Related papers: A measure of the multiverse
I review recent progress in defining probability distributions in the inflationary multiverse.
I describe reasons to think we are living in an eternally inflating multiverse where the observable "constants" of nature vary from place to place. The major obstacle to making predictions in this context is that we must regulate 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.
The "new standard cosmology", based on the theory of inflation, has very impressive observational support. I review some outstanding problems of the new cosmology and the global view of the universe -- the multiverse -- that it suggests. I…
We explore the idea that the dynamics of the inflationary multiverse is encoded in its future boundary, where it is described by a lower dimensional theory which is conformally invariant in the UV. We propose that a measure for the…
Theory testing in the physical sciences has been revolutionized in recent decades by Bayesian approaches to probability theory. Here, I will consider Bayesian approaches to theory extensions, that is, theories like inflation which aim to…
In the present paper we show that the functor of idempotent probability measures satisfies all of conditions with an additional claim of uniform metrizability of functors.
This paper is devoted to the introduction and study of a new family of multivariate elicitable risk measures. We call the obtained vector-valued measures multivariate expectiles. We present the different approaches used to construct our…
A measure of complexity based on a probabilistic description of physical systems is proposed. This measure incorporates the main features of the intuitive notion of such a magnitude. It can be applied to many physical situations and to…
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…
In this lecture I will review some recent progress in improving the accuracy of the calculation of density perturbations resulting from inflation.
I explore the use of sets of probability measures as a representation of uncertainty.
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…
We investigate the measure problem in the framework of inflationary cosmology. The measure of the history space is constructed and applied to inflation models. Using this measure, it is shown that the probability for the generalized single…
A suitable scalar metric can help measure multi-calibration, defined as follows. When the expected values of observed responses are equal to corresponding predicted probabilities, the probabilistic predictions are known as "perfectly…
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"…
This paper is intended to offer a pedagogical treatment of cosmological modeling and inflationary cosmology. In recent years, inflation has become accepted as a standard scenario making predictions that are testable by observations of the…
This article gives a brief overview of the status of attempts to constrain inflation using observations, and examines prospects for future developments.
Evidence for fine-tuning of physical parameters suitable for life can perhaps be explained by almost any combination of providence, coincidence or multiverse. A multiverse usually includes parts unobservable to us, but if the theory for it…
We generalize the notion of monetary value measures developed with category theory in [Adachi, 2014] by extending their base category from the category \c{hi} to the category of probability spaces Prob introduced in [Adachi and Ryu, 2016].