De l'art de mesurer la constante de Hubble en cherchant notre place au milieu de nulle part

La longue marche vers une "cosmologie de précision"

The plots below show the time evolution of our knoweldge of the Hubble Constant H₀, the scaling between radial velocity and distance in kilometers per second per Megaparsec, since it was first determined by Lemaitre, Robertson and Hubble in the late 1920's. The first major revision to Hubble's value was made in the 1950's due to the discovery of Population II stars by W. Baade. That was followed by other corrections for confusion, etc. that pretty much dropped the accepted value down to around 100 km/s/Mpc by the early 1960's.

The last plot shows modern (post Hubble Space Telescope) determinations, including results from gravitational lensing and applications of the Sunyaev-Zeldovich effect. Note the very recent convergence to values near 65 +/- 10 km/sec/Mpc (about 13 miles per second per million light-years)... Currently, the old factor of two discrepancy in the determination of the cosmic distance scale has been reduced to a dispersion of the order of 10 km/s out of 65-70, or 15-20%. Quite an improvement!

One major additional change in the debate since the end of the 20th century has been the discovery of the accelerating universe (cf. Perlmutter et al. 1998 and Riess et al. 1998) and the development of "Concordance" Cosmology. In the early 1990's, one of the strongest arguments for a low (~50 km/s/Mpc) value of the Hubble Constant was the need to derive an expansion age of the universe that was older than, now, the oldest stars, those found in globular star clusters. The best GC ages in 1990 were in the range 16-18 Gyr. The expansion age of the Universe depends primarily on the Hubble constant but also on the value of various other cosmological parameters, most notably then the mean mass density over the closure density, Ω_M. For an "empty" universe, the age is just 1/H₀ or 9.7 Gyr for H₀=100 km/s/Mpc and 19.4 Gyr for 50 km/s/Mpc. For a universe with Ω_M=1.000, the theorist's favorite because that is what is predicted by inflation, the age is 2/3 of that for the empty universe. So if the Hubble Constant was 70 km/s/Mpc, the age of an empty universe was 13.5 Gyr, less than the GC ages, and if Ω_M was 1.000 as favored by the theorists, the expansion age would only be 9 Gyr, much much less than the GC ages. Conversely if H₀ was 50 km/s/Mpc, and Ω_M was the observers' favorite value of 0.25, the age came out just about right. Note that this still ruled out Ω_M= 1.000 though, inspiring at least one theorist to proclaim that H₀ must be 35! The discovery of acceleration enabled the removal of much of this major remaining discrepancy in timescales, that between the expansion age of the Universe and the ages of the oldest stars, those in globular clusters. The introduction of a Cosmological constant, &Lambda, one of the most probable causes for acceleration, changes the computation of the Universe's expansion age. A positive Ω_Λ increases the age. The Concordance model has an H₀=72 km/s/Mpc, an Ω= 1.0000... made up of Ω_Λ=0.73 and Ω_M=0.27. Those values yield an age for the Universe of ~ 13.7 Gyr. This alone would not have solved the timescale problem, but a revision of the subdwarf distance scale based on significantly improved paralaxes to nearby subdwards from the ESA Hiparcos mission, increased the distances to galactic globular clusters and thus decreased their estimated ages. The most recent fits of observed Hertzsprung-Russel diagrams to theoretical stellar models (isochrones) by the Yale group (Demarque, Pinsonneault and others) indicates that the mean age of galactic globulars is more like 12.5 Gyr, comfortably smaller than the Expansion age.

John P. Huchra, Copyright 2008

Les derniers pas...

The recent Planck observations of the cosmic microwave background (CMB) lead to a Hubble constant of H₀=67.3±1.2 km/s/Mpc for the base six-parameter ΛCDM model (Planck Collaboration 2013, hereafter P13). This value is in tension, at about the 2.5σ level, with the direct measurement of H₀=73.8 ± 2.4 km/s/Mpc reported by Riess et al (2011 R11). If these numbers are taken at face value, they suggest evidence for new physics at about the 2.5σ level (for example, exotic physics in the neutrino or dark energy sectors...). The exciting possibility of discovering new physics provides strong motivation to subject both the CMB and H₀ measurements to intense scrutiny. This paper presents a reanalysis of the R11 Cepheid data. The  H₀ measurement from these data has the smallest error and has been used widely in combination with CMB measurements for cosmological parameter analysis (e.g. Hinshaw et al. 2012; Hou et al. 2012; Sievers et al. 2013). The study reported here was motivated by certain aspects of the R11 analysis: the R11 outlier rejection algorithm (which rejects a large fraction, ∼ 20%, of the Cepheids), the low reduced χ2 values of their fits, and the variations of some of the parameter values with different distance anchors, particularly the metallicity dependence of the period-luminosity relation... 

[The] figure [below] compares these two estimates of H₀ with the P13 results from the [Planck+WP+highL (ACT+South Pole Telescope)+BAO (2dF Galaxy Redshift and SDSS redshift) surveys)] likelihood for the base ΛCDM cosmology and some extended ΛCDM models. I show the combination of CMB and Baryon Acoustic Oscillations [BAO] data since H₀ is poorly constrained for some of these extended models using CMB temperature data alone. (For reference, for this data combination H₀=67.80±0.77 km/s/Mpc in the base ΛCDM model.) The combination of CMB and BAO data is certainly not prejudiced against new physics, yet the H₀ values for the extended ΛCDM models shown in this figure all lie within 1σ of the best fit value for the base ΛCDM model. For example, in the models exploring new physics in the neutrino sector, the central value of H₀ never exceeds 69.3 km/s/Mpc. If the true value of H₀ lies closer to, say, H₀=74 km/s/Mpc , the dark energy sector, which is poorly constrained by the combination of CMB and BAO data, seems a more promising place to search for new physics. In summary, the discrepancies between the Planck results and the direct H₀ measurements... are not large enough to provide compelling evidence for new physics beyond the base ΛCDM cosmology.

The direct estimates (red) of H₀ (together with 1σ error bars) for the NGC 4258 distance anchor  and for all three distance anchors. The remaining (blue) points show the constraints from P13 for the base ΛCDM cosmology and some extended models combining CMB data with data from baryon acoustic oscillation surveys. The extensions are as follows: mν, the mass of a single neutrino species; mν + Ωk, allowing a massive neutrino species and spatial curvature; N_eff , allowing additional relativistic neutrino-like particles; N_eff +m_sterile, adding a massive sterile neutrino and additional relativistic particles; N_eff+mν, allowing a massive neutrino and additional relativistic particles; w, dark energy with a constant equation of state w = p/ρ; w + wa , dark energy with a time varying equation of state. I give the 1σ upper limit on mν and the 1σ range for N_eff . 

H0 Revisited

George Efstathiou

(Submitted on 14 Nov 2013 (v1), last revised 8 Feb 2014 (this version, v2))

"cosmologie de précision" : un terme à prendre avec des pincettes 

Cosmology, to be precise…

Chercher notre place au milieu de nulle part...

Tel pourrait être le propos de la cosmologie dans une perspective anthropologique. Mais ce blog ci n'est pas le lieu pour ce genre de débat. Le blogueur préfère laisser la parole de fin à une grande dame de l'enseignement de l'astronomie en France Lucienne Gougenheim en espérant que ce qui précède illustre bien l'actualité de sa conclusion générale extraite d'un exposé pédagogique sur la constante de Hubble et l'âge de l'Univers daté de 1996

• La distance n'est pas le seul paramètre qui conditionne la valeur de H₀...
• La nature de la chandelle standard est complexe ; même quand nous avons une bonne connaissance théorique de la propriété qui sert de critère de distance, il convient de discuter l'importance des différents paramètres dont elle dépend.
• On ne passe de la connaissance de H₀ à celle de d'âge de l'univers que dans le cadre d'un modèle cosmologique.
• ...un problème complexe ne peut se comprendre (et en conséquence se résoudre) que par la prise en compte de l'ensemble des paramètres dont il dépend...