# Dark Energy an effect of inhomogeneity?

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1. Oct 3, 2014

### CKH

This new paper Local Large-Scale Structure and the Assumption of Homogeneity claims that a combined analysis of several surveys indicates that there is a substantial local under-density in the universe on the order of 800 MPC in size.

Previous work done by other authors suggests that an
inhomogeneity of this order is sufficient to account for what has been interpreted as Dark Energy.

The authors also suggest that the local under-density may account for the mismatch between the local measurements of the Hubble constant and that inferred from the Planck CMB data.

2. Oct 3, 2014

### marcus

It's strange your Keenan et al paper (2014) does not mention David Wiltshire's papers of some half dozen years back. Like this:
http://arxiv.org/abs/0712.3984

As I recall he argued persistently for several years that the effect of a positive cosmological constant could be mimicked by our simply being in the middle of an underdense region, by inhomogeneity in other words. Or some such thing. I may have it wrong but it had to do with attributing accelerated expansion to inhomogeneity.

He's a NewZealander cosmologist, at U. Canterbury I think. certainly reputable. but couldn't convince people and the idea never caught on.

Last edited: Oct 3, 2014
3. Oct 3, 2014

### bapowell

I remember back in 2005 when Kolb et al. came out with their paper claiming that accelerated expansion could be due to the backreaction of long-wavelength perturbations (http://arxiv.org/pdf/astro-ph/0506534.pdf). But I also remember a slew of critical papers following on its heals (see http://arxiv.org/pdf/astro-ph/0506449.pdf). Clearly I've not been following this idea closely...is it still viable?

4. Oct 3, 2014

### marcus

I can't tell you, Brian. You know a lot more about this than I do in any case.

Some more recent Wiltshire papers. This seems to me to be a very thorough and accessible explanation of his ideas:
http://arxiv.org/pdf/1311.3787v1.pdf
and it refers to observational findings described here:
http://arxiv.org/abs/1201.5371

CKH, I can't pretend to being very interested in this alternative approach, or having more than very superficial understanding of it. I just contribute the links because your Keenan et al article did not cite Wiltshire. And his work seems relevant to the topic.

My attitude is that Lambda is a curvature constant which belongs in the Einstein equation because it is allowed by the symmetry of the theory.

$$\Large \bar F ={ c^4 \over 8\pi G}$$
$$\Large G_{\mu \nu} + \Lambda g_{\mu \nu} = {1\over \bar F} T_{\mu \nu}$$
The symmetry allows for two constants: a force (measured in newtons) and a curvature (measured in inverse area units m-2)
so when the equation is written it should include those two constants, one cannot a priori assume that one of them is zero.

But Lambda, the curvature constant MIGHT be zero. AFAICS there is no reason for it to be, but for many years many people thought it was, and now they think it is
Λ = 1.12 x 10-52 m-2

They could be wrong of course, but I think it is just as likely a priori to be that as to be zero. This does not involve any mysterious "energy". It is just a constant curvature that occurs in an equation.

The force constant that appears in the equation has a pretty well-established value which you can get, in newtons, if you paste this into google:
c^4/(8pi G) and press return. Google will activate its calculator and say
(c^4) / (8 * pi * G) = 4.8157858 × 1042 newtons
Instead of Fbar let's call that force something else. Let's call that force F
It governs the interaction of matter with geometry because it tells how much matter energy density it takes to produce a certain curvature. You multiply the curvature by F and you get an energy density in joules per cubic meter, or equivalently in pascals, newtons per square meter.
By our standards geometry is STIFF because it takes a big energy density to produce what is by our standards a small curvature. So
F is the stiffness of geometry, and it is a large force, by our human standards.

For example, Lambda is a small curvature. In Google code it is 1.12*10^-52 m^-2 so why not multiply it by
F and see how much energy density would be needed if (hypothetically) that curvature were not just an intrinsic built in feature of geometry but were caused by some imagined energy. So we can paste in this:
(c^4/(8pi G))*1.12*10^-52 m^-2
Google calculator will say 5.39368009 × 10-10 pascals
That is 0.539 nanojoules per cubic meter

That is what the pretended "dark energy" density is. It is just a way of talking about a certain intrinsic curvature which cosmologists tend to assume is constant throughout all space for all time.
That's my attitude and you see it contrasts with Wiltshire and with your Keenan et al paper. they seem to think that having a small inherent constant curvature is wrong and needs to be explained away. I'd recommend just accepting it. (and don't call it an "energy")

Last edited: Oct 3, 2014
5. Oct 3, 2014

### CKH

marcus,
It's not my paper;). I didn't look carefully at the references. The paper makes no claim about originating the idea that an under-density could explain DE. As you say, that idea has been around for some time. The paper only claims to find an under-density (by combining some surveys) of a magnitude that other authors have asserted is adequate to explain DE.

The idealized expanding universe is smooth (dust model) but the real universe isn't, so the uneven distribution of matter on large scales may affect our interpretation of observations. The under-density claimed is substantial. The paper claims that beyond the under-density, the density is 1.5 times as great as locally.

bapowell,
I don't know whether there is any current consensus about the magnitude of inhomogeneity required for such an effect, but some effect could exist. Apparently the GR analysis is difficult. There are more recent papers than those you cited. I don't have links offhand.

This is interesting stuff. Of course it will be challenged and it may well prove wrong. There's a Nobel prize that might be tarnished and hundreds of papers discussing the theory of DE that could end up as rubbish. There is even the L in LCDM at risk. I wonder if the under-density itself challenges any existing LCDM predictions.

I'll be watching for responses. Some fur may fly or possibly the paper will be quickly discredited in some way and dismissed.

Maybe the Large Synoptic Survey will help confirm or deny this under-density, but that's years away. There is also some extended survey of SN 1a planned, but I don't recall the details of that project.

Disproof of DE would not be a negative for cosmology IMO.

6. Oct 3, 2014

### CKH

marcus,
I find it odd that you are glib about whether this "slight curvature" exists or not. It was a rather unexpected find, even yielding a Nobel prize. The discovery of DE has since provoked much theoretical work, observation and debate. If the energy is just some unimportant consequence of a slight curvature, then the claim that 75% of the universe is made of this stuff and that the destiny of the universe is at stake are trivialized. Why do cosmologist bother puzzling over this finding? How is inflation theory affected by DE since inflation is supposed to tell us that the universe is extremely flat (maybe not that flat)?

Citing nanojoules per cubic meter can be used in a pretence of triviality, but it exceeds by three times the remainder of the universe of which 80% is also as yet a mystery. If energy is stuff than can just appear out of equations, why not matter and radiation? Perhaps we could have some real fun with that.

IMO this does matter. We may question whether a cosmological constant has any reality, which in the past was denied (by its very inventor) only to be re-invoked by others when an apparent need arose. Shouldn't cosmology concern itself with reality rather than theoretical games that toy with parameters?