Cosmological introduction

The term “cosmological coincidence” usually refers to the fact that the Dark Energy era seems to succeed to the Matter dominated era quite precisely at ‘our’ time, that is to say to coincide with a particular cosmological time of ridiculously low probability, although [9], for instance, discusses the way this ‘chance’ is usually interpreted, hence the relevance of the coincidence problem.

The range of admissible numerical values for the cosmological parameters has been step by step reduced from the 2000s to latest 2016 results, thanks to the increasing power of instruments such as WMAP, Planck, the Sloan Digital Sky Survey II (SDSS-II) and many others and to the colossal theoretical and experimental work achieved by considerable teams of astrophysicists, cosmologists, engineers and others.

For the Hubble constant H₀, i.e. the value of H(z) = ȧ/a, where a = 1/(1+z), at redshift z = 0, a ~9% gap has appeared between two types of observations: i) an indirect, mostly rooted in predictions derived from measurements of the CMB, giving a Hubble value H₀ ~ 67 km/s/Mpc [10] when applying the consensus, ΛCDM  cosmological model, which combines Baryonic and Cold (or more recently possibly warm) Dark matter CDM with a cosmological constant playing the role of Dark Energy and ii) a more  directly measured value H₀ ~ 73.24 km/s/Mpc, hence resulting from ‘local’ observations, i.e. on quite nearby galaxies.

The issue is important because this determines the extent of validity of the Standard Model of Cosmology, somehow framed by energy density ratios by definition summing to 1, including an Ω_k accounting for the energy density embedded in the universe average curvature, hence null for quasi-Euclidean or ‘flat’.

The value of H₀ = 73.24 km/s/Mpc [7] gives an Ω_M,0 = Ω_b,0 + Ω_DM,0 ~ 0.26, hence an Ω_Λ,0 ~ 0.74, assuming Ω_k ~ 0, when using h²Ω_b and h²Ω_DM usually found from Planck, WMAP and other instruments [10, 11].

Another recent paper [13] concludes on the following results Ω_M,0 (or Ω_M) ~ 0.266 ± 0.016, Ω_Λ ~ 0.740 ± 0.018 and w = – 1.15 (+ 0.123, – 0.121) from the observation of 581 SNe Ia up to z ~ 0.5.

A very recent paper [12] has proposed that the gap could be offset by recalculating the effect from the fact that the observers (‘we’, i.e. the Earth, the Milky Way and the Local group) are currently assumed to be located in an under-dense region of the universe – a subvoid – through modified calculations from the way this fact was already accounted in the consensus ‘local’ [7] value determination of H₀ ~73.24. Its argument is that observations beyond z = 0.6 should be taken into account so as to consider supernovae out of the local under-density. However [8] reconstructs an H(z) function, using previous results [7], with z up ~1.3.

It is not known, at the time of publishing the present paper, what will be the final impacts of contributions such as this one but they may not erase the fact of the direct, local measurements and their implications, such as the questions about the precise factors underlying the Dark Energy and Dark Matter effects.

Still more recent observational paper [14] emphasizes a difference between  TT, TE cross-correlations and EE polarization modes, with results concentrating the discrepancy on these modes with, in summary, a central value of H₀ = 73.4 and Ω_M = 0.2593, hence Ω_Λ ~ 0.7407, while authors preferred TE mode gives H₀ = 63.4, hence Ω_M = 0.3684 and therefore Ω_Λ ~ 0.63. Actually the TT results of [11] give Ω_b = 0.0458 and Ω_DM = 0.21345 and even though their own authors prefer the TE results, the manner of integration of somehow disparate results, such as TT, TE and EE modes, seems debatable, and cf. [7, 8].

All these results are provisional and the object of current complementary analyzes and further tests, thanks to increasingly precise and diversified observational results. However they suggest it may be useful to actualize predictions once submitted and to provide more details about our approach to the two following questions: what may play the role of Dark Energy and why this coincidence with ‘our’ times.

These proposals come in sections 3 and 4, after an introductory perspective to their particular type of look at the cosmological issues in 2.

References

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2. Conferences I3E CCCA’12, Marseille 2012 & ISC-Complex Systems, Orleans University, June 2013, Future = Complexity
3. Mezard, Optimization and Physics: On the satisfiability of random Boolean formulae, arXiv:cond-math/0212448, 2002
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5. Journeau, New Concepts of Dimensions and Consequences, AIP n°1018, http://dx.doi.org/10.1063/1.4728011, 2008
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7. G. Riess et al, A 2.4% Determination of the Local Value of the Hubble Constant, arXiv1604.01424 astro-ph, 5 Apr 2016
8. L. Bernal, L. Verde, A.G. Riess, The trouble with H₀, arXiv:1607.05617, [astro-ph.CO], 2016
9. Bianchi, C. Rovelli, Why all these prejudices against a constant?  arXiv: 1002.3966 [astro-ph.CO]
10. Planck 2015 results XIII. Cosmological parameters, arXiv 1502.01589 [astro-ph.CO] Feb. 2015
11. Bennett et al., NINE-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE (WMAP) OBSERVATIONS: FINAL MAPS AND RESULTS, The Astrophysical Journal Supplement Series, 208:20 (54pp), 2013 October doi:1088/0067-0049/208/2/20
12. Campbell, M. Fraser, G. Gilmore, How SN Ia host-galaxy properties affect cosmological parameters, ArXiv: 1602.02596 v1 [astro-ph.CO], 8 Feb 2016
13. E. Romano, Hubble trouble or Hubble bubble? arXiv:1609.04081v1 [astro-ph.CO] 14 Sep
14. Louis et al, THE ATACAMA COSMOLOGY TELESCOPE: TWO-SEASON ACTPOL SPECTRA AND PARAMETERS, ArXiv:1610.02360v1 [astro-ph.CO] 7 Oct 2016