Related papers: Measures for a Multidimensional Multiverse
Predictions in an eternally inflating multiverse are meaningless unless we specify the probability measure. The scale-factor cutoff is perhaps the simplest and most successful measure which avoid catastrophic problems such as the youngness…
We present a simple method for assessing the predictive performance of high-dimensional models directly in data space when only samples are available. Our approach is to compare the quantiles of observables predicted by a model to those of…
Fundamental to our understanding of planetary bulk compositions is the relationship between their masses and radii, two properties that are often not simultaneously known for most exoplanets. However, while many previous studies have…
In theories in which the cosmological constant Lambda takes a variety of values in different ``subuniverses,'' the probability distribution of its observed values is conditioned by the requirement that there must be someone to measure it.…
The CAH+ measure regulates the infinite spacetime volume of the multiverse by constructing a surface of constant comoving apparent horizon (CAH) and then removing the future lightcones of all points on that surface (the latter prescription…
We endeavour to estimate numerous multi-dimensional means of various probability distributions on a common space based on independent samples. Our approach involves forming estimators through convex combinations of empirical means derived…
Context. Explaining the accelerated expansion of the Universe is one of the fundamental challenges in physics today. Cosmography provides information about the evolution of the universe derived from measured distances, assuming only that…
In a spatially flat Friedmann-Lema\^{i}tre-Robertson-Walker universe, we investigate a unified cosmic fluid scenario endowed with bulk viscosity in which the coefficient of the bulk viscosity has a power law evolution. The power law in the…
Likelihood fitting to two-point clustering statistics made from galaxy surveys usually assumes a multivariate normal distribution for the measurements, with justification based on the central limit theorem given the large number of…
Voids are dominant features of the cosmic web. We revisit the cosmological information content of voids and connect void properties with the parameters of the background universe. We combine analytical results with a suite of large n-body…
Weinberg et al. calculated the anthropic likelihood of the cosmological constant using a model assuming that the number of observers is proportional to the total mass of gravitationally collapsed objects, with mass greater than a certain…
Spatial curvature is one of the fundamental cosmological parameters that is routinely constrained from observations. The forward modelling of observations, in particular of large-scale structure, often relies on large cosmological…
The fully general calculation of the cosmic error on N-point correlation functions and related quantities is presented. More precisely, the variance caused by the finite volume, discreteness, and edge effects is determined for {\em any}…
We consider the statistical analysis of data on high-dimensional spheres and shape spaces. The work is of particular relevance to applications where high-dimensional data are available--a commonly encountered situation in many disciplines.…
For a given spatial distribution of the lenses and distribution of the transverse velocity of the lens relative to the line-of-sight, a probability distribution for the lens mass for a single observed event is derived. In addition, similar…
We discuss how, in a Universe restricted to the causal region connected to the observer, General Relativity implies the quantum nature of physical phenomena and directly leads to a string theory scenario, whose dynamics is ruled by a…
After reviewing the cosmological constant problem - why is Lambda not huge? - I outline the two basic approaches that had emerged by the late 1980s, and note that each made a clear prediction. Precision cosmological experiments now indicate…
For known gravitational lens systems the redshift distribution of the lenses is compared with theoretical expectations for $10^{4}$~Friedmann-Lema\^\i tre~cosmological models, which more than cover the range of possible cases. The…
The study of measurements in quantum mechanics exposes many of the ways in which the quantum world is different. For example, one of the hallmarks of quantum mechanics is that observables may be incompatible, implying among other things…
A 2D foam can be characterised by its distribution of bubble areas, and of number of sides. Both distributions have an average and a width (standard deviation). There are therefore at least two very different ways to characterise the…