Related papers: Measures for a Transdimensional Multiverse
The 2015 Planck data release tightened the region of the allowed inflationary models. Inflationary models with convex potentials have now been ruled out since they produce a large tensor to scalar ratio. Meanwhile the same data offers…
A wide variety of vacua, and their cosmological realization, may provide an explanation for the apparently anthropic choices of some parameters of particle physics and cosmology. If the probability on various parameters is weighted by…
We propose a new scenario of nonequilibirum multiverse. We quantified the potential landscape and the flux landscape for the Bousso-Polchinski type of multiverse. The potential landscape quantifies the weight of each universe. When the…
A four-dimensional universe, arising from a flux compactification of Type IIB string theory, contains scalar fields with a potential determined by topological and geometric parameters of the internal -hidden- dimensions. We show that…
Spherical symmetry arguments are used to produce a general device to convert identities and inequalities for the $p$th absolute moments of real-valued random variables into the corresponding identities and inequalities for the $p$th moments…
For a positive measure set of nonuniformly expanding quadratic maps on the interval we effect a multifractal formalism, i.e., decompose the phase space into level sets of time averages of a given observable and consider the associated {\it…
We discuss eternal inflation in context of classical probability spaces defined by a triplet: sample space, $\sigma$-algebra and probability measure. We show that the measure problem is caused by the countable additivity axiom applied to…
As is known, factor analysis is a popular method to reduce dimension for high-dimensional data. For matrix data, the dimension reduction can be more effectively achieved through both row and column directions. In this paper, we introduce a…
A Multiverse can arise from landscapes without de Sitter minima. It can be populated during a period of eternal inflation without trans-Planckian field excursions and without flat potentials. This Multiverse can explain the values of the…
In the context of eternal inflation, cosmological predictions depend on the choice of measure to regulate the diverging spacetime volume. The spectrum of inflationary perturbations is no exception, as we demonstrate by comparing the…
Multiplicative invariance is a well-studied property of subsets of the unit interval. The theory in the complex plane is less developed. This paper introduces an analogous definition for multiplicative invariance in the complex plane…
In this work the role of extra dimensions in the accelerated universe through the scenario of higher-dimensional Friedmann-Robertson-Walker (FRW) cosmology has been studied. For this purpose, we first consider warped space-time in the…
Quantum gravitational effects may affect the large scale dynamics of the universe. Phenomenologically, quantum gravitational effect at large distances can be encoded in an extended uncertainty principle that admits a minimal measurable…
A new moving domain wall solution is obtained for a flat 3-universe. This consists of a bulk metric depending on both time and the extra coordinate, plus a dynamically interacting domain wall, admitted by the metric and inhabited by the…
In this paper we consider the implications of the "landscape" paradigm for the large scale properties of the universe. The most direct implication of a rich landscape is that our local universe was born in a tunnelling event from a…
We present a measure-theoretic condition for a property to hold ``almost everywhere'' on an infinite-dimensional vector space, with particular emphasis on function spaces such as $C^k$ and $L^p$. Like the concept of ``Lebesgue almost…
We show that the geometry of cutoffs on eternal inflation strongly constrains predictions for the timescales of vacuum domination, curvature domination, and observation. We consider three measure proposals: the causal patch, the fat…
We present a multifractal formalism for measures on infinite dimensional metric spaces, in terms of scales instead of dimensions in the classical multifractal analysis. We prove a multifractal formalism with a suitable scaling, called…
In the standard model of universe the increase in mass of our observed expansive and isotropic relativistic Universe is explained by the hypothetical assumption of matter objects emerging on the horizon (of the most remote visibility).…
The implications of string theory for understanding the dimension of decompactified spacetime are discussed. Results from a computer model designed to simulate expansion of the early universe during the string dominated phase are presented.…