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| measure problem (cosmology) | |
|---|---|
| Name | measure problem (cosmology) |
| Field | Cosmology |
| Introduced | 1980s |
| Notable people | Alan Guth, Andrei Linde, Steven Weinberg, Alexander Vilenkin |
measure problem (cosmology)
The measure problem in cosmology concerns how to assign probabilities to observations in models with infinite or extremely large multiverse ensembles such as Eternal inflation, the string theory landscape, and cosmological scenarios proposed by Alan Guth, Andrei Linde, Alexander Vilenkin, Steven Weinberg, and others. It arises when comparing predictions of inflationary cosmology, quantum cosmology, and string theory to data from missions like Planck (spacecraft), Wilkinson Microwave Anisotropy Probe, and observatories including Hubble Space Telescope, Very Large Telescope, and Keck Observatory. The problem connects to debates involving the anthropic principle, the cosmological constant problem, and probability measures used in statistical interpretations of multiverse models advanced by researchers at institutions such as Princeton University, Harvard University, California Institute of Technology, and University of Cambridge.
The core issue is defining a regulator or probability distribution over an infinite set of spacetime regions produced by mechanisms like Eternal inflation and the string theory landscape, where parameters such as the cosmological constant, baryon-to-photon ratio, and properties of fundamental particles can vary among pocket universes. Prominent contributors including Alan Guth, Andrei Linde, Alexander Vilenkin, Steven Weinberg, and Raphael Bousso have emphasized that naive counting yields ambiguities analogous to paradoxes studied by Georg Cantor in set theory and by probabilists at Princeton University and University of Cambridge. Observationally relevant comparisons involve datasets from Planck (spacecraft), Sloan Digital Sky Survey, and Supernova Cosmology Project.
Early recognition of measure ambiguities traces to investigations of cosmic inflation in the 1980s by Alan Guth and later formalization by Andrei Linde and Alexander Vilenkin during the 1980s and 1990s. Debates intensified with the formulation of the string theory landscape by Leonard Susskind and others in the 2000s, and with anthropic reasoning advocated by Steven Weinberg and critiqued by figures at Perimeter Institute and Institute for Advanced Study. Key episodes include the prediction of the cosmological constant magnitude influenced by anthropic arguments, discussions at conferences such as those hosted by Perimeter Institute and workshops involving Raphael Bousso, Joe Polchinski, and Michael Douglas, and formal treatments in papers by Alan Guth, Andrei Linde, Alexander Vilenkin, Raphael Bousso, Juan Maldacena, and Edward Witten.
Various regulators and measures have been proposed: the proper-time cutoff, scale-factor cutoff, light-cone time cutoff, causal diamond measure, comoving-volume measures, and the pocket-based counting measures developed by Andrei Linde and Alexander Vilenkin. Mathematicians and physicists drawing on methods from Georg Cantor-inspired set theory, measure theory at University of Cambridge, and ergodic arguments by researchers at California Institute of Technology have contrasted global versus local measures. Formal frameworks utilize techniques reminiscent of canonical quantization by Paul Dirac and path-integral approaches related to work by Richard Feynman and Stephen Hawking. Implementations engage mathematical objects studied by John von Neumann and probability theorists historically associated with Princeton University.
Prominent prescriptions include the scale-factor cutoff suggested by Alexander Vilenkin and collaborators, the causal diamond measure advocated by Raphael Bousso and Ben Freivogel, the stationary measure proposal explored by Alan Guth and Andrei Linde, and anthropic selection rules inspired by Steven Weinberg and debates around the anthropic principle as discussed by Brandon Carter. Alternative approaches involve invoking the holographic principle developed by Gerard 't Hooft and Leonard Susskind, quantum cosmology proposals associated with James Hartle and Stephen Hawking, and Bayesian frameworks exercised by researchers at Oxford University and Harvard University. Computational studies by groups at Stanford University, Perimeter Institute, and Institute for Advanced Study have tested prescriptions against toy landscapes influenced by Michael Douglas and statistical surveys related to flux compactification scenarios by Joe Polchinski.
Different measures yield divergent predictions for quantities like the observed cosmological constant, the amplitude of primordial density fluctuations relevant to results from Planck (spacecraft), the prevalence of Boltzmann brains debated by Don Page and Sean Carroll, and the expected distribution of low-energy parameters in the Standard Model as framed by Nima Arkani-Hamed and David Gross. Choices of measure influence anthropic arguments put forward by Steven Weinberg and selection effects studied by researchers at Perimeter Institute and Santa Fe Institute. Cosmological parameter estimation using data from Planck (spacecraft), Sloan Digital Sky Survey, and Supernova Cosmology Project can be sensitive to measure assumptions, affecting inferred priors in Bayesian analyses employed at University of Cambridge and Princeton University.
Critics including researchers at Perimeter Institute, University of Oxford, and Caltech highlight that no consensus exists on a unique, well-motivated measure compatible with known physics, and concerns persist about regulator dependence, predictive power, and empirical testability. The Boltzmann brain problem raised by Don Page and Sean Carroll challenges many prescriptions, while debates remain over the role of the anthropic principle championed by Steven Weinberg versus alternatives favored by scholars at Institute for Advanced Study and Harvard University. Open questions link to foundational issues in quantum gravity explored by Edward Witten and Juan Maldacena, and to statistical properties of the string theory landscape investigated by Michael Douglas and Joe Polchinski.