×

Is cosmological tuning fine or coarse? (English) Zbl 1485.83133

Summary: 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.

MSC:

83F05 Relativistic cosmology
58J47 Propagation of singularities; initial value problems on manifolds
92B05 General biology and biomathematics
94A17 Measures of information, entropy
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] B. Carter, Large number coincidences and the anthropic principle in cosmology, Int. Astron. Union Symp.63 (1974) 291. · doi:10.1017/s0074180900235638
[2] P. Davies, The accidental universe, Cambridge University Press, Cambridge, U.K. (1982).
[3] S. Hawking, A brief history of time, Bantam Books, New York, NY, U.S.A. (1988).
[4] Hoyle, F., The universe: past and present reflections, Ann. Rev. Astron. Astrophys., 20, 1-36 (1982) · doi:10.1146/annurev.aa.20.090182.000245
[5] S. Weinberg, Life in the universe, Sci. Amer.271 (1994) 44.
[6] J.D. Barrow and F.J. Tipler, The anthropic cosmological principle, Oxford University Press, Oxford, U.K. (1988).
[7] Adams, Fred C., The degree of fine-tuning in our universe — and others, Phys. Rept., 807, 1-111 (2019) · doi:10.1016/j.physrep.2019.02.001
[8] G.F. Lewis and L.A. Barnes, A fortunate universe: life in a finely tuned cosmos, Cambridge University Press, Cambridge, U.K. (2016).
[9] Tegmark, Max; Aguirre, Anthony; Rees, Martin; Wilczek, Frank, Dimensionless constants, cosmology and other dark matters, Phys. Rev. D, 73 (2006) · doi:10.1103/PhysRevD.73.023505
[10] M.J. Rees, Just six numbers: the deep forces that shape the universe, Basic Books, New York, NY, U.S.A. (2000). · Zbl 0962.83001
[11] L.A. Barnes, A reasonable little question: a formulation of the fine-tuning argument, Ergo6 (2019) 1220. · doi:10.3998/ergo.12405314.0006.042
[12] Sandora, McCullen, Multiverse Predictions for Habitability: the Number of Stars and their Properties, Universe, 5, 149 (2019) · doi:10.3390/universe5060149
[13] Sandora, McCullen, Multiverse Predictions for Habitability: number of Potentially Habitable Planets, Universe, 5, 157 (2019) · doi:10.3390/universe5060157
[14] Sandora, McCullen, Multiverse Predictions for Habitability: fraction of Planets that Develop Life, Universe, 5, 171 (2019) · doi:10.3390/universe5070171
[15] Sandora, McCullen, Multiverse Predictions for Habitability: fraction of Life that Develops Intelligence, Universe, 5, 175 (2019) · doi:10.3390/universe5070175
[16] R. Collins, The teleological argument: an exploration of the fine-tuning of the universe, in Blackwell companion to natural theology, W.L. Craig and J.P. Moreland eds., Wiley-Blackwell, (2012), pg. 202. · doi:10.1002/9781444308334.ch4
[17] J. Bernoulli, Ars conjectandi, Thurneysen Brothers, Basel, Switzerland (1713). · JFM 30.0210.01
[18] W.A. Dembski and R.J. Marks, Bernoulli’s principle of insufficient reason and conservation of information in computer search, in 2009 IEEE international conference on systems, man and cybernetics, IEEE, October 2009, pg. 2647. · doi:10.1109/icsmc.2009.5346119
[19] W. Tschirk, The principle of indifference does not lead to contradictions, Int. J. Statist. Probabil.5 (2016) 79. · doi:10.5539/ijsp.v5n4p79
[20] T. McGrew, Probabilities and the fine-tuning argument: a sceptical view, Mind110 (2001) 1027. · doi:10.1093/mind/110.440.1027
[21] M. Colyvan, J.L. Garfield and G. Priest, Problems with the argument from fine tuning, Synthese 145 (2005) 325. · Zbl 1083.03502 · doi:10.1007/s11229-005-6195-0
[22] R. Penrose, The road to reality, Random House, U.S.A. (2004).
[23] R. Penrose, Time-asymmetry and quantum gravity, in Quantum gravity 2: a second Oxford symposium, C.J. Isham, R. Penrose and D.W. Sciama eds., Oxford University Press, Oxford, U.K. (1981), pg. 244.
[24] Martel, Hugo; Shapiro, Paul R.; Weinberg, Steven, Likely values of the cosmological constant, Astrophys. J., 492, 29 (1998) · doi:10.1086/305016
[25] Barnes, Luke A., The Fine-Tuning of the Universe for Intelligent Life, Publ. Astron. Soc. Austral., 29, 529 (2012) · doi:10.1071/AS12015
[26] Barnes, Luke A., Testing the Multiverse: Bayes, Fine-Tuning and Typicality (2017)
[27] L.A. Barnes, Fine-tuning in the context of Bayesian theory testing, Eur. J. Phil. Sci.8 (2017) 253. · Zbl 1398.62389 · doi:10.1007/s13194-017-0184-2
[28] E.T. Jaynes, Probability theory: the logic of science, Cambridge University Press, Cambridge, U.K. (2003). · Zbl 1045.62001
[29] J. Berger, Statistical decision theory and Bayesian analysis, Springer, New York, NY, U.S.A. (1985). · Zbl 0572.62008 · doi:10.1007/978-1-4757-4286-2
[30] Jaynes, E. T., Information Theory and Statistical Mechanics, Phys. Rev., 106, 620-630 (1957) · Zbl 0084.43701 · doi:10.1103/PhysRev.106.620
[31] Jaynes, E. T., Information Theory and Statistical Mechanics. II, Phys. Rev., 108, 171-190 (1957) · Zbl 0084.43701 · doi:10.1103/PhysRev.108.171
[32] L. McGrew and T. McGrew, On the rational reconstruction of the fine-tuning argument, Phil. Christi7 (2005) 425. · Zbl 0416.54037 · doi:10.5840/pc20057235
[33] K. Conrad, Probability distributions and maximal entropy, http://www.math.uconn.edu/∼kconrad/blurbs/analysis/entropypost.pdf, (2005).
[34] T.M. Cover and J.A. Thomas, Elements of information theory, second edition, Wiley, U.S.A. (2006). · Zbl 1140.94001
[35] S.Y. Park and A.K. Bera, Maximum entropy autoregressive conditional heteroskedasticity model, J. Econometrics150 (2009) 219. · Zbl 1429.62691 · doi:10.1016/j.jeconom.2008.12.014
[36] G. Casella and R.L. Berger, Statistical inference, second edition, Cengage Learning, U.S.A. (2006). · Zbl 0699.62001
[37] S. Thorvaldsen and O. Hössjer, Using statistical methods to model the fine-tuning of molecular machines and systems, J. Theor. Biol.501 (2020) 110352. · Zbl 1455.92065 · doi:10.1016/j.jtbi.2020.110352
[38] Uzan, Jean-Philippe, Varying Constants, Gravitation and Cosmology, Living Rev. Rel., 14, 2 (2011) · Zbl 1215.83012 · doi:10.12942/lrr-2011-2
[39] C. Xue et al., Precision measurement of the newtonian gravitational constant, National Sci. Rev.7 (2020) 1803. · doi:10.1093/nsr/nwaa165
[40] Tegmark, Max; Rees, Martin J., Why is the Cosmic Microwave Background fluctuation level 10**(-5)?, Astrophys. J., 499, 526-532 (1998) · doi:10.1086/305673
[41] Cline, James M.; Jeon, Sangyong; Moore, Guy D., The Phantom menaced: Constraints on low-energy effective ghosts, Phys. Rev. D, 70 (2004) · doi:10.1103/PhysRevD.70.043543
[42] W.A. Dembski and R.J. Marks II, Conservation of information in search: measuring the cost of success, IEEE Trans. Syst., Man, Cybern. A, Syst., Humans39 (2009) 1051. · doi:10.1109/tsmca.2009.2025027
[43] R. Marks and D.A. Díaz-Pachón, Generalized active information: extensions to unbounded domains, BIO-Complexity2020 (2020) 1. · doi:10.5048/bio-c.2020.3
[44] D.A. Díaz-Pachón, J.P. Sáenz and J.S. Rao, Hypothesis testing with active information, Statist. Probabil. Lett.161 (2020) 108742. · Zbl 1440.62074 · doi:10.1016/j.spl.2020.108742
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.