorem (which requires imposing appropriate boundary conditions for it to make sense at all, of course). Imposing boundary conditions, indeed, ``closes'' the system, if it leads to solutions of Einstein's equations, coupled to matter. So then the question is, what kind of boundary conditions lead to solutions of Einstein's equations that have certain properties, that are mathematically useful and physically interesting. There do exist

boundary conditions with zero cosmological constant, as well as boundary conditions with non-zero cosmological constant, that lead to interesting solutions.

The energy-momentum tensor isn't a ``pseudo-tensor'', by the way.

Dear Stam,

Thanks very much for your clear clarification of the question.

If you don't mind looking in Erik Verlinde's paper "On the Origin of Gravity

and the Laws of Newton" I would be very happy to have your comments on it and thus on the hypothesis that laws of gravity are not fundamental but emerge as an entropic force (see attached file).

I have read Verlinde's paper-but it doesn't have anything to do with the subject under discussion here. Whether or not gravity is an ``emergent entropic force'' or not, doesn't bear on conserved quantities in classical gravity and the cosmological constant. And it seems that it is not obvious just what meaning can be given to the term ``entropic force''.

Stam,

You are right to say that there is no straightforward relation between my question about whether our universe is closed or not and 2010 Verlinde's paper.

However as Erik Verlinde says in his 2010 paper "If the gravity and space time can indeed be explained as emergent phenomena, this should have important implications for many areas in which gravity plays a central role. It would be especially interesting to investigate the consequences for cosmology".

So, you dispute the term "entropic force", even in the example of the elasticity of a polymer molecule?

For polymers ``entropic force'' has a well-defined meaning. For gravity it seems difficult to assign it such a meaning. And that's why, despite a lot of work, following Verlinde, the results don't seem to provide the insights hoped for. So what exactly might be meant by ``emergence'' in this context is not clear. And, once more, it doesn't shed any light into the Einstein-Hilbert action and its boundary conditions.

Ok, Stam. Thank you for your responses.