Related papers: Testing the Multiverse: Bayes, Fine-Tuning and Typ…
Valid ideas that physical reality is vastly larger than human perception of it, and that the perceived part may not be representative of the whole, exist on many levels and have a long history. After a brief general inventory of those ideas…
Cosmological observations are beginning to reach a level of precision that allow us to test some of the most fundamental assumptions in our working model of the Universe. One such an assumption is that gravity is governed by the General…
We discuss the possibility that the inflationary paradigm, undoubtfully today's best framework to understand all the present cosmological data, may still have some viable challengers. The underlying idea for such discussions is that…
The theory of cosmological perturbations is the main tool which connects theories of the early universe (based on new fundamental physics such as string theory) with cosmological observations. In these lectures, I will provide an…
I motivate and discuss some recent work on theories with varying constants, and consider some possible observational consequences and tests. Particular emphasis is given to models which can (almost) exactly mimic the predictions of standard…
Bayesian probability theory is used to analyze the oft-made assumption that humans are typical observers in the universe. Some theoretical calculations make the {\it selection fallacy} that we are randomly chosen from a class of objects by…
The Standard Model of Particle Physics has been verified to unprecedented precision in the last few decades. However there are still phenomena in nature which cannot be explained, and as such new theories will be required. Since terrestrial…
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…
We review some of the common methods for model selection: the goodness of fit, the likelihood ratio test, Bayesian model selection using Bayes factors, and the classical as well as the Bayesian information theoretic approaches. We…
Bayesian statistics is based on the subjective definition of probability as {\it ``degree of belief''} and on Bayes' theorem, the basic tool for assigning probabilities to hypotheses combining {\it a priori} judgements and experimental…
In this work we present a brief discussion about modified and extended cosmological models using current observational tests. We show that according to these astrophysical samples based in late universe measurements, theories like $f(R)$…
Observational tests during the next decade may determine if the evolution of the Universe can be understood from fundamental physical principles, or if special initial conditions, coincidences, and new, untestable physical laws must be…
We are on the verge of the first precision testing of the inflationary cosmology as a model for the origin of structure in the Universe. I review the key predictions of inflation which can be used as observational tests, in the sense of…
Bayesian hypothesis testing is investigated when the prior probabilities of the hypotheses, taken as a random vector, are quantized. Nearest neighbor and centroid conditions are derived using mean Bayes risk error as a distortion measure…
The physical processes that determine the properties of our everyday world, and of the wider cosmos, are determined by some key numbers: the 'constants' of micro-physics and the parameters that describe the expanding universe in which we…
The idea of a multiverse -- an ensemble of universes -- 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 universe appears to be…
In this thesis we will primarily demonstrate how additional scalar degrees of freedom - which are motivated from many high-energy embeddings - open up new observational windows onto the physics of inflation. We construct a Bayesian…
Inflation is a bold and expansive extension of the Standard Cosmology. It holds the promise to extend our understanding of the Universe to within 10^{-32}sec of the big bang and answer most of the pressing questions in cosmology. Its…
Bayesian Inference is a powerful approach to data analysis that is based almost entirely on probability theory. In this approach, probabilities model {\it uncertainty} rather than randomness or variability. This thesis is composed of a…
Probability theory can be modified in essentially one way while maintaining consistency with the basic Bayesian framework. This modification results in copies of standard probability theory for real, complex or quaternion probabilities.…