Allowed Ranges and Priors for Fundamental Parameters in Fine‑Tuning Analyses

Determine whether the Planck mass scale provides the correct cutoff for parameter values considered in fine‑tuning studies, ascertain the actual span of allowed values for other fundamental parameters, and characterize whether the prior probability distribution over these allowed values is uniform or otherwise.

Background

Quantifying fine‑tuning probabilistically depends on defining a finite, well‑motivated parameter space and a prior over it. The paper highlights that assuming infinite ranges renders probabilities ill‑defined, motivating suggestions to restrict ranges (e.g., below the Planck scale).

However, the appropriateness of such cutoffs, the true span of allowed values for other parameters, and the correct prior over those values remain unsettled, undermining precise fine‑tuning estimates.

References

However, it is unclear whether the Planck scale is the correct cut-off point, exactly what span of values is actually possible for other parameters, and whether all allowed values have the same a priori probability (Adams 2019, 97-100; Hossenfelder 2021).

— Does a Fine-Tuned Universe Tell Us Anything About God?  (2502.12083 - Hincks, 12 Feb 2025) in Section: The Difficulty in Quantifying Fine-Tuning

Finally, for more general axion-like fields, the space of possible masses, decay constants, and couplings is enormous. Unless a distribution or selection principle can be derived from a more fundamental theory (e.g., from a specified string compactification), selecting an axion-like particle as DM risks appearing ad hoc. In this respect, the challenge is again whether the `successful region’ of parameter space is sufficiently typical to satisfy Generalised Copernicanism.

— Dark Matters of Principle: Principles in the Dark Matter Paradigm  (2608.25954 - Duerr et al., 26 Aug 2026) in Section 4, subsection “Axions,” paragraph “Regulative principles,” item “Generalised Copernicanism”