Gauging Fine-Tuning

TL;DR

This paper develops a mathematical framework to quantify fine-tuning in physical models, providing measures applicable to diverse settings and illustrating them with astrophysical examples involving dark matter and cosmic inflation.

Contribution

It introduces a novel formalism for measuring fine-tuning, encompassing local and global perspectives, applicable to models with multiple observables and parameters.

Findings

Quantifies fine-tuning in dark matter models with primordial black holes.

Analyzes fine-tuning in cosmic inflation scenarios affecting habitable dark-matter halos.

Provides a general mathematical framework for diverse physical systems.

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.