Related papers: The Continuum of Discrete Trajectories in Eternal …
An eternally inflating universe produces an infinite amount of spatial volume, so every possible event happens an infinite number of times, and it is impossible to define probabilities in terms of frequencies. This problem is usually…
The definition of probabilities in eternally inflating universes requires a measure to regulate the infinite spacetime volume, and much of the current literature uses a global time cutoff for this purpose. Such measures have been found to…
Eternal inflation is a seemingly generic consequence of theories that give rise to accelerated expansion of the universe and possess multiple vacuum states. Making predictions in an eternally inflating universe is notoriously difficult…
Probabilities in eternal inflation are traditionally defined as limiting frequency distributions, but a unique and unambiguous probability measure remains elusive. In this paper, we present a different approach, based on Bayesian reasoning.…
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"…
The basic workings of inflationary models are summarized, along with the arguments that strongly suggest that our universe is the product of inflation. I describe the quantum origin of density perturbations, giving a heuristic derivation of…
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…
We study various probability measures for eternal inflation by applying their regularization prescriptions to models where inflation is not eternal. For simplicity we work with a toy model describing inflation that can interpolate between…
We use the stochastic approach to investigate the measure for slow roll eternal inflation. The probability for the universe of a given Hubble radius can be calculated in this framework. In a solvable model, it is shown that the probability…
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 basic workings of inflationary models are summarized, along with the arguments that strongly suggest that our universe is the product of inflation. The mechanisms that lead to eternal inflation in both new and chaotic models are…
The basic workings of inflationary models are summarized, along with the arguments that strongly suggest that our universe is the product of inflation. The mechanisms that lead to eternal inflation in both new and chaotic models are…
I summarize the arguments that strongly suggest that our universe is the product of inflation. The mechanisms that lead to eternal inflation in both new and chaotic models are described. Although the infinity of pocket universes produced by…
In recent literature on eternal inflation, a number of measures have been introduced which attempt to assign probabilities to different pocket universes by counting the number of each type of pocket according to a specific procedure. We…
Problems with uniform probabilities on an infinite support show up in contemporary cosmology. This paper focuses on the context of inflation theory, where it complicates the assignment of a probability measure over pocket universes. The…
An improved volume-weighted probability measure for eternal inflation is proposed. For the models studied in this paper it leads to simple and intuitively expected gauge-invariant results.
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…
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 consider the eternal inflation scenario of the slow-roll/chaotic type with the additional element of an objective collapse of the wave function. The incorporation of this new agent to the traditional inflationary setting might represent…
Lecture notes as per the title. In the first part, the concepts of a measurable space, measurable maps between measurable spaces and that of a measure on a measurable space are introduced, after which the fundamentals of the theory of…