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One of the biggest mysteries in physics is how the universe looked and behaved during its earliest moments. Mathematically, physicists study this using so-called cosmological correlators. These correlators contain all information about the early universe. However, it is also notoriously difficult to obtain these correlators and extract this physical information.

My dissertation develops new mathematical tools that make extracting this information more manageable. The key idea here is called reducibility. Simply put, reducibility is the observation that, instead of trying to solve a complex problem all at once, it is often easier to break it up into more manageable chunks and solve these chunks separately.

For cosmological correlators, we have identified exactly how solving them can be split up like this. We find the simplest building block they consist of, and then construct the correlators themselves from these building blocks. We call these building blocks minimal representation functions and using them, can greatly simplify solving cosmological correlators. Therefore, these techniques can allow us to obtain a deeper understanding of the early universe.

We have focused here on cosmological correlators, but it bears mentioning that the underlying mathematics, using so-called differential equations and their reductions, is more broadly applicable. In the future, we hope that these techniques will find applications in many other parts of physics.