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Is it possible to know cosmological fine-tuning?

Daniel Andrés Díaz-Pachón, Ola Hössjer, Calvin Mathew

Abstract

Fine-tuning studies whether some physical parameters, or relevant ratios between them, are located within so-called life-permitting intervals of small probability outside of which carbon-based life would not be possible. Recent developments have found estimates of these probabilities that circumvent previous concerns of measurability and selection bias. However, the question remains if fine-tuning can indeed be known. Using a mathematization of the epistemological concepts of learning and knowledge acquisition, we argue that most examples that have been touted as fine-tuned cannot be formally assessed as such. Nevertheless, fine-tuning can be known when the physical parameter is seen as a random variable and it is supported in the nonnegative real line, provided the size of the life-permitting interval is small in relation to the observed value of the parameter.

Is it possible to know cosmological fine-tuning?

Abstract

Fine-tuning studies whether some physical parameters, or relevant ratios between them, are located within so-called life-permitting intervals of small probability outside of which carbon-based life would not be possible. Recent developments have found estimates of these probabilities that circumvent previous concerns of measurability and selection bias. However, the question remains if fine-tuning can indeed be known. Using a mathematization of the epistemological concepts of learning and knowledge acquisition, we argue that most examples that have been touted as fine-tuned cannot be formally assessed as such. Nevertheless, fine-tuning can be known when the physical parameter is seen as a random variable and it is supported in the nonnegative real line, provided the size of the life-permitting interval is small in relation to the observed value of the parameter.
Paper Structure (16 sections, 4 theorems, 36 equations, 1 table, 1 algorithm)

This paper contains 16 sections, 4 theorems, 36 equations, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Mathematical Framework for Learning and Knowledge Acquisition
  3. Learning and Knowledge in Cosmology
  4. On Knowing Fine-tuning
  5. The crucial choice of F
  6. Random distributions
  7. Bounded parameter space
  8. The real line as parameter space
  9. Positive line as parameter space
  10. Examples
  11. Critical density of the universe
  12. Gravitational force
  13. Higgs Vacuum Expectation Value
  14. Amplitude of primordial fluctuations
  15. Baryon-Photon Ratio
  16. ...and 1 more sections

Key Result

Theorem 1

The proposition can be fully learned and known. A sufficient condition for learning and knowledge acquisition of $p_1$, compared to an ignorant person, is having $\mathrm{TP}_{\max}<1$.

Theorems & Definitions (18)

  • Definition 1: Fine-tuning
  • Remark 1
  • Definition 2: Learning
  • Remark 2
  • Definition 3: Knowledge
  • Remark 3
  • Theorem 1
  • proof
  • Remark 4
  • Theorem 2
  • ...and 8 more