"A cloud is made of billows upon billows upon billows that look like clouds. As you come closer to a cloud you don't get something smooth, but irregularities at a smaller scale." -

Benoit Mandelbrot

It isn't just the clouds that appear smooth, but aren't if you zoom in close. In fact, it isn't just the mathematical curiosity known as the Mandelbrot set that's full of irregularities and ever increasing complexity as you zoom in.

**the entire Universe itself**has these properties.

"Excuse me," you might say. "My Universe is certainly *not* smooth."

And of course, you'd be right. All you have to do is look into your own backyard.

Because a cubic meter of Earth weighs a bit more than a couple of **tonnes**. But a cubic meter *off* of the Earth? A cubic meter of interplanetary space? Well, that weighs practically nothing!

In other words, when we talk about *smoothness* of the Universe, we're talking about how different one place is from another in terms of "amount of stuff," or density. We call this property homogeneity, or "sameness" in different locations.

Our Solar System is incredibly *in*homogeneous, in fact. The densest places have something like 10^{30} times as much stuff as the least dense places. But when we talk about the Universe as a whole, we need to look at scales significantly larger than just our paltry Solar System.

In fact, you might imagine that if you look on much larger scales, maybe the Universe is significantly smoother. Rather than look at Solar System-sizes, maybe we need to look at galactic scales?

And it turns out that, on these scales (a million light years or so), the Universe is still very *in*homogeneous. If you took a bubble a million light years in diameter and put it around a very dense region (like a large galaxy), and compared it with an identical bubble placed around the emptiness of intergalactic space, the densities you'd find would indeed be very different.

But they're *only* different by about a factor of a million. Yeah, that's right. **Only a million.** When you consider that looking at an Earth-sized bubble gave a factor of **10 ^{30}** difference, a million (10

^{6}) doesn't seem so big, does it?

So what if we start looking at *very, very large* scales?

Above is a map of galaxies, on the scale of about a ** billion** light years. Once you start looking on scales this large, one region of space doesn't appear much different than another. In fact, on scales this size,

*every*region of the Universe has roughly the same density. Take a look at how much the above image resembles this generic simulation of structure in the Universe.

At this level, you can put a bubble a billion light years in diameter around the *densest* spot in our Universe and one around the *least dense* spot in our Universe, and the two regions will differ by **less than 0.1%**.

On the largest scales observable, our theory predicts that one region will differ from another by just a few parts in **100,000**, consistent with the minuscule fluctuations we observe in the Cosmic Microwave Background.

In fact, because we understand the physics of how structure forms, we can look at a region of space, count the galaxies in that space, and (so long as we properly account for bias) test just how homogeneous our Universe is. Whether or not our predictions match up with theory gives us yet another cross-check of both our standard cosmological model,

as well as a test of the theory of gravity upon which we base our model: General Relativity.

Recently, a scientific finding has been gaining a bit of buzz, as well it should when an observation doesn't quite match what we predict. One of the best types of indicators we've been using for our observations of large-scale structure are known as Luminous Red Galaxies, which are bright, abundant, and easily identifiable.

But something may be amiss with these LRGs. Shawn Thomas and his colleagues have found structures in the Universe stretching over *three billion light years*, containing an overabundance of LRGs from what our theory predicts! In other words, from looking at these LRGs, the Universe, on these very large scales, is *less* smooth than we expect! Previous studies -- for instance, with the Sloan Digital Sky Survey -- had seen observations in line with predictions, but there are a number of interesting possibilities for what these structures mean.

We *could* be looking, specifically, at a region of particularly sharp density contrast. It's statistically unlikely, but certainly plausible.

We could also be seeing an effect of bias; perhaps we do not correctly understand how Luminous Red Galaxies form given the overall concentration of matter.

Finally, there could be a contamination of the sample by nearby red stars, leading many galaxies that are luminous but *not* red to be mis-identified as LRGs.

I greatly prefer any of these to any of New Scientist's wild speculations, but the upcoming SDSS data release should actually decide the issue.

It's always amazingly interesting when an observation in the Universe surprises us, and while it's *almost* always an anomalous effect that is capable of being explained by what is currently known, every once in a while nature surprises us, and gives us the opportunity to learn something new about the way the Universe works! (A very interesting critique of this paper and its interpretations were recently put forth by Peter Coles, which is worth reading for those of you interested in further details.)

Is this anomaly that we're seeing now merely something that will be easily explained away, or are we on the precipice of finding a hole in something as major as our understanding of gravity? Fortunately, we should know the answer in just a few months; stay tuned. In the meantime, enjoy thinking about the possibilities!

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Does it make any sense to suppose that these galaxies have been captured by a line singularity ("cosmic filament")?

In the first estimate of inhomogeneity, was dark matter included?

I'll have to reread and follow your links.

This is a topic is one that very much interests me.

As for your comment, "Fortunately, we should know the answer in just a few months." I'm a bit more patient than that. Who knows what conflicting evidence may arise.

But I await your upcoming soon blog; but first I must prepare myself by following your links. And trying to understand (beyond my current limited understanding) what is at issue and what are the issue. And then maybe I'll come back here and ask a few questions.

Thanks for this interesting update.

Wish I was blessed with the mathematical mind. Love the blog. Keep going, you're doing much good for the world.

Very interesting post, yet suprisingly few comments. The question of homogeneity and isotropy of Universe has always bugged me in terms of why do physicist insist on it so much.

You take a look at cosmology 101 or astrophysics 101, and more likely than not, one of the first statements you'll hear is "Universe is homogeneous and isotropic". I understand that this is one of the pillars of standard cosmological model, but it looks to me that this is perhaps more of philosophical need than the actual state of universe. I will try to explain why i thik so.

If we take a look at some small pond or a lake... doesn't really matter. Is it homogeneous and isotropic? Well... yes and no. If we look at it from "outside" and far enough away, then yes. But this is a biased view, is it not? If we apply it to the whole world around us, we can very well say that everything and anything we observe is homogeneous and isotropic.. as long as we are far enough away. Be it a cup of coffe or a wall or a plank of wood. Everything is smooth.

If you look at the 1 square meter patch of grass and and a patch of cloth, both green, from i.e. 500m you can argue they are same. Yet we know that if we move closer, they are everything but.

We see structures everywhere around us. Even at the smallest scales. What is string theory, if not theory about structures? So why do physicists shun so much about structures on large scale. To me it only seems logical and natural for the Universe to be one big structure. As long as the metric of spacetime is not significantly disturbed, everything is OK with the standard model. And we do see structures on large scales. We do see filaments. And who knows what else waits to be observed?

I love how Peter Cole explained this: "On small scales galaxies whizz around at speeds of hundreds of kilometres per second relative to each other, but averaged over larger and larger volumes the bulk flow should get smaller and smaller, eventually coming to zero in a frame in which the Universe is exactly homogeneous and isotropic." I can't help but think of this as Absolute Zero in temperature. Can we really reach 0' Kelvin? I think not. It will always be some miniscule percentage of temperature. And I think quantum physics shows this. Same with universe. Can we really talk about absulutelly zero speed? Again, I think not. I mean, yes we can, we can imagine it. But the universe we observe now and whenever will never be mathematical 0. In other words we can never observe the universe so far away as for it to be homogeneous and same everywhere. We would have to be faaaaaar away, OUTSIDE of the universe, to make such claims. And that's just silly.

So again, I don't understand why we want to convince ourselves into something which is counter intuitive. For all our purposes and needs, the universe isn't homogeneous and for isotropy...(looks the same...) that's biased from the start :D. Looks to whom? How can you possibly argue and prove that someone 30 billion L.Y. from us sees more or less the same thing?? And why is it even important? :)

Hi Ethan,

I would like to know whether the diameter of the "3D-broad-brush" (better "-sphere"), which seems to determine galaxy-locations, couldn't be the result of limited range of gravity?

Especially, because everywhere in the universe this "3D-brush"-width does not vary much in fine filaments, but voids do have very variant extents. There seems to exist a maximum distance between gravitationally bound galaxies related to their outer regional stars, mutually.

3D-honeycomb similar structures with no specific "void"-sizes are the result and their ridges can have a large variety of wideness.

With this we cannot reach perfect smoothness, because at any scale there could be somewhere a void, which is bigger...

What do you think about such a hypothesis?

Ama sadece bir milyon yaklaÅÄ±k bir faktÃ¶r farklÄ± konum. Yeah, that's right. Only a million. When you consider that looking at an Earth-sized bubble gave a factor of 10 30 difference, a million (10 6 ) doesn't seem so big, does it? Evet, bu doÄru Sadece bir milyon DÃ¼nya bÃ¼yÃ¼klÃ¼ÄÃ¼nde bir baloncuk bakarak 10 30 farkÄ± bir faktÃ¶r verdiÄi gÃ¶z Ã¶nÃ¼ne alÄ±ndÄ±ÄÄ±nda, bir milyon (10 6) Ã§ok bÃ¼yÃ¼k gÃ¶rÃ¼nmÃ¼yor, deÄil mi ?

1Also of note is how the usual contrarian crowd are doing their best to minimize the fallout in the comments.

Let me post a stupid layman's comment:

If 73% of the universe is dark matter (not that we seem to know what that is) and 23% of the universe is dark energy (not that we know what that is either) it seems quite difficult to make any really intelligent guesses about the universe when we can only observe 4% of it. It's surely not that we are not learning stuff, but we seem to be learning about 4% of what is there. And that's not much.

"not that we seem to know what that is"

a) in what way don't we know?

b) why is that a problem?

c) why the dismissive "if 73% is dark matter" if you don't think you know what it is?

Same with Dark Energy.

"it seems quite difficult to make any really intelligent guesses about the universe when we can only observe 4% of it. "

How much of the spectrum of EM radiation can we observe? .001% Is this a problem?

"but we seem to be learning about 4% of what is there. And that’s not much."

YOU lift it, then. See how little it feels like to you then, eh?