# Multiverse—Too Much or Not Enough?

## Abstract

**:**

Or, had I not been such a commonsensical chap, I might be defending not only a plurality of possible worlds, but also a plurality of impossible worlds, whereof you speak truly by contradicting yourself.David Lewis

## 1. Introduction

## 2. A Philosopher’s Paradise

- A sentence is necessarily true if, and only if, it is true in every possible world.
- A sentence is possibly true if, and only if, it is true in some possible worlds.

## 3. A Context for Cosmology

## 4. Multiverses (In Plural)

- The multi-domain multiverse: Alluded to by Ellis.8
- The inflationary multiverse: Eternal cosmological inflation leading to innumerable generations of bubble universes.
- The brane multiverse: This is an outcome of the M-theory.
- The cyclic multiverse: Collisions between branes producing big bangs separating subsequent universes.
- The landscape multiverse: A combination of inflationary cosmology with string theory.
- The quantum multiverse: This is implied by the realistically understood many-worlds interpretation of quantum mechanics.
- The holographic multiverse: Stems from the hypothesis that the entire universe can be viewed as information on the two-dimensional cosmological horizon.
- The simulated multiverse: That is, simulated by a supercomputer.
- The ultimate multiverse: All mathematical structures are instantiated as real universes.

## 5. It Is Too Much

## 6. It is Not Enough

## Funding

## Conflicts of Interest

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1 | In this essay, all “multiverses” and “universes” will be democratically written with small letters. |

2 | In general, the space of solutions to the vacuum Einstein equations is a smooth infinite-dimensional manifold. However, in a neighbourhood of a solution with symmetries (it is enough for a solution to have a single Killing vector field) the solutions cannot be parametrised in a smooth way by elements of a linear space. In other words, at such a solution there is no tangent space to the space of solutions; just as there is no tangent space at the vertex of a cone. |

3 | Structural stability is, in principle, a property of a dynamical system. It says that small perturbations do not affect the qualitative behaviour of nearby trajectories. In many cases, solutions to Einstein equations can be represented as trajectories of a dynamical system. |

4 | Strictly speaking, in this context it is not the space of solutions of Einstein’s equations that is taken into account, but rather the space of all Lorentz metrics, only some of them could be solutions to Einstein’s equations. |

5 | Not to be confused with the “ensemble of universes” as the space of solutions to Einstein’s equations. |

6 | This does not mean, however, that it disappears from cosmological texts; on the contrary, references and longer debates abound. |

7 | By a multi-domain universe, Ellis understands an infinite universe in which very far-away space-time domains are regarded as separate universes. |

8 | Green claims that in an infinite universe the same “local universe” must replicate itself across space. |

9 | Although a multiverse consisting of a finite number of universes is in principle possible, it seems rather artificial. |

10 | Capitalized by the quoted authors. |

11 | A quick reminder: A category consists of a collection of objects and a collection of morphisms (also called arrows) between objects. Morphisms can be composed (provided the head of one arrow coincides with the tail of the other arrow), and the composition of morphisms is associative. There exist identity morphisms satisfying the usual identity axioms. Richness of categories is enormous: from simple ones (like the category consisting of a single object and a single identity morphism) to categories covering large areas of mathematics. |

12 | Intuitionistic logic is the one in which the excluded middle law (p or not p) is not valid and the axiom of choice cannot be used; see [31]. |

13 | Topoi (or toposes) form a class of categories especially related to the theory of sets. Although a topos can contain objects that are much richer and considerably different from sets, the abstract categorical properties of topoi are essentially the same as those known from the theory of sets; see [31]. |

14 | Paraconsistent logic is, in a sense, dual with respect to intuitionistic logic; in it the noncontradiction law (it is not true that p and not p) is not valid; see [32]. |

15 | A functor transforms one category into another category (objects into objects, morphisms into morphisms) in such a way that all defining axioms are preserved. |

16 | By the term “local framework” Bell understands a topos with an object of natural numbers. |

17 | For the role of category theory in physics, see [34]. |

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**MDPI and ACS Style**

Heller, M.
Multiverse—Too Much or Not Enough? *Universe* **2019**, *5*, 113.
https://doi.org/10.3390/universe5050113

**AMA Style**

Heller M.
Multiverse—Too Much or Not Enough? *Universe*. 2019; 5(5):113.
https://doi.org/10.3390/universe5050113

**Chicago/Turabian Style**

Heller, Michael.
2019. "Multiverse—Too Much or Not Enough?" *Universe* 5, no. 5: 113.
https://doi.org/10.3390/universe5050113