Related papers: Measures for a Multidimensional Multiverse
Recently, a new framework for describing the multiverse has been proposed which is based on the principles of quantum mechanics. The framework allows for well-defined predictions, both regarding global properties of the universe and…
Eternal inflation predicts our observable universe lies within a bubble (or pocket universe) embedded in a volume of inflating space. The interior of the bubble undergoes inflation and standard cosmology, while the bubble walls expand…
In the multiverse hypothesis, a range of universes exist with differing values of our physical constants. Here, we investigate how the probabilities of observing our values of these constants depend on the assumptions made about the…
Many theories of the early universe predict the existence of a multiverse where bubbles continuously nucleate giving rise to observers in their interior. In this paper, we point out that topological defects of several dimensionalities will…
Working on doubling metric spaces, we construct generalised dyadic cubes adapting ultrametric structure. If the space is complete, then the existence of such cubes and the mass distribution principle lead into a simple proof for the…
We analyze the statistical properties of bubble models for the large-scale distribution of galaxies. To this aim, we realize static simulations, in which galaxies are mostly randomly arranged in the regions surrounding bubbles. As a first…
Generalized dimensions of multifractal measures are usually seen as static objects, related to the scaling properties of suitable partition functions, or moments of measures of cells. When these measures are invariant for the flow of a…
We apply the principles of quantum mechanics and quantum cosmology to predict probabilities for our local observations of a universe undergoing false vacuum eternal inflation. At a sufficiently fine-grained level, histories of the universe…
Cosmological distances as a function of redshift depend on the effective curvature density via the effect on the geometrical path of photons from large scale spatial curvature and its effect on the expansion history, H(z). Cosmological…
The distribution of visible matter in the universe, such as galaxies and galaxy clusters, has its origin in the week fluctuations of density that existed at the epoch of recombination. The hierarchical distribution of the universe, with its…
A Five dimensional Kaluza-Klein space-time is considered in the presence of a perfect fluid source with variable G and $\Lambda$. An expanding universe is found by using a relation between the metric potential and an equation of state. The…
Large-scale structure surveys can be used to measure the dipole in the cosmic microwave background (CMB), in the luminosity distances inferred from type-Ia supernova observations, and in the spatial distribution of galaxies and quasars. The…
It has been recently suggested that probabilities of different events in the multiverse are given by the frequencies at which these events are encountered along the worldline of a geodesic observer (the "watcher"). Here I discuss an…
Generalized statistical models of voids and hierarchical structure in cosmology are developed. The often quoted negative binomial model and frequently used thermodynamic model are shown to be special cases of a more general distribution…
Probabilities for observations in cosmology are conditioned both on the universe's quantum state and on local data specifying the observational situation. We show the quantum state defines a measure for prediction through such conditional…
Generalized quantum measurements with N distinct outcomes are used for determining the density matrix, of order d, of an ensemble of quantum systems. The resulting probabilities are represented by a point in an N-dimensional space. It is…
As observers of the universe we are physical systems within it. If the universe is very large in space and/or time, the probability becomes significant that the data on which we base predictions is replicated at other locations in…
The fundamental laws and constants of our universe seem to be finely tuned for life. The various multiverse hypotheses are popular explanations for the fine tuning. This paper reviews the four main suggestions on inference in the presence…
Spaces with locally varying scale of measurement, like multidimensional structures with differently scaled dimensions, are pretty common in statistics and machine learning. Nevertheless, it is still understood as an open question how to…
I explain the difficulty of making various concepts of and relating to probability precise, rigorous and physically significant when attempting to apply them in reasoning about objects (e.g., spacetimes) living in infinite-dimensional…