Is Cosmological Tuning Fine or Coarse?

TL;DR

This paper uses a Bayesian MaxEnt approach to assess the probability of cosmological fine-tuning, providing an invariant upper bound that depends on the relative size of life-permitting intervals, with applications to various constants.

Contribution

It introduces a Bayesian MaxEnt framework to evaluate cosmological tuning probabilities, ensuring invariance and respecting the weak anthropic principle.

Findings

The ratio of gravitational constant to Hubble constant squared appears finely tuned.

The amplitude of primordial fluctuations is not finely tuned.

The approach is general and applicable to various cosmological constants.

Abstract

The fine-tuning of the universe for life, the idea that the constants of nature (or ratios between them) must belong to very small intervals in order for life to exist, has been debated by scientists for several decades. Several criticisms have emerged concerning probabilistic measurement of life-permitting intervals. Herein, a Bayesian statistical approach is used to assign an upper bound for the probability of tuning, which is invariant with respect to change of physical units, and under certain assumptions it is small whenever the life-permitting interval is small on a relative scale. The computation of the upper bound of the tuning probability is achieved by first assuming that the prior is chosen by the principle of maximum entropy (MaxEnt). The unknown parameters of this MaxEnt distribution are then handled in such a way that the weak anthropic principle is not violated. The MaxEnt assumption is "maximally noncommittal with regard to missing information." This approach is sufficiently general to be applied to constants of current cosmological models, or to other constants possibly under different models. Application of the MaxEnt model reveals, for example, that the ratio of the universal gravitational constant to the square of the Hubble constant is finely tuned in some cases, whereas the amplitude of primordial fluctuations is not.