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Measure, Topology and Probabilistic Reasoning in Cosmology

Curiel, Erik (2014) Measure, Topology and Probabilistic Reasoning in Cosmology. [Preprint]

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Abstract

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
spaces, working through many examples from cosmology. I focus on
the relation of topological to measure-theoretic notions of and
relating to probability, how they diverge in unpleasant ways in the
infinite-dimensional case, and are even difficult to work with on
their own. Even in cases where an appropriate family of spacetimes
is finite-dimensional, and so admits a measure of the relevant sort,
however, it is always the case that the family is not a compact
topological space, and so does not admit a physically significant,
well behaved probability measure. Problems of a different but still
deeply troubling sort plague arguments about likelihood in that
context, which I also discuss. I conclude that most standard forms
of argument used in cosmology to estimate the likelihood of the
occurrence of various properties or behaviors of spacetimes have
serious mathematical, physical and conceptual problems.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Curiel, Erikerik@strangebeautiful.com
Additional Information: Submitted to *Foundations of Physics*
Keywords: cosmology probability infinite-dimensional spaces measure theory topology anthropic arguments typicality
Subjects: Specific Sciences > Physics > Cosmology
Specific Sciences > Mathematics
Specific Sciences > Probability/Statistics
Specific Sciences > Physics > Relativity Theory
Depositing User: Dr. Erik Curiel
Date Deposited: 16 Sep 2015 13:04
Last Modified: 16 Sep 2015 13:04
Item ID: 11677
Subjects: Specific Sciences > Physics > Cosmology
Specific Sciences > Mathematics
Specific Sciences > Probability/Statistics
Specific Sciences > Physics > Relativity Theory
Date: 2014
URI: http://philsci-archive.pitt.edu/id/eprint/11677

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