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Measure and Probability in Cosmology by Schiffrin, Joshua S.; Wald, Robert M. is a scholarly article available to read on EtoBox.

What is Measure and Probability in Cosmology about?

General relativity has a Hamiltonian formulation, which formally provides a canonical (Liouville) measure on the space of solutions. In ordinary statistical physics, the Liouville measure is used to compute probabilities of macrostates, and it would seem natural to use the similar measure arising in general relativity to compute probabilities in cosmology, such as the probability that the universe underwent an era of inflation. Indeed, a number of authors have used the restriction of this measure to the space of homogeneous and isotropic universes with scalar field matter (minisuperspace)---namely, the Gibbons-Hawking-Stewart measure---to make arguments about the likelihood of inflation. We argue here that there are at least four major difficulties with using the measure of general relativity to make probability arguments in cosmology: (1) Equilibration does not occur on cosmological length scales. (2) Even in the minisuperspace case, the measure of phase space is infinite and the computation of probabilities depends very strongly on how the infinity is regulated. (3) The inhomogeneous degrees of freedom must be taken into account (we illustrate how) even if one is interested only

Author

Schiffrin, Joshua S.; Wald, Robert M.

Published

2012

Language

EN