Related papers: Measures for a Transdimensional Multiverse
The possibility that the multiverse corresponds to physical reality deserves serious investigation. Having three different important theories,(quantum mechanics, string theory and inflation), predict the existence of the multiverse is…
The recently proposed "reheating-volume" (RV) measure promises to solve the long-standing problem of extracting probabilistic predictions from cosmological "multiverse" scenarios involving eternal inflation. I give a detailed description of…
The change of the effective dimension of spacetime with the probed scale is a universal phenomenon shared by independent models of quantum gravity. Using tools of probability theory and multifractal geometry, we show how dimensional flow is…
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…
For a given metric measure space $(X,d,\mu)$ we consider finite samples of points, calculate the matrix of distances between them and then reconstruct the points in some finite-dimensional space using the multidimensional scaling (MDS)…
Multidimensional scaling (MDS) is a popular technique for mapping a finite metric space into a low-dimensional Euclidean space in a way that best preserves pairwise distances. We study a notion of MDS on infinite metric measure spaces,…
We discuss the effect of the quantum fluctuations at high energies on the final shape of compact extra dimensions. The quantum fluctuations produce a wide range of the initial extra metrics in causally disconnected regions (pocket…
A Gauss-Bonnet term naturally appears in the action for gravity when one considers the existence of space time with dimensions more than 1+3. A variety of inflationary models can be obtained within such a framework, once the scale factor…
Random, multifield functions can set generic expectations for landscape-style cosmologies. We consider the inflationary implications of a landscape defined by a Gaussian random function, which is perhaps the simplest such scenario. Many key…
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 present a framework in which well-defined predictions are obtained in an eternally inflating multiverse, based on the principles of quantum mechanics. We show that the entire multiverse is described purely from the viewpoint of a single…
In the mini-superspace approximation to cosmology, the canonical measure can be used to compute probabilities when a cutoff is introduced in the phase space to regularize the divergent measure. However, the region initially constrained by a…
Everlasting inflation has far-reaching implications for cosmology and the standing of self-localizing inferences made by observers, which have been subjects of renewed interest in light of the growing acceptance of theory landscapes and the…
A mechanism of inflation from higher dimensions compactification is studied. An Early Universe capable of providing exponential growth for some dimensions and exponential contraction for others, giving therefore an explanation for the big…
We discuss the duality, conjectured in earlier work, between the wave function of the multiverse and a 3D Euclidean theory on the future boundary of spacetime. In particular, we discuss the choice of the boundary metric and the relation…
In generic models of cosmological inflation, quantum fluctuations strongly influence the spacetime metric and produce infinitely many regions where the end of inflation (reheating) is delayed until arbitrarily late times. The geometry of…
We give an introduction to the cosmological multiverse, aimed at an audience of artists. We discuss general relativity -- our modern theory of gravity -- and the cosmological constant, which is widely believed to be responsible for the…
A quantum theory of the universe consists of a theory of its quantum dynamics and a theory of its quantum state The theory predicts quantum multiverses in the form of decoherent sets of alternative histories describing the evolution of the…
In this paper we introduce a simple discrete stochastic model of eternal inflation that shares many of the most important features of the continuum theory as it is now understood. The model allows us to construct a multiverse and rigorously…
The idea of a multiverse -- an ensemble of universes -- has received increasing attention in cosmology, both as the outcome of the originating process that generated our own universe, and as an explanation for why our universe appears to be…