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In new Physical examination letters (PRL), scientists are investigating the possibility of non-trivial or exotic topologies in the universe to explain some of the anomalies observed in the cosmic microwave background (CMB).

Our cosmological model of the universe, based on quantum mechanics and general relativity, deals with the geometry of the universe, influenced by matter and energy, which for most purposes is considered flat.

However, it says nothing about the topology of the universe itself: is it infinite, does it have cycles, etc. PRL research focuses on this aspect of the universe and whether current models and data allow for the existence of these exotic or non-trivial topologies.

The research is being carried out as part of the COMPACT collaboration, consisting of an international team of scientists. One of the study’s co-authors, Prof. Glenn D. Starkman of Case Western Reserve University in Ohio, USA, spoke to Phys.org about the team’s work.

Discussing his motivation to pursue this work, he said: “The possibility of the universe having an ‘interesting’ topology is well within our standard model of physics, yet it is generally considered exotic.”

“I’ve long worried that we’d miss an extraordinary discovery about our universe if we just looked the other way. Meanwhile, there is increasing evidence that the universe is not “statistically isotropic”, ie. that the physics is the same in all directions.. Topology is a very natural way for anisotropy to creep into our universe.”

Cosmic microwave background

CMB is a type of radiation belonging to the microwave spectrum. Predicted in 1940 as a remnant of the Big Bang, it was discovered in 1965 by accident.

After the Big Bang, which is how the current universe exists, there was nothing but a soup of fundamental particles and gases at extremely high temperatures and pressures, often called the primordial soup.

As the universe expanded, it also cooled. This caused the fundamental particles to combine to form atoms. By this time, photons interacted with these fundamental particles and scattered, preventing them from traveling freely. But after atoms began to form, photons traveled more freely, about 380,000 years after the Big Bang.

This marks the spread of the CMB, which is thought to be the “afterglow” of the Big Bang. It contains important information about the early universe and the subsequent processes that led to the formation of large-scale structures such as stars and galaxies.

The CMB is present everywhere and for the most part has the same temperature. However, there are small fluctuations and anomalies in the CMB data that are not explained.

The researchers in PRL study suggests that these fluctuations and anomalies in CMB measurements can be explained by considering non-trivial topologies of the universe, meaning that we should not view it as ‘flat’.

Space topology

Topology is a branch of mathematics that deals with the shape and structure of objects. The rules of topology are quite different from the rules of geometry. While geometry and topology are different concepts, geometry influences topology.

Geometry defines how space is curved (space-time is considered flat at small scales), and topology defines the overall connectivity of space.

If we must have flat space, we cannot have topologies where space curves inwards or has loops. This means that in order to travel between two points, we will have to take a straight line with no detours or detours.

Prof Starkman explained: “The universe could be like an old-timey video game where leaving the right side of the screen will see you pop out to the left, so you can go back to where you started in a straight line. That’s called multi-connectivity.”

Essentially, the rectilinear path suggests that despite the appearance of continuous movement, the underlying topology of space allows for unexpected connectivity, where what appears to be a linear trajectory can actually loop back on itself.

Matching temperature circles

If the universe were to be “multi-connected” (ie have a non-trivial topology), we would observe corresponding temperature loops. This is because light traveling from a source (such as a star) can take two different paths and reach the observer (Earth) from two directions.

This leaves similar temperature fluctuations on a CMB map (or heat map), resulting in matching temperature circles. However, there is no evidence to suggest the existence of these coincident temperature cycles.

“The lack of matching temperature loops is what tells us the length of the shortest closed loop through us, but it doesn’t tell us the length of the loops through other places,” Prof Starkman said.

The lack of coincident temperature loops in the CMB data suggests that if a non-trivial topology exists, the loops passing through our location (Earth) must be relatively small.

This places a limit on the length of these cycles. Prof. Starkman explained: “If the CMB anomalies are due to cosmic topology, then the length of the shortest loops through us should not be more than about 20-30% longer than the diameter of the last scattering surface – a sphere with a radius equal to of the distance light has traveled in the history of the universe.”

Future restrictions and searches

In light of the above limitation and the search for a non-trivial topology, researchers suggest additional ways to discover such a topology in the future.

In particular, they mention changes in the statistical patterns of temperature fluctuations in the CMB data, as well as in the large-scale structure of the universe. These fluctuations or alternations would come to light if a non-trivial topology were present.

But these discoveries require enormous computing power, and the researchers propose using machine learning algorithms to speed up the calculations and mine the CMB data to discover non-trivial topology.

“Topology search will be resumed after a hiatus of about a decade. We hope to discover a cosmic topology and thereby understand the origin of the anisotropy of our universe and gain insight into the processes responsible for the initial formation of our universe,” Prof. Starkman concluded.

The study also highlights that even in the absence of explicitly coincident circles, the presence of statistical anisotropy (or anomalies) in the CMB indicates the potential existence of detectable information about the structure and topology of the universe.