## How Do We Know the Universe is Flat? Discovering the Topology of the Universe

Whenever we talk about the expanding Universe, everyone wants to know how this is going to end. Sure, they say, the fact that most of the galaxies we can see are speeding away from us in all directions is really interesting. Sure, they say, the Big Bang makes sense, in that everything was closer together billions of years ago.

But how does it end? Does this go on forever? Do galaxies eventually slow down, come to a stop, and then hurtle back together in a Big Crunch? Will we get a non-stop cycle of Big Bangs, forever and ever?

We’ve done a bunch of articles on many different aspects of this question, and the current conclusion astronomers have reached is that because the Universe is flat, it’s never going to collapse in on itself and start another Big Bang.

But wait, what does it mean to say that the Universe is “flat”? Why is that important, and how do we even know?

Before we can get started talking about the flatness of the Universe, we need to talk about flatness in general. What does it mean to say that something is flat?

If you’re in a square room and walk around the corners, you’ll return to your starting point having made 4 90-degree turns. You can say that your room is flat. This is Euclidian geometry.

But if you make the same journey on the surface of the Earth. Start at the equator, make a 90-degree turn, walk up to the North Pole, make another 90-degree turn, return to the equator, another 90-degree turn and return to your starting point.

In one situation, you made 4 turns to return to your starting point, in another situation it only took 3. That’s because the topology of the surface you were walking on decided what happens when you take a 90-degree turn.

You can imagine an even more extreme example, where you’re walking around inside a crater, and it takes more than 4 turns to return to your starting point.

Another analogy, of course, is the idea of parallel lines. If you fire off two parallel lines at the North pole, they move away from each other, following the topology of the Earth and then come back together.

Got that? Great.

Now, what about the Universe itself? You can imagine that same analogy. Imaging flying out into space on a rocket for billions of light-years, performing 90-degree maneuvers and returning to your starting point.

You can’t do it in 3, or 5, you need 4, which means that the topology of the Universe is flat. Which is totally intuitive, right? I mean, that would be your assumption.

But astronomers were skeptical and needed to know for certain, and so, they set out to test this assumption.

In order to prove the flatness of the Universe, you would need to travel a long way. And astronomers use the largest possible observation they can make. The Cosmic Microwave Background Radiation, the afterglow of the Big Bang, visible in all directions as a red-shifted, fading moment when the Universe became transparent about 380,000 years after the Big Bang.

When this radiation was released, the entire Universe was approximately 2,700 C. This was the moment when it was cool enough for photons were finally free to roam across the Universe. The expansion of the Universe stretched these photons out over their 13.8 billion year journey, shifting them down into the microwave spectrum, just 2.7 degrees above absolute zero.

With the most sensitive space-based telescopes they have available, astronomers are able to detect tiny variations in the temperature of this background radiation.

And here’s the part that blows my mind every time I think about it. These tiny temperature variations correspond to the largest scale structures of the observable Universe. A region that was a fraction of a degree warmer become a vast galaxy cluster, hundreds of millions of light-years across.

The Cosmic Microwave Background Radiation just gives and gives, and when it comes to figuring out the topology of the Universe, it has the answer we need. If the Universe was curved in any way, these temperature variations would appear distorted compared to the actual size that we see these structures today.

But they’re not. To best of its ability, ESA’s Planck space telescope, can’t detect any distortion at all. The Universe is flat.

Well, that’s not exactly true. According to the best measurements astronomers have ever been able to make, the curvature of the Universe falls within a range of error bars that indicates it’s flat. Future observations by some super Planck telescope could show a slight curvature, but for now, the best measurements out there say… flat.

We say that the Universe is flat, and this means that parallel lines will always remain parallel. 90-degree turns behave as true 90-degree turns, and everything makes sense.

But what are the implications for the entire Universe? What does this tell us?

Unfortunately, the biggest thing is what it doesn’t tell us. We still don’t know if the Universe is finite or infinite. If we could measure its curvature, we could know that we’re in a finite Universe, and get a sense of what its actual true size is, out beyond the observable Universe we can measure.

We know that the volume of the Universe is at least 100 times more than we can observe. At least. If the flatness error bars get brought down, the minimum size of the Universe goes up.

And remember, an infinite Universe is still on the table.

Another thing this does, is that it actually causes a problem for the original Big Bang theory, requiring the development of a theory like inflation.

Since the Universe is flat now, it must have been flat in the past, when the Universe was an incredibly dense singularity. And for it to maintain this level of flatness over 13.8 billion years of expansion, in kind of amazing.

In fact, astronomers estimate that the Universe must have been flat to 1 part within 1×10^57 parts.

Which seems like an insane coincidence. The development of inflation, however, solves this, by expanding the Universe an incomprehensible amount moments after the Big Bang. Pre and post inflation Universes can have vastly different levels of curvature.

In the olden days, cosmologists used to say that the flatness of the Universe had implications for its future. If the Universe was curved where you could complete a full journey with less than 4 turns, that meant it was closed and destined to collapse in on itself.

And it was more than 4 turns, it was open and destined to expand forever.

Well, that doesn’t really matter any more. In 1998, the astronomers discovered dark energy, which is this mysterious force accelerating the expansion of the Universe. Whether the Universe is open, closed or flat, it’s going to keep on expanding. In fact, that expansion is going to accelerate, forever.

I hope this gives you a little more understanding of what cosmologists mean when they say that the Universe is flat. And how do we know it’s flat? Very precise measurements in the Cosmic Microwave Background Radiation.

Is there anything that all pervasive relic of the early Universe can’t do?

## Best-Ever Topographic Map of Earth from NASA and Japan

[/caption]NASA and Japan recently announced a new and improved digital topographic map of Earth, which was produced with detailed measurements from NASA’s Terra spacecraft.

The new data covers over 99 percent of Earth’s landmass and spans from 83 degrees north latitude to 83 degrees south. Each elevation measurement point in the data is only 30 meters apart.

How were scientists able to improve on previous generations of detailed topographic maps?

The new model, known as a global digital elevation model, was created from images collected by the Japanese Advanced Spaceborne Thermal Emission and Reflection Radiometer, or ASTER, instrument aboard NASA’s Terra spacecraft. To create a “stereo pair” image,scientists can take two slightly offset images and combine them to create a three-dimensional effect of depth.

The previous version of the global digital elevation model was released in June of 2009 by NASA and Japan’s Ministry of Economy, Trade and Industry.

“The ASTER global digital elevation model was already the most complete, consistent global topographic map in the world,” said ASTER program scientist Woody Turner, “With these enhancements, its resolution is in many respects comparable to the U.S. data from NASA’s Shuttle Radar Topography Mission, while covering more of the globe.”

The ASTER team added 260,000 stereo-pair images to improve the previous model, which improved spatial resolution, increased horizontal and vertical accuracy, and provided the ability to identify lakes as small as 1 kilometer in diameter.

“This updated version of the ASTER global digital elevation model provides civilian users with the highest-resolution global topography data available,” said ASTER science team lead Mike Abrams. “These data can be used for a broad range of applications, from planning highways and protecting lands with cultural or environmental significance, to searching for natural resources.”

Joining together in a collaborative effort, NASA and METI are contributing data for the ASTER topographic map to the Group on Earth Observations, for use in the group’s Global Earth Observation System of Systems. No, the previous statement wasn’t a typo – the “system of systems” is an international effort, which uses shared Earth observation data to help monitor and forecast global environmental changes.

One of five instruments launched on Terra in 1999, ASTER acquires images from visible to thermal infrared wavelengths, with spatial resolutions ranging from about 15 to 90 meters. ASTER’s science team is a joint effort between the United States and Japan.

The ASTER data was validated by NASA, METI, Japan’s Earth Remote Sensing Data Analysis Center (ERSDAC), and the U.S. Geological Survey, with additional support from the U.S. National Geospatial-Intelligence Agency and other collaborators. NASA’s Land Processes Distributed Active Archive Center is handling the distribution of the new ASTER global digital elevation model.

If you’d like to download the ASTER global digital elevation model to study at no cost, you can do so at: https://lpdaac.usgs.gov/ or http://www.ersdac.or.jp/GDEM/E/4.html

Source: NASA/JPL Press Release

## Astronomy Without A Telescope – The Edge of Greatness

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The so-called End of Greatness is where you give up trying to find more superlatives to describe large scale objects in the universe. Currently the Sloan Great Wall – a roughly organised collection of galactic superclusters partitioning one great void from another great void – is about where most cosmologists draw the line.

Beyond the End of Greatness, it’s best just to consider the universe as a holistic entity – and at this scale we consider it isotropic and homogenous, which we need to do to make our current cosmology math work. But at the very edge of greatness, we find the cosmic web.

The cosmic web is not a thing we can directly observe since its 3d structure is derived from red shift data to indicate the relative distance of galaxies, as well as their apparent position in the sky. When you pull all this together, the resulting 3d structure seems like a complex web of galactic cluster filaments interconnecting at supercluster nodes and interspersed by huge voids. These voids are bubble-like – so that we talk about structures like the Sloan Great Wall, as being the outer surface of such a bubble. And we also talk about the whole cosmic web being ‘foamy’.

It is speculated that the great voids or bubbles, around which the cosmic web seems to be organised, formed out of tiny dips in the primordial energy density (which can be seen in the cosmic microwave background), although a convincing correlation remains to be demonstrated.

As is well recorded, the Andromeda Galaxy is probably on a collision course with the Milky Way and they may collide in about 4.5 billion years. So, not every galaxy in the universe is rushing away from every other galaxy in the universe – it’s just a general tendency. Each galaxy has its own proper motion in space-time, which it is likely to continue to follow despite the underlying expansion of the universe.

It may be that much of the growing separation between galaxies is a result of expansion of the void bubbles, rather than equal expansion everywhere. It’s as though once gravity loses its grip between distant structures – expansion (or dark energy, if you like) takes over and that gap begins to expand unchecked – while elsewhere, clusters and superclusters of galaxies still manage to hold together. This scenario remains consistent with Edwin Hubble’s finding that the large majority of galaxies are rushing away from us, even if they are not all equally rushing away from each other.

van de Weygaert et al are investigating the cosmic web from the perspective of topology – a branch of geometry which looks at spatial properties which are preserved in objects undergoing deformation. This approach seems ideal to model the evolving large scale structure of an expanding universe.

The paper below represents an early step in this work, but shows that a cosmic web structure can be loosely modelled by assuming that all data points (i.e. galaxies) move outwards from the central point of the void they lie most proximal to. This rule creates alpha shapes, which are generalised surfaces that can be built over data points – and the outcome is a mathematically modelled foamy-looking cosmic web.

Further reading: van de Weygaert et al. Alpha Shape Topology of the Cosmic Web.