One Infinite Universe
Sometimes referred to as a Level 1 Multiverse, this hypothesis postulates an infinite, contiguous Universe that contains an infinite number of Hubble volumes. Every part of the Universe must have the same physical laws, values for constants and particles, but most will have different ways in which matter and energy are distributed, including dark matter. It is not clear to me whether the distribution of dark energy could be different as this appears to be an intrinsic property of space itself that seems to remain constant as the Universe expands. As the theory assumes an infinite number of Hubble volumes, it follows that some of them would be identical to ours. In fact, from a mathematical stand point, there would be an infinite number of identical universes! The Hubble volume is that region of the Universe beyond which everything recedes at or above the speed of light due to the cosmological expansion of the Universe. Thus, we can have no knowledge of what occurs beyond our Hubble volume of the Universe.
This theory does not provide any explanation for how the physical constants acquired values that provide the environment in which we live, as it theorizes that these values are constant throughout the infinity of the universe. It is one idea that could be detected. It is possible that there could have been a gravitational interaction between our Hubble Volume and an adjacent volume that left a sort of "cosmic footprint" in our Universe, but this is highly speculative.
Astronomy & Cosmology - Alternative Universes
Lee Smolin's fecund universes theory suggests that when a black hole collapses, a new universe is created. Particles, physical laws and constants would probably vary from those in the parent Universe. Thus, any universe creates as many new universes as it has black holes, and these universes go on to create their own new universes. Of course, if the laws and constants of a universe precludes to production of black holes, that universe would fail to "reproduce". This is, perhaps, why the theory is sometimes called the "cosmological natural selection" theory.
An Infinity of Universes
The chaotic inflation hypothesis is an extension of cosmic inflation theory first proposed by Alan Guth and later elaborated by Andrei Linde and others. The theory proposes an overarching multiverse that is expanding; stretching the fabric of space. At some point, a tiny region of that space becomes a "pocket" or "bubble" within the Multiverse, and starts its own expansion. This happens over and over again; an infinite number of times, with the "bubbles" themselves giving rise to additional universes. Some experience their own cosmic inflation, at their own rate, others will not undergo inflation so would be very small. Some may not expand at all, or will almost immediately collapse in black holes. Assuming they all start with their forces in a unified force that breaks, that symmetry breaking could produce all manner of different particles and physical constants. We evolved in one that is conducive to our type of life. Many of the universes bubbles could be completely empty; some could contain all manner of exotic particles and energy.
The ideas in this page are all variations on the idea that there is an infinity of universes of which our Universe is just a single member.
Hugh Everett's Many-worlds Interpretation
The Many-worlds Interpretation is discussed as a section under Quantum Physics.