TY - JOUR

T1 - Is cosmological tuning fine or coarse?

AU - Díaz-Pachón, Daniel Andrés

AU - Hössjer, Ola

AU - Marks, Robert J.

N1 - Publisher Copyright:
© 2021 IOP Publishing Ltd and Sissa Medialab.

PY - 2021/7

Y1 - 2021/7

N2 - 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.

AB - 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.

KW - gravity

KW - initial conditions and eternal universe

KW - physics of the early universe

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U2 - 10.1088/1475-7516/2021/07/020

DO - 10.1088/1475-7516/2021/07/020

M3 - Article

AN - SCOPUS:85111494159

VL - 2021

JO - Journal of Cosmology and Astroparticle Physics

JF - Journal of Cosmology and Astroparticle Physics

SN - 1475-7516

IS - 7

M1 - 020

ER -