Related papers: Measure and Probability in Cosmology
The Hamiltonian structure of general relativity provides a natural canonical measure on the space of all classical universes, i.e., the multiverse. We review this construction and show how one can visualize the measure in terms of a…
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…
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…
I explain the difficulty of making various concepts of and relating to probability precise, rigorous and physically significant when attempting to apply them in reasoning about objects (e.g., spacetimes) living in infinite-dimensional…
One of the most frustrating issues in early universe cosmology centers on how to reconcile the vast choice of universes in string theory and in its most plausible high energy sibling, eternal inflation, that jointly generate the string…
The assumption that a complete description of an early state of the universe does not privilege any position or direction in space leads to a unified account of probability in cosmology, macroscopic physics, and quantum mechanics. Such a…
Using a Liouville measure, similar to the one proposed recently by Gibbons and Turok, we investigate the probability that single-field inflation with a polynomial potential can last long enough to solve the shortcomings of the standard hot…
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…
Quantum mechanics introduces the concept of probability at the fundamental level, yielding the measurement problem. On the other hand, recent progress in cosmology has led to the "multiverse" picture, in which our observed universe is only…
Probabilities for observations in cosmology are conditioned both on the universe's quantum state and on local data specifying the observational situation. We show the quantum state defines a measure for prediction through such conditional…
The total canonical (Liouville-Henneaux-Gibbons-Hawking-Stewart) measure is finite for completely nonsingular Friedmann-Lemaitre-Robertson-Walker classical universes with a minimally coupled massive scalar field and a positive cosmological…
We explore the phenomenological implications of generalizing measures to a multidimensional multiverse. We consider a simple model in which the vacua are nucleated from a $D$-dimensional parent spacetime through dynamical compactification…
Anomaly-free perturbations of loop quantum cosmology reveal a deformed space-time structure, in which the signature changes when the energy density is $\rho=\rho_c/2$. Furthermore, in loop quantum cosmology, one can obtain an effective…
At the minisuperspace level of homogeneous models, the bare probability for a classical universe has a huge peak at small universes for the Hartle-Hawking `no-boundary' wavefunction, in contrast to the suppression at small universes for the…
Inflationary cosmology attempts to provide a natural explanation for the flatness and homogeneity of the observable universe. In the context of reversible (unitary) evolution, this goal is difficult to satisfy, as Liouville's theorem…
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…
Inflation predicts that quantum fluctuations determine the large scale structure of the Universe. This raises the striking possibility that quantum mechanics, developed to describe nature at short distances, can be tested by studying nature…
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…
The measure problem of cosmology is how to assign normalized probabilities to observations in a universe so large that it may have many observations occurring at many different spacetime locations. I have previously shown how the Boltzmann…
Modern scientific cosmology pushes the boundaries of knowledge and the knowable. This is prompting questions on the nature of scientific knowledge. A central issue is what defines a 'good' model. When addressing global properties of the…