Related papers: Topos-theoretic Model of the Deutsch multiverse
We introduce an abstract topos-theoretic framework for building Galois-type theories in a variety of different mathematical contexts; such theories are obtained from representations of certain atomic two-valued toposes as toposes of…
For digital images, there is an established homotopy equivalence relation which parallels that of classical topology. Many classical homotopy equivalence invariants, such as the Euler characteristic and the homology groups, do not remain…
General relativity does not allow one to specify the topology of space, leaving the possibility that space is multi-- rather than simply--connected. We review the main mathematical properties of multi--connected spaces, and the different…
Topological models involving matter couplings to Donaldson-Witten theory are presented. The construction is carried using both, the topological algebra and its central extension, which arise from the twisting of $N=2$ supersymmetry in four…
An idea of the universe as a self-contained system of interacting fields as a closed doublon network is developed. The characteristic scale of this system is considered emergent from general principles. Self similarity of patterns in the…
This paper is the fourth in a series whose goal is to develop a fundamentally new way of building theories of physics. The motivation comes from a desire to address certain deep issues that arise in the quantum theory of gravity. Our basic…
The many-worlds interpretation of quantum mechanics predicts the formation of distinct parallel worlds as a result of a quantum mechanical measurement. Communication among these parallel worlds would experimentally rule out alternatives to…
We investigate the geometry of a quantum universe with the topology of the four-torus. The study of non-contractible geodesic loops reveals that a typical quantum geometry consists of a small semi-classical toroidal bulk part, dressed with…
The presence of compact extra dimensions in cosmological scenarios in the context of f(T)-like gravities is discussed. For the case of toroidal compactifications, the analysis is performed in an arbitrary number of extra dimensions.…
The three cosmological conjectures to which our work refers are: the phenomenon called geodesic incompleteness, the physical gravitational $\theta_G$-term that would characterize the 1-parameter family of inequivalent vacua of quantum…
Multiverse scenarios are common place in contemporary high energy physics and cosmology, although many consider them simply as bold speculations. In any case there is nothing like a single theory or a unified model of the multiverse.…
What is the shape of the Universe? Is it curved or flat, finite or infinite ? Is space "wrapped around" to create ghost images of faraway cosmic sources? We review how tessellations allow to build multiply-connected 3D Riemannian spaces…
The topos approach to the formulation of physical theories includes a new form of quantum logic. We present this topos quantum logic, including some new results, and compare it to standard quantum logic, all with an eye to conceptual…
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…
In the field of quantum simulation of condensed matter phenomena by artificially engineering the Hamiltonian of an atomic, molecular or optical system, the concept of `synthetic dimensions' has recently emerged as a powerful way to emulate…
We propose and investigate a new algorithm for quantifying the topological properties of cosmological density fluctuations. We first motivate this algorithm by drawing a formal distinction between two definitions of relevant topological…
Homotopy Type Theory with a univalent universe $\,\mathcal{U}_0$ is interpreted at the strength of finite order arithmetic. We eliminate Grothendieck universes, avoid the axiom of replacement, and bound all uses of separation.
The integration procedure for multidimensional cosmological models with multicomponent perfect fluid in spaces of constant curvature is developed. Reduction of pseudo-Euclidean Toda-like systems to the Euclidean ones is done. Some known…
A generalization of topos theory is proposed giving an abstract realization of such categories as, say, the categories of manifolds and of Grothendieck schemes on the one hand, and permitting one, on the other hand, a view on…
Higher dimensional solutions are obtained for a homogeneous, spatially isotropic cosmological model in Wesson theory of gravitation. Some cosmological parameter are also calculated for this model.