# What is the shape of the universe?

One of the biggest questions in cosmology concerns the shape of the universe. This is not about the distribution of galaxies or the structure of the cosmic web. No, we are talking about the topology of spacetime! According to Einstein’s laws, space and time can be bent by the presence of a heavy mass – this causes gravity. Furthermore, dark energy can also distort spacetime – this causes the cosmic expansion. Determining the exact shape of spacetime can tell us whether the universe is finite or infinite. It can also indicate whether spacetime will continue to expand or ever collapse again.

Astrophysicists theorize that the universe has one of three possible geometric shapes: spherical geometry (positive curvature), Euclidean geometry (zero curvature), or hyperbolic geometry (negative curvature).

## What is the prevailing theory?

The shape of the universe is basically its local and global geometry. Local attributes are described by its curvature while the topology of the universe describes its general global attributes. The shape of the universe can be described using three properties:

1. Flat, open, or closed.
2. Finite or infinite.
3. Connectivity (is the universe simply connected or multiply connected space).

It is generally believed that the universe is flat. That means that if you average all curvatures due to gravity and dark energy, the universe will have an approximately zero curvature. If you shoot two laser beams parallel to each other, they will always move parallel to each other in a flat universe. If the universe is not flat, sooner or later the laser beams will bend away from each other.

Take earth for example, locally it appears to be flat. However, if two people will walk north parallel to each other eventually they will meet at the same point at the North Pole.

## Evidence the universe is flat

The Planck space telescope, which made observations from 2009 to 2013, mapped the cosmic microwave background radiation (CBM). That is a small amount of light that is left over from the Big Bang and that has been scattered all over the universe.

We see evidence for the flatness of the universe in CBM. Studying the data from Planck, researchers learned that the temperature of the CMB is quite uniform. In places there are slight variations in temperature, but you can cancel them out – the average will remain about the same. This is exactly what you would expect when the universe is flat. If the universe had a curvature, this should be visible in the CMB in the form of temperature differences. In other words, a whole part of the CMB should be warmer or colder than you would expect from sheer chance and randomness.

## Curved universe?

However, cosmologists have recently found an anomaly in the CMB. It has not yet been proven that this deviation is significant, there is 1% probability this is a random variation. Nevertheless, cosmologists have come up with all kinds of explanations.

One set of Planck observations shows that CMB has more to do with gravitational lens than expected. Cosmologist Alessandro Melchiorri of Sapienza University calculated that this could be because the shape of our universe is different from what we thought. They published their results in the scientific journal Nature Astronomy.

### Extra dark matter

All other cosmological observations suggest that the universe is flat. That is, it has no curvature, just like a sheet of paper. The observed deviation suggests the universe could be spherical – a closed universe. That would mean that if you travel far enough in a certain direction, you would end up where you left.

The researchers draw this conclusion because the extra gravitational lenses indicate the presence of extra dark matter. It would draw the universe into a finite sphere, instead of a flat plane.

If the universe is indeed closed, it could pose a major problem for our understanding of the cosmos. Another cosmological puzzle is that the universe appears to be expanding faster than it should. Data obtained by the WMAP mission suggest that the expansion of the universe is accelerating. This finding implies the existence of a form of matter with a strong negative pressure, such as the cosmological constant. This matter is sometimes referred to as dark energy. If dark energy plays a significant role in the evolution of the universe, then it is very likely that the universe will continue to expand forever.

This is difficult to explain with our current standard model of cosmology, which is based on a flat universe. The team calculated that things would get even more complicated if the universe turned out to be spherical.

The researchers also name a number of other cosmic contradictions that we have yet to explain. All in all, they find the situation so worrying that they speak of a ‘cosmological crisis’. According to the researchers, in a closed universe, these anomalies are even more serious than previously thought.

### Soccer Ball shaped universe

This is not the first time, however, that the flat universe theory is challenged. In 2003, astrophysicists Jean-Pierre Luminet proposed the idea that the universe is shaped like a soccer ball. Luminet’s theory is based on a series of big bang data that indicates that the universe is a spherical ball. It also suggests that its surface is tilled by 12 curved regular pentagons. This cosmic hall of mirrors reflects the stars inside it. This reflection, according to this study, suggests that the universe is infinite. Although in reality what we see as a continuous prolongation of stars is nothing more than a repetition of their image.

## Further experiments

The usual explanation of the formation of the universe includes a period just after the big bang called inflation. During this period the universe expanded rapidly. Our current inflation models automatically yield a flat universe. So if the universe is actually closed, those models would have to be adjusted.

No one has yet found a way to reconcile these Planck observations with the many cosmological measurements that are inconsistent with them. There is therefore a chance that this Planck measurement is nothing more than a statistical anomaly.More data will show in the coming years whether we should take this anomaly seriously. The Atacama Cosmology Telescope (ACT) and the Simons Array located near the Simons Observatory in Chile, are currently making observations of the CMB. Their goals are to study how the universe began, what it is made of, and how it evolved to its current state. These experiments will be able to measure gravitational lenses with even more precision than Planck satellites. Then it will become clear whether the current theory about the shape of the universe should be updated or not.

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