Indeed one of the most profound mysteries of cosmology. It is not easy to answer, because we can only observe a finite portion of the universe, called the observable universe, which is limited by the speed of light and the age of the universe.
Beyond that, there may be regions of space that we will never see, even with the most advanced telescopes.
Some scientists think that the universe is infinite, meaning that it has no boundaries and extends forever in all directions.
This would imply that there are infinitely many galaxies, stars, planets and even copies of ourselves in the cosmos.
However, this idea is not proven, and it raises some paradoxes and problems, such as the Olbers' paradox, which asks why the night sky is not infinitely bright if there are infinitely many stars.
Other scientists think that the universe is finite, meaning that it has a certain size and shape, but it may or may not have an edge.
For example, some models suggest that the universe is like a giant doughnut, called a torus, which has no edges or vertices.
The torus is important as a mathematical object, but it is not clear if it describes the actual shape of the universe.
Another possibility is that the universe is like a sphere that is expanding in all directions.
In this case, there would be no edge to the universe, but there would be a limit to how far we can see.
To determine the size and shape of the universe, we need to measure its curvature, which tells us how much space bends due to gravity and energy.
According to Einstein's theory of general relativity, the curvature of the universe depends on its density and expansion rate.
If the density of the universe is higher than a critical value, then the universe is closed and finite. If the density is lower than the critical value, then the universe is open and infinite.
If the density is exactly equal to the critical value, then the universe is flat and could be either finite or infinite.
The best way to measure the curvature of the universe is to observe the cosmic microwave background (CMB), which is the oldest light in the universe, dating back to about 380,000 years after the Big Bang.
The CMB shows tiny fluctuations in temperature and polarization that reveal information about the early history and structure of the universe.
By analyzing these fluctuations with satellites such as COBE, WMAP and Planck, scientists have found that the curvature of the universe is very close to zero, meaning that it is almost flat.
However, this does not tell us whether it is finite or infinite, because both possibilities are consistent with a flat geometry.
Verdict:
There is no definitive answer to whether the universe is infinite or not. We can only say that it is very large, much larger than what we can observe, and that it may or may not have an end.
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