Gauging Fine-Tuning

Abstract

We introduce a mathematical framework for quantifying fine-tuning in general physical settings. In particular, we identify two distinct perspectives on fine-tuning, namely, a local and a global perspective --- and develop corresponding measures. These measures apply broadly to settings characterized by an arbitrary number of observables whose values are dependent on an arbitrary number of parameters. We illustrate our formalism by quantifying fine-tuning as it arises in two pertinent astrophysical settings: (i) in models where a significant fraction of the dark matter in the universe is in the form of primordial black holes, and (ii) in scenarios that derive the fraction of protons in habitable dark-matter halos from underlying models of cosmic inflation.

13 pages, 6 figures

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Cited by in corpus (7)

• On the Primordial Black Hole Mass Function for Broad Spectra
• Primordial black holes from single-field inflation: a fine-tuning audit
• Do we need fine-tuning to create primordial black holes?
• Exploring primordial black holes and gravitational waves with R-symmetric GUT Higgs inflation
• Extreme Primordial Black Holes
• Lectures on Naturalness, String Landscape and Multiverse
• Development of generic no-scale inflation