"A growing number of physicists, myself included, are convinced that the thing we call ‘the universe’ — namely space, with all the matter and energy it contains — is not the whole of reality. According to quantum theory — the deepest theory known to physics — our universe is only a tiny facet of a larger multiverse, a highly structured continuum containing many universes."

David Deutsch, from an excellent article he wrote for Frontiers magazine called David Deutsch’s Many Worlds.

Parallel Universes

Abstract: I survey physics theories involving parallel universes, which form a natural four-level hierarchy of multiverses allowing progressively greater diversity.
Level I: A generic prediction of inflation is an infinite ergodic universe, which contains Hubble volumes realizing all initial conditions - including an identical copy of you about 10^{10^29} meters away.
Level II: In chaotic inflation, other thermalized regions may have different effective physical constants, dimensionality and particle content.
Level III: In unitary quantum mechanics, other branches of the wavefunction add nothing qualitatively new, which is ironic given that this level has historically been the most controversial.
Level IV: Other mathematical structures give different fundamental equations of physics. The key question is not whether parallel universes exist (Level I is the uncontroversial cosmological concordance model), but how many levels there are. I discuss how multiverse models can be falsified and argue that there is a severe "measure problem" that must be solved to make testable predictions at levels II-IV.

The Mathematical Universe

Abstract: I explore physics implications of the External Reality Hypothesis (ERH) that there exists an external physical reality completely independent of us humans. I argue that with a sufficiently broad definition of mathematics, it implies the Mathematical Universe Hypothesis (MUH) that our physical world is an abstract mathematical structure. I discuss various implications of the ERH and MUH, ranging from standard physics topics like symmetries, irreducible representations, units, free parameters and initial conditions to broader issues like consciousness, parallel universes and Godel incompleteness. I hypothesize that only computable and decidable (in Godel's sense) structures exist, which alleviates the cosmological measure problem and help explain why our physical laws appear so simple. I also comment on the intimate relation between mathematical structures, computations, simulations and physical systems.

The Structure of the Multiverse

Abstract: The structure of the multiverse is determined by information flow.

Machines, Logic and Quantum Physics

Abstract: Though the truths of logic and pure mathematics are objective and independent of any contingent facts or laws of nature, our knowledge of these truths depends entirely on our knowledge of the laws of physics. Recent progress in the quantum theory of computation has provided practical instances of this, and forces us to abandon the classical view that computation, and hence mathematical proof, are purely logical notions independent of that of computation as a physical process. Henceforward, a proof must be regarded not as an abstract object or process but as a physical process, a species of computation, whose scope and reliability depend on our knowledge of the physics of the computer concerned.

The problem of what exists

Abstract: Popular multiverse models such as the one based on the string theory landscape require an underlying set of unexplained laws containing many specific features and highly restrictive prerequisites. I explore the consequences of relaxing some of these prerequisites with a view to discovering whether any of them might be justified anthropically. Examples considered include integer space dimensionality, the immutable, Platonic nature of the laws of physics and the no-go theorem for strong emergence. The problem of why some physical laws exist, but others which are seemingly possible do not, takes on a new complexion following this analysis, although it remains an unsolved problem in the absence of an additional criterion.

Multiverse cosmological models

Abstract: Recent advances in string theory and inflationary cosmology have led to a surge of interest in the possible existence of an ensemble of cosmic regions, or universes, among the members of which key physical parameters, such as the masses of elementary particles and the coupling constants, might assume different values. The observed values in our cosmic region are then attributed to an observer selection effect (the so-called anthropic principle). The assemblage of universes has been dubbed the multiverse. In this paper I review the multiverse concept and the criticisms that have been advanced against it on both scientific and philosophical grounds.