The multiverse is not based on rational ground, but it is an extension of the multiworld interpretation of quantum mechanics.

The multiworld interpretation is based on the idea that every quantum-event happens. But each event happens in a different "world". Where the "world" is a local environment. With "observing" you choose a world, somehow.

The interpretation is false, because a quantum-event is not a single event. It is a continuous process, like each radioactive decay may happen at any time. And each "photon" observation happens at any time.
So even a single event would create infinite number of worlds, and each following event would create infinite number of worlds again.
It also gives some kind of god-power to some "observer", which is not well defined.

The interpretation is popular because:
Mathematicians do not care about infinite, but also do not understand how many infinites this interpretation would produce.
And theoretical physicians do not care about infinite, because they just want some numerical answer.
A lot of theorists misuse the multiworld interpretation to claim that the "world" is actually a simulation or the "observer" is some god-like entity.

The physical reality:
But in physical reality, most of these quantum mechanics interpretations are based on Einstein's interpretation of the photoelectric effect.
And that has been falsified.
How it is falsified is explained in more detail here