Verse and Dimensions: Structures
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When the (10+1)D universe of M-theory is interpreted as a multiverse, the (3+1)D Dirichlet membranes (D3-branes) that can have observable universes embedded in them can be interpreted as universes.
Multiverses
Most universes are born from a multiverse in which there are multiple to perhaps an immeasurable number – which may or may not contain humans or life at all. In fact, some of them may be so hostile that chemistry or physics as we know them do not function properly.
Other information
Travel between universes is possible for extremely advanced civilizations through the use of portals, dark energy, time maneuvering, or other space-warping mechanisms. Additionally, cosmic entities can traverse through universes easily. Most universes shall eventually "die" as the second law of thermodynamics ensures that energy becomes less and less usable over time. This may not always be the case with alternate physical laws, though.
A universe can have any amount of dimensions from 1 to Aleph-one.
Types of Universes
Due to special properties a universe can have, it may be categorized differently from most since it's not just the laws of physics and possibilities that are different.
Multiversally bounded
These are universes that are born in multiverses, born from big bangs. These are the most likely to give birth to powerful civilizations since they are more safe and less bounded than other types of universes.
Soverses
If a universe is kicked out of a multiverse or is created outside of a multiverse, then it is categorized as a soverse, which is short for solo universe. These universes are usually more static than most since it is dangerous for an object with the dimensionality level as much as a universe to enter intermultiversal space. Even if a life where to from on a soverse, it is very unlikely for it thrive let alone survive long periods of time, even if they a civilization emerges, it is unlikely for it to reach Type V because of the huge distances between it and a multiverse.
Innaturalis
Latin for "unatural" any universe falling into this category is created by an advanced civilization or cosmic entity. They are not born from big bangs and are usually unnaturally organized and/or have properties meant to create and/or keep certain things. If a universe falls into this category, it could still be categorized as Multiversally bounded or Soverse.
Pocket Universe
These are universes in which they come from a host universe; they are pockets of physics and possibilities different from the original universe but is not different enough to break free from it whether in space or time. They often confused with parallel universes because they are slight changes in possibility and laws of physics, but if they still exist in the same timeline or the smaller universe is still inside of the larger, than it is a pocket universe.
Multiverse
A multiverse is a set of a finite or possible infinite number of universes, frequently interpreted as a space containing distinct, typically non-interacting universal "bubbles". Occasionally, the term is used to define the hypothetical set of every single possible universe, including the universe in which we live.
A number of distinct multiverse hypotheses exist that can describe multiverses in various ways, but in essence the feature in common is that they involve multiple universes or realities distinct from each other and from the one that we, or at minimum a single observer, experiences.
The various universes within a multiverse are called "parallel universes,” "other universes,” or "alternate universes.” It is possible to classify a multiverse based on what types of universes it contains and how they relate to each other (see Altverse).
Dimensionality
The dimensionality of a multiverse depends on the specific interpretation of the multiverse taken.
A simple conception of a multiverse is 5-Dimensional space, with several four dimensional universe-"lines" arranged in a stack in a 5 dimensional space.
One can also construct a multiverse with the same dimensionality as the universes it contains; if the universes are finitely large, they can simply sit inside a larger space like bubbles in a volume of water. Provided that the multiverse is negatively curved, one can even fit infinitely many infinitely large universes of the same dimensionality inside. In this model, each infinite universe is a horohyperball bounded by a horohypersphere. Using a Poincare hyperball model to model the geometry of such a multiverse, every representation of an infinite universe would be a hyperball tangent to the outer boundary of the unit hyperball.
The most extreme conception of the multiverse has them be infinite dimensional, with the coordinates of a point in the multiverse representing the complete state of the universe located at that position (such a multiverse can also be called a phaseverse).
Multiverses as Generalization
A feature common among many cosmologies is to take a multiverse as a generalization or abstraction of the universes it contains: for example, whereas a single universe might have a single mathematical basis for its laws of physics, a fixed number of dimensions, a single set of fundamental constants, and an initial condition, a multiverse can be constructed in which every universe has three of these four held constant but the other is free to vary between universes. One operation by which this may be done is the power-set, which has the useful property in that the "size", in one sense, of a multiverse containing infinitely large universes is one beth number larger than that of those universes.
In this model, it then becomes feasible to introduce a megaverse as a structure that behaves like a "multiverse of multiverses", perhaps losing another feature in common among the universes it contains, and to continue ad infinitum in what is called an archverse chain.
Tegmark Multiverses
While his writing is inconsistent with the description given above, it is nonetheless common for discussions of the multiverse to bring up the work of physicist Max Tegmark, who proposes that cosmology may be layered up to four levels deep, each one requiring fewer assumptions about physics than before. As such, these levels are outlined below for whatever reference purposes they may be needed for.