As a cosmologist, I often carry around a universe or two in my pocket. Not entire, infinitely large universes, but maybe a few billion light years or so across. Enough to be interesting.
Of course, these are not “real” universes; rather they are universes I have simulated on a computer.
The basic idea of simulating a universe is quite simple. You need “initial conditions” which, for me, is the state of the universe just after the Big Bang.
To this, you add the laws of physics, such as: how gravity pulls on mass, how gas flows into galaxies, and how stars are born, live, and die….