Related papers: Uniform probability in cosmology
We report an inconsistency found in probability theory (also referred to as measure-theoretic probability). For probability measures induced by real-valued random variables, we deduce an "equality" such that one side of the "equality" is a…
In this paper, we give a possible solution to the cosmological constant problem. It is shown hat the traditional approach, based on volume weighting of probabilities, leads to an incoherent onclusion: the probability that a randomly chosen…
The probability of there being sufficient inflation to solve the fine-tuning associated with the horizon and flatness problems has recently been shown to be exponentially small, within the context of classical general relativity. Here this…
The idea of a multiverse -- an ensemble of universes or universe domains -- 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…
An unresolved question in inflationary cosmology is the assignment of probabilities to different types of events that can occur in the eternally inflating multiverse. We explore the possibility that the resolution of this "measure problem"…
We show that most of cutoff measures of the multiverse violate some of the basic properties of probability theory when applied repeatedly to predict the results of local experiments. Starting from minimal assumptions, such as Markov…
In the history of cosmology physical paradoxes played important role for development of contemporary world models. Within the modern standard cosmological model there are both observational and conceptual cosmological paradoxes which…
There has not been an established mathematical measure of evidence. Some Bayesians have argued that probability can be an objectively correct measure of ``rational degrees of belief,'' which we do not distinguish from evidence. However,…
We consider the measure problem in standard slow-roll inflationary models from the perspective of loop quantum cosmology (LQC). Following recent results by Ashtekar and Sloan, we study the probability of having enough e-foldings and focus…
Cosmology contributes a good deal to the investigation of variation of fundamental physical constants. High resolution data is available and allows for detailed analysis over cosmological distances and a multitude of methods were developed.…
A comparison of the standard models in particle physics and in cosmology demonstrates that they are not compatible, though both are well established. Basics of modern cosmology are briefly reviewed. It is argued that the measurements of the…
We present an elementary account of mathematical cosmology through a series of important unsolved problems. We introduce the fundamental notion of `a cosmology' and focus on the issue of singularities as a theme unifying many current,…
The matching of our epoch of existence with the approximate equality of dark energy and dark matter energy densities is an apparent further fine-tuning, beyond the already troubling 120 orders of magnitude that separate dark energy from the…
Models of inflationary cosmology can lead to variation of observable parameters ("constants of Nature") on extremely large scales. The question of making probabilistic predictions for today's observables in such models has been investigated…
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…
The measure problem of cosmology is how to obtain normalized probabilities of observations from the quantum state of the universe. This is particularly a problem when eternal inflation leads to a universe of unbounded size so that there are…
The universe we observe is homogeneous on super-horizon scales, leading to the ``cosmic homogeneity problem''. Inflation alleviates this problem but cannot solve it within the realm of conservative extrapolations of classical physics. A…
After commenting briefly on the role of the typicality assumption in science, we advocate a phenomenological approach to the cosmological measure problem. Like any other theory, a measure should be simple, general, well-defined, and…
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…
It is commonly stated that we have entered the era of precision cosmology in which a number of important observations have reached a degree of precision, and a level of agreement with theory, that is comparable with many Earth-based physics…