Gauging Fine-Tuning

Understand

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.