Dark energy from the cosmic boundary

Question

So as I understand it, the Einstein-Hilbert action basically just says that, in the absence of matter, the spacetime manifold will try to minimize its total curvature.  Which is super elegant and intuitive; it seems to say spacetime is "stretched tight", like the minimal surface formed by a drum head or soap film, with the caveat that it is curvature rather than area that is minimized (not sure if there's a more fitting analogy...).
And when we derive the corresponding field equation, we get $R_{munu} = 0$.  But we know that the vacuum Ricci tensor is not zero, according to dark energy, although it is the next best thing: isotropic and homogeneous, at least regionally.
But if the cosmos has certain boundary conditions, then even when the manifold is minimized, its curvature will not disappear completely, just like the soap film.  But it will tend to eliminate local distortions.  So this could explain the very smooth curvature we see in the vacuum, i.e. dark energy.  In other words, when the global EH action is constrained by the boundary, it no longer implies Ricci-flatness.
Now, the most natural candidate for the "boundary" of the cosmos is its singularities: the big bang, and black holes.  So it's like the soap film is anchored only at a discrete set of points.  Though of course there could be other kinds of boundaries we haven't seen yet.
Right away I have a conceptual hang-up, which is that, even to speak of boundary conditions, it seems like we would need an outer embedding space, so that we could fix the relative configuration of the boundary points in that outer space.  Which could be fine, but perhaps it's not ideal.  So one question is whether cosmic singularities, considered as an intrinsic boundary, could give rise to our universe under the EH action.
But mostly I'm just hoping anyone can weigh in on this general idea.  And here's the great news: it has already been studied in exquisite detail, in this paper.  But the math they employ is over my head, so I'm not positive it's exactly the same idea, though it appears to be.  In particular, they use an action that has extra terms, and a connection with torsion, although from the description I get the impression those are merely mathematical tricks in order to solve the field equations, and at the end of the day they are proposing nothing more than the EH action.  Furthermore, they make no mention of embedding, which would appear to affirm the validity of the "discrete intrinsic boundary".  But again, I can't follow it well enough to be sure.  Finally, from statistical black hole data, they derive a value for $Lambda$ that is allegedly very consistent with the observed value.
So any input on any of the above would be most welcome, and thanks for reading this far.

Cham · Accepted Answer

This idea was explored by several authors, in different ways.  I aven't read the paper you cited, but have read some other papers wich exposes a simpler view (I believe T. Padmanabhan wrote something about this).
So consider an observer $mathcal{O}$ doing all of its measures at cosmic time $t_0$ ("today").  There's a cosmic horizon around him, and he doesn't have access to the future right now.  His observations give him informations about the past only, "down" to the Big Bang event.  So he only have access to a finite portion of the whole of spacetime.  We could state that any reasonable physical action wrote by an observer should reflect his lack of information, a bit like what we do with entropy in statistical mechanics to get the macroscopic density of states (the Grand-canonical ensemble, for example).
So the observer $mathcal{O}$ introduces a Lagrange multiplier $Lambda/kappa sim mathrm{L}^{-4}$ to impose a constraint on the hypervolume of spacetime that the observer have access to:
begin{align}tag{1}
S_{mathcal{O}} &= frac{1}{2 kappa} int_{mathcal{M}_{mathcal{O}}} R , sqrt{-g} : d^4 x - frac{Lambda}{kappa} int_{mathcal{M}_{mathcal{O}}} sqrt{-g} : d^4 x + text{matter terms} [1ex]
&equiv frac{1}{2 kappa} int_{mathcal{M}_{mathcal{O}}} (R - 2 Lambda) , sqrt{-g} : d^4 x + text{matter terms}, tag{2}
end{align}
where $mathcal{M}_{mathcal{O}}$ is the finite part of spacetime that the observer could have access to.
Then the cosmological constant could be interpreted as the Lagrange multiplier that is associated to a finite spacetime hypervolume constraint.  This hypervolume would be defined by all times from the Big Bang up to the present cosmic time $t_0$ (i.e time of presence of a local observer), and all spatial points inside the observer's horizon.  So the second integral of (1) stays finite.
This interpretation implies a subtle connection between the action functionnal and a kind of "cosmic entropy", as a measure of the lack of information about the state of the whole universe.
According to this idea, we could say that the cosmological constant has its origin from the spacetime boundaries implied by the presence of an observer, which necessarily have only limited access to the whole of spacetime.
I'm not sure all this idea is actually sound.  The action is then implicitely subjective, and the "constant" $Lambda$ may depend implicitely on the observer's time $t_0$, which is weird! (it may be related to the anthropic principle in some way).  I find the "topological" origin of $Lambda$ very interesting, though.

Dark energy from the cosmic boundary

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