Related papers: Proof of Conway's Lost Cosmological Theorem
John Conway proved that every audioactive sequence (a.k.a. look-and-say) decays into a compound of 94~elements, a statement he termed the cosmological theorem. The underlying audioactive process can be modeled by a finite-state machine,…
Hawking proposed that the cosmological constant is probably zero in quantum cosmology. Duff claimed that Hawking's proof is invalidated. Using the right configuration for the wave function of the universe, we provide a complete proof.
We present a short new proof of Cobham's theorem without using Kronecker's approximation theorem, making it suitable for generalization beyond automatic sequences.
We present an accurate detailed exposition of the proof of existence of the Alexander-Conway polynomial (of links in 3-dimensional space). Other proofs were given by J. Alexander, J. Conway, V. Mantourov and L. Kauffman.
A generating function for cabled Wilson loops in three-dimensional BF theories is defined, and a careful study of its behavior for vanishing cosmological constant is performed. This allows an exhaustive description of the unframed knot…
The cosmological constant is an unexplained until now phenomena of nature that requires an explanation through string effects. The apparent discrepancy between theory and experiment is enourmous and has already been explained several times…
The validity of the cosmic no-hair theorem is investigated in the context of Newtonian cosmology with a perfect fluid matter model and a positive cosmological constant. It is shown that if the initial data for an expanding cosmological…
An overview is given of the current status of the theory and observations of the acceleration of the expansion of the observable part of the Universe. Contents 1. Historical Introduction 2. Friedmann equations and cosmological acceleration…
We give a purely logical proof of the J. Conway and S. Kochen Free Will theorem concerning undeterminacy in Quantum Mechanics (Notices of the AMS, February 2009, Vol. 56/2, p. 226). The logical method seems to be very powerful.
The interplay between string theory and cosmology is very promising. Since string theory will yield a quantum theory of space-time and unify all forces of nature, it has the potential of addressing many of the conceptual problems of the…
Observations of distances to Type-Ia supernovae can be explained by cosmological models that include either a gigaparsec-scale void, or a cosmic flow, without the need for Dark Energy. Instead of invoking dark energy, these inhomogeneous…
We introduce the notion of an asymptotically automatic sequence, which generalises the notion of an automatic sequence, and we prove a variant of Cobham's theorem for the newly introduced class of sequences.
We prove a computable version of the Hall Harem Theorem where the matching realizes a unary function with controlled sizes of cycles. We apply it to non-amenable computable coarse spaces. As a result, we obtain a computable version of the…
We initiate a formal study of logical inferences in context of the measure problem in cosmology or what we call cosmic logic. We describe a simple computational model of cosmic logic suitable for analysis of, for example, discretized…
An effective time--dependent cosmological constant can be recovered for higher--order theories of gravity by extending to these ones the no--hair conjecture. The results are applied to some specific cosmological models.
Quantum cosmology has traditionally been studied at the level of symmetry-reduced minisuperspace models, analyzing the behavior of wave functions. However, in the absence of a complete full setting of quantum gravity and detailed knowledge…
This paper continues the development of a discrete space-time concept that is recently used in the explanation of the cosmological constant. Instead of order estimation, a more theoretical treatment of the theory is introduced. Based on the…
A number of diagrammatic "cutting rules" have recently been developed for the wavefunction of the Universe which determines cosmological correlation functions. These leverage perturbative unitarity to relate particular "discontinuities" in…
We give a short geometric proof of the Kochen-Specker no-go theorem for non-contextual hidden variables models. Note added to this version: I understand from Jan-Aake Larsson that the construction we give here actually contains the original…
Under the hypothesis that the cosmological constant vanishes in the true ground state with lowest possible energy density, we argue that the observed small but finite vacuum-like energy density can be explained if we consider a theory with…