One of the hardest things we can try to map is the universe, with its dimensions and shape poorly debated among scientists and experts. New instruments made in the last decade are attempting to help us resolve a long-lived mystery that is not only crucial to effectively mapping the universe, but can tell us something about the fate of the universe one day.
What is the Shape of the Universe?
The exact shape of the universe is difficult to measure given we have relatively limited ways in which measurements can be made over very long distances. The universe is about 13.8 billion years and it is only physically possible to measure 13.8 billion light years away, meaning that if the universe is still expanding we could not see that expansion. Nevertheless, measuring the critical density of the universe relative to the actual density allows us to know the possible shape. One possibility is the universe is curved like a planet and is closed, which occurs when the actual density is more than the critical density. Another possibility is that it is curved but more like a saddle, which is considered an open universe, a phenomenon that occurs when the critical density is more than the actual density. A final possibility is that it is flat, where critical density and actual density are equal. A flat universe is what most cosmologists believe the shape of the universe to be as they believe it is expanding, which is better explained by a flat universe.
Mapping the Cosmic Microwave Background
However, there are clues the universe has left us that allow measurements of the dimensions and scale of space to be possible, enabling a possibly more accurate map to be made. The Planck satellite, a satellite jointly commissioned by the European Space Agency (ESA) and NASA, has been sent to map different aspects of space and capture a variety of data that can allow us to make measurements to better understanding the universe’s dimensions. Interstellar dust and microwaves in our galaxy, for instance, have been measured, from which researchers developed a map of the distribution of these to be made for the first time. The most important measure to understanding the dimensions of space could be cosmic microwave background (CMB), which is leftover radiation from soon after the birth of the universe in the Big Bang. This light has expanded from the initial explosion and continues to race across the universe for perhaps the last 13.8 billion years.
In 2018, a map of CMB was detailed by Planck and the data were released to scientists. While theorists have often assumed the universe might be flat, and thus expanding outwards, the raw data data surprised scientists as the CMB suggested that the shape for the universe is bounded, meaning that the universe is shaped more like a planet. However, even with the data from Planck, the issue is not resolved. For one, some scientists think that contaminants from the universe may corrupt the measurements, meaning that the universe’s shape may still be flat. In fact, astronomers suggest that using multiple measurements from different Earth-based sensors and other instruments suggests the universe is still flat. On the other hand, others see the measurement as being accurate and that the universe has boundaries and is curvy. To these scientists, Planck’s instrumentation means we can now more properly measure the shape of the universe and produce a better way to even map it. Additionally, a curved and closed universe explains phenomena such as dark matter, which is seen as a substance that makes up a large percentage of the universe. One possibility is that a flat universe would not be able to hold so much dark matter. Greater matter should bend light and observations using CMB suggest the universe has more dark matter than generally believed, which would also shape it as it affects the universe’s overall mass.
The answers to the shape of the universe are now not as agreed upon as they may have been previously. Observations of critical components of the universe, dark matter, dark energy, and inflation, that is expansion of the universe, are theorized by cosmologists but have not been observed and explained using standard physics. This means mapping the universe is still unclear as matter and energy that make up much of the universe, and how they change and shape the universe, are still not easily understood and debated. What recent work has shown is that the universe is probably more complex in makeup and how it follows physical laws than we think. It is hoped that more data from different forms of sensors will allow us to use a variety of proxies to determine the shape of our universe.
 For more on a flat universe, see: https://www.space.com/universe-shape-flat-closed-debate.html.
 For more on a curvy and bounded universe, see: Di Valentino, E., Melchiorri, A. & Silk, J. Planck evidence for a closed Universe and a possible crisis for cosmology. Nat Astron 4, 196–203 (2020). https://doi.org/10.1038/s41550-019-0906-9.