Different regions of our Universe can have slightly more mass or energy than others, and understanding how this affects galaxy formation and evolution is crucial for accurate theoretical predictions in large-scale structure. For example, in overdense regions there is more mass to form more massive galaxies as Fig.~\ref{fig:sepuni_1} illustrates, and this must be factored in when we try to predict the spatial distribution of galaxies in the Universe. I have been interested in studying this environmental dependence of galaxy formation using a numerical simulation technique called Separate Universe (SU) simulation. These are N-body simulations that simulate structure formation inside these special regions. These simulations get their name because they are based on the principle that structures like galaxies or galaxy clusters inside large-scale perturbations behave exactly as if they were inside a different (or separate) universe; for instance, galaxies forming inside regions with more mass than average, form exactly as they would form if they were inside a Universe that simply contained more mass overall. Thus, rather than running very large-volume, expensive simulations that can encompass the large-scale perturbations, it is much more efficient to simulate a smaller volume with different cosmological parameters that mimic the desired perturbation.

In a series of papers [1–3], I have developed SU simulations with the galaxy formation model ILLUSTRISTNG (www.tng-project.org/), which is a state-of-art model of galaxy formation and evolution in cosmological simulations. These were the first ever SU simulations with galaxy formation physics taken into accout (previous simulations included only the action of gravity), and they opened the door to begin uncovering previously unknown aspects about galaxy formation, in particular, its dependence on the large-scale environment. The potential of this new simulation technique is only now starting to be explored, but these first simulations led to a number of interesting new results already. These include:

\begin{enumerate}

\item The fact that, although galaxy formation physics like stellar or black hole feedback can have a marked impact on an important and very popular statistic in cosmology called the {\it 2-point function}, they affect only very marginally the way this statistic depends on the large-scale environment [1]. This discovery made it possible to model a number of other statistics (generically called $N$-point functions with $N>2$) in a way that is appreciably easier than previously thought [4].

\item The fact that galaxies and dark matter halos form with different efficiencies inside large-scale gravitational perturbations and relative baryon-dark matter density perturbations [2,3]. This has crucial ramifications to the study of the physical mechanisms in the early Universe that generated these types of perturbations [5,6].

\item The fact that the mean number of galaxies that live inside dark matter halos can be a sensitive function of the large-scale environment [7]. This has important implications to our understanding of how galaxies populate dark matter halos accross the Universe.

\end{enumerate}