Related papers: Probabilities in the landscape
In this paper, we show how the structure of the landscape potential of the primordial Universe may be probed through the properties of the primordial density perturbations responsible for the origin of the cosmic microwave background…
In this paper we introduce a new probability distribution on (0,1), associated with the I-function, namely, the I-function distribution. This distribution generalizes several known distributions with positive support. It is also shown that…
Recent approaches to the problem of inferring a continuous probability distribution from a finite set of data have used a scalar field theory for the form of the prior probability distribution. This letter presents a more general form for…
This Colloquium reviews statistical models for money, wealth, and income distributions developed in the econophysics literature since the late 1990s. By analogy with the Boltzmann-Gibbs distribution of energy in physics, it is shown that…
Slowroll after tunneling is a crucial step in one popular framework of the multiverse---false vacuum eternal inflation (FVEI). In a landscape with a large number of fields, we provide a heuristic estimation for its probability. We find that…
The paper investigates the historical and contemporary pursuit-worthiness of cosmic inflation-the rationale for working on it (rather than necessarily the evidential support for claims to its approximate truth): what reasons existed, and…
In many applications of the probabilistic method, one looks to study phenomena that occur ``with high probability''. More recently however, in an attempt to understand some of the most fundamental problems in combinatorics, researchers have…
We offer some summation formulas that appear to have great utility in probability theory. The proofs require some recent results from analysis that have thus far been applied to basic hypergeometric functions.
It is fair to say that the deepest mystery in our understanding of nature is the birth of our universe. Much of the dilemma over the last decades comes from the extraordinarily small probability that the universe started with the high…
We provide an introduction to selected recent advances in the mathematical understanding of Einstein's theory of gravitation.
We study boundary crossing probability in the context of stochastic inflation. We prove that for a generic multi-field inflationary potential, the probability that the inflaton reaches infinitely far regions in the field space is critically…
This article discusses density perturbations in inflationary models, offering a pedagogical description of how these perturbations are generated by quantum fluctuations in the early universe. A key feature of inflation is that that rapid…
Because of their quantum fluctuations, axion fields had a chance to experience field excursions traversing many minima of their potentials during inflation. We study this situation by analyzing the dynamics of an axion-spectator field…
In this short review, the predictions of inflation are presented and compared to the most recent measurements of the Cosmic Microwave Background (CMB) anisotropy. It is argued that inflation is compatible with these observations but that…
An introductory account is given of the inflationary cosmology, which postulates a period of accelerated expansion during the Universe's earliest stages. The historical motivation is briefly outlined, and the modelling of the inflationary…
In this paper, we propose a new class of distributions by exponentiating the random variables associated with the probability density functions of composite distributions. We also derive some mathematical properties of this new class of…
After 25 years of its existence, inflationary theory gradually becomes the standard cosmological paradigm. However, we still do not know which of the many versions of inflationary cosmology will be favored by the future observational data.…
We propose a new class of inflationary models in which inflation takes place while the inflaton is climbing up a potential hill due to a coupling to gravity. We study their attractor behavior, and investigate its relation with known…
The Kolmogorov axioms for probability functions are placed in the context of signed meadows. A completeness theorem is stated and proven for the resulting equational theory of probability calculus. Elementary definitions of probability…
The standard model of cosmology is based on the hot Big Bang theory and the inflationary paradigm. Recent precise observations of the temperature and polarization anisotropies in the cosmic microwave background and the matter distribution…