Abstract
By using type Ia supernovae (SNIa) to provide the luminosity distance (LD) directly, which depends on the value of the Hubble constant H 0 = 100h km ∙ s-1 ∙ Mpc-1, and the angular diameter distance from galaxy clusters or baryon acoustic oscillations (BAOs) to give the derived LD according to the distance duality relation, we propose a model-independent method to determine h from the fact that different observations should give the same LD at a given redshift. Combining the Sloan Digital Sky Survey II (SDSS-II) SNIa from the MLCS2k2 light curve fit and galaxy cluster data, we find that at the 1σ confidence level (CL), h = 0:5867 ± 0:0303 for the sample of the elliptical β model for galaxy clusters, and h = 0:6199 ± 0:0293 for that of the spherical β model. The former is smaller than the values from other observations, whereas the latter is consistent with the Planck result at the 2σ CL and agrees very well with the value reconstructed directly from the H(z) data. With the SDSS-II SNIa and BAO measurements, a tighter constraint, h = 0:6683 ± 0:0221, is obtained. For comparison, we also consider the Union 2.1 SNIa from the SALT2 light curve fitting. The results from the Union 2.1 SNIa are slightly larger than those from the SDSS-II SNIa, and the Union 2.1 SNIa + BAOs give the tightest value. We find that the values from SNIa + BAOs are quite consistent with those from the Planck and the BAOs, as well as the local measurement from Cepheids and very-low-redshift SNIa.
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W. L. Freedman, B. F. Madore, B. K. Gibson, L. Ferrarese, D. D. Kelson, S. Sakai, J. R. Mould, R. C. JrKennicutt, H. C. Ford, J. A. Graham, J. P. Huchra, S. M. G. Hughes, G. D. Illingworth, L. M. Macri, P. B. Stetson, Final results from the Hubble Space Telescope key project to measure the Hubble constant, Astrophys. J. 553 (1), 47 (2001)
A. Riess, L. Macri, S. Casertano, H. Lampeitl, H. C. Ferguson, A. V. Filippenko, S. W. Jha, W. Li, R. Chornock, A 3% solution: Determination of the Hubble constant with the Hubble Space Telescope Wide Field Camera 3, Astrophys. J. 730 (2), 119 (2011)
C. L. Bennett, D. Larson, J. L. Weiland, N. Jarosik, G. Hinshaw, et al., Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) observations: Final maps results, Astrophys. J. Suppl. 208 (2), 20 (2013)
G. Hinshaw, D. Larson, E. Komatsu, D. N. Spergel, C. L. Bennett, et al., Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) observations: Cosmological parameter results, Astrophys. J. Suppl. 208 (2), 19 (2013)
C. L. Bennett, D. Larson, J. L. Weiland, G. Hinshaw, The 1% concordance Hubble constant, Astrophys. J. 794 (2), 135 (2014)
E. Calabrese, M. Archidiacono, A. Melchiorri, B. Ratra, Impact of H 0 prior on the evidence for dark radiation, Phys. Rev. D 86 (4), 043520 (2012)
G. Chen, B. Ratra, Median statistics the Hubble constant, Publ. Astron. Soc. Pac. 123 (907), 1127 (2011)
P. A. R. Ade, et al., Planck 2013 results. XVI. Cosmological parameters, Astron. Astrophys. 571, A16 (2014)
P. A. R. Ade, et al., Planck 2015 results. XIII. Cosmological parameters, arXiv: 1502. 01589
É. Aubourg, et al., Cosmological implications of baryon acoustic oscillation measurements, Phys. Rev. D 92 (12), 123516 (2015)
L. Anderson, E. Aubourg, S. Bailey, F. Beutler, V. Bhardwaj, et al., The clustering of galaxies in the SDSSIII Baryon Oscillation Spectroscopic Survey: Baryon Acoustic Oscillations in the Data Release 10 11 galaxy samples, Mon. Not. R. Astron. Soc. 441 (1), 24 (2014)
M. Betoule, R. Kessler, J. Guy, J. Mosher, D. Hardin, et al., Improved cosmological constraints from a joint analysis of the SDSS-II SNLS supernova samples, Astron. Astrophys. 568, A22 (2014)
V. Marra, L. Amendola, I. Sawicki, W. Valkenburg, Cosmic variance the measurement of the local Hubble parameter, Phys. Rev. Lett. 110 (24), 241305 (2013)
S. N. Zhang Y. Z. Ma, Direct measurement of evolving dark energy density super-accelerating expansion of the universe, arXiv: 1303. 6124
G. Efstathiou, H 0 revisited, Mon. Not. R. Astron. Soc. 440 (2), 1138 (2014)
M. Rigault, G. Aldering, M. Kowalski, Y. Copin, P. Antilogus, et al., Confirmation of a star formation bias in Type Ia supernova distances its effect on the measurement of the Hubble constant, Astrophys. J. 802, 20 (2015)
A. E. Romano, S. A. Vallejo, Directional dependence of the local estimation of H 0 the nonperturbative effects of primordial curvature perturbations, Europhys. Lett. 109 (3), 39002 (2015)
A. E. Romano, S. A. Vallejo, Low red-shift effects of local structure on the Hubble parameter in presence of a cosmological constant, Eur. Phys. J. C 76 (4), 216 (2016)
D. Spergel, R. Flauger, R. Hlozek, Planck data reconsidered, Phys. Rev. D 91 (2), 023518 (2015)
E. M. L. Humphreys, M. J. Reid, J. M. Moran, L. J. Greenhill, A. L. Argon, Toward a new geometric distance to the active galaxy NGC 4258. III. Final results the Hubble constant, Astrophys. J. 775 (1), 13 (2013)
F. Beutler, C. Blake, M. Colless, D. H. Jones, L. Staveley-Smith, L. Campbell, Q. Parker, W. Saunders, F. Watson, The 6dF galaxy survey: Baryon acoustic oscillations the local Hubble constant, Mon. Not. R. Astron. Soc. 416 (4), 3017 (2011)
E. A. Kazin, J. Koda, C. Blake, N. Padmanabhan, S. Brough, et al., The WiggleZ Dark Energy Survey: Improved distance measurements to z = 1 with reconstruction of the baryonic acoustic feature, Mon. Not. R. Astron. Soc. 441 (4), 3524 (2014)
T. Delubac, J. E. Bautista, N. G. Busca, J. Rich, D. Kirkby, et al., Baryon acoustic oscillations in the Ly forest of BOSS DR11 quasars, Astron. Astrophys. 574, A59 (2015)
C. H. Chuang, F. Prada, A. J. Cuesta, et al., The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: Single-probe measurements the strong power of f(z)nsigma_8(z) on constraining dark energy, Mon. Not. R. Astron. Soc. 433, 3559 (2013)
M. D. P. Hemantha, Y. Wang, C. H. Chuang, Measurement of H(z) DA(z) from the two-dimensional power spectrum of Sloan Digital Sky Survey luminous red galaxies, Mon. Not. R. Astron. Soc. 445 (4), 3737 (2014)
C. Cheng Q. G. Huang, An accurate determination of the Hubble constant from Baryon Acoustic Oscillation datasets, Sci. China: Phys. Mech. Astron. 58 (9), 599801 (2015)
V. C. Busti, C. Clarkson, M. Seikel, Evidence for a lower value for H 0 from cosmic chronometers data? Mon. Not. R. Astron. Soc. 441(1), L11 (2014)
M. Bonamente, M. K. Joy, S. J. LaRoque, J. E. Carlstrom, E. D. Reese, K. S. Dawson, Determination of the cosmic distance scale from Sunyaev-Zel’dovich effect Chandra X-ray measurements of high redshift galaxy clusters, Astrophys. J. 647 (1), 25 (2006)
I. Ferreras, A. Pasquali, S. Malhotra, J. Rhoads, S. Cohen, R. Windhorst, N. Pirzkal, N. Grogin, A. M. Koekemoer, T. Lisker, N. Panagia, E. Daddi, N. P. Hathi, Early-type galaxies in the PEARS survey: Probing the stellar populations at moderate redshift, Astrophys. J. 706 (1), 158 (2009)
M. Longhetti, P. Saracco, P. Severgnini, R. D. Ceca, F. Mannucci, R. Bender, N. Drory, G. Feulner, U. Hopp, The Kormendy relation of massive elliptical galaxies at z’ 1:5. Evidence for size evolution? Mon. Not. R. Astron. Soc. 374 (2), 614 (2007)
E. Gaztañaga, A. Cabré, L. Hui, Clustering of Luminous Red Galaxies IV: Baryon acoustic peak in the line-of-sight direction a direct measurement of H(z), Mon. Not. R. Astron. Soc. 399 (3), 1663 (2009)
J. Simon, L. Verde, R. Jimenez, Constraints on the redshift dependence of the dark energy potential, Phys. Rev. D 71 (12), 123001 (2005)
D. Stern, R. Jimenez, L. Verde, M. Kamionkowski, S. A. Stanford, Cosmic Chronometers: Constraining the equation of state of dark energy (I): H(z) measurements, J. Cosmol. Astropart. Phys. 2 (02), 8 (2010)
D. J. Eisenstein, I. Zehavi, D. W. Hogg, R. Scoccimarro, M. R. Blanton, et al., Detection of the baryon acoustic peak in the large-scale correlation function of SDSS luminous red galaxies, Astrophys. J. 633 (2), 560 (2005)
J. A. S. Lima J. V. Cunha, A 3% determination of H 0 at intermediate redshifts, Astrophys. J. 781(2), L38 (2014)
R. F. L. Holanda, V. C. Busti, G. P. da Silva, Robustness of H 0 determination at intermediate redshifts, Mon. Not. R. Astron. Soc. 443(1), L74 (2014)
E. De Filippis, M. Sereno, M. W. Bautz, G. Longo, Measuring the three-dimensional structure of galaxy clusters. 1. Application to a sample of 25 clusters, Astrophys. J. 625 (1), 108 (2005)
R. Kessler, A. Becker, D. Cinabro, J. Vanderplas, J. A. Frieman, et al., First-year Sloan Digital Sky Survey-II (SDSS-II) supernova results: Hubble diagram cosmological parameters, Astrophys. J. Suppl. 185 (1), 32 (2009)
R. Amanullah, C. Lidman, D. Rubin, G. Aldering, P. Astier, et al., Spectra light curves of six type Ia supernovae at 0:511 < z < 1: 12 the Union2 compilation, Astrophys. J. 716, 712 (2010)
S. Jha, A. G. Riess, R. P. Kirshner, Improved distances to type Ia supernovae with multicolor light curve shapes: MLCS2k2, Astrophys. J. 659 (1), 122 (2007)
J. Guy, P. Astier, S. Baumont, D. Hardin, R. Pain, et al., SALT2: Using distant supernovae to improve the use of Type Ia supernovae as distance indicators, Astron. Astrophys. 466 (1), 11 (2007)
N. Suzuki, D. Rubin, C. Lidman, G. Aldering, R. Amanullah, et al., V. improving the dark energy constraints above z > 1 building an early-type-hosted supernova sample, Astrophys. J. 746 (1), 85 (2012)
B. A. Bassett M. Kunz, Cosmic distance-duality as probe of exotic physics acceleration, Phys. Rev. D 69 (10), 101305 (2004)
B. A. Bassett M. Kunz, Cosmic acceleration vs. axion-photon mixing, Astrophys. J. 607 (2), 661 (2004)
M. Kunz B. A. Bassett, A Tale of Two Distances, arXiv: astro-ph/0406013
R. Nair, S. Jhingan, D. Jain, Cosmic distance duality cosmic transparency, J. Cosmol. Astropart. Phys. 1212, 028 (2012)
H. Lampeitl, R. C. Nichol, H. J. Seo, T. Giannantonio, C. Shapiro, et al., First-year Sloan Digital Sky Survey-II (SDSS-II) supernova results: consistency constraints with other intermediate-redshift datasets, Mon. Not. R. Astron. Soc. 401 (4), 2331 (2009)
Z. Li, P. Wu, H. Yu, Cosmological-modelindependent tests for the distance-duality relation from Galaxy Clusters Type Ia Supernova, Astrophys. J. 729(1), L14 (2011)
R. F. L. Holanda, J. A. S. Lima, M. B. Ribeiro, Testing the distance-duality relation with galaxy clusters type Ia supernovae, Astrophys. J. 722(2), L233 (2010)
P. Wu, Z. Li, X. Liu, H. Yu, Cosmic distance-duality relation test using type Ia supernovae the baryon acoustic oscillation, Phys. Rev. D 92 (2), 023520 (2015)
P. R. Bevington D. K. Robinson, Data reduction error analysis for the physical sciences, 3rd Ed., edited by P. R. Bevington K. D. Robinson, MA: McGraw-Hill, 2003
E. D. Reese, J. E. Carlstrom, M. Joy, J. J. Mohr, L. Grego, W. L. Holzapfel, Determining the cosmic distance scale from interferometric measurements of the Sunyaev-Zel’dovich effect, Astrophys. J. 581 (1), 53 (2002)
B. S. Mason, S. T. Myers, A. C. S. Readhead, A Measurement of H 0 from the Sunyaev-Zel’dovich Effect, Astrophys. J. 555, L11 (2001)
B. A. Bassett R. Hlozek, Baryon acoustic oscillations, arXiv: 0910. 5224
C. Blake, S. Brough, M. Colless, C. Contreras, W. Couch, et al., The WiggleZ Dark Energy Survey: Joint measurements of the expansion growth history at z < 1, Mon. Not. R. Astron. Soc. 425 (1), 405 (2012)
X. Xu, A. J. Cuesta, N. Padmanabhan, D. J. Eisenstein, C. K. McBride, Measuring DA H at z = 0: 35 from the SDSS DR7 LRGs using baryon acoustic oscillations, Mon. Not. R. Astron. Soc. 431 (3), 2834 (2013)
L. Samushia, B. A. Reid, M. White, W. J. Percival, A. J. Cuesta, et al., The clustering of galaxies in the SDSSIII Baryon Oscillation Spectroscopic Survey: Measuring growth rate geometry with anisotropic clustering, Mon. Not. R. Astron. Soc. 439 (4), 3504 (2014)
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Wu, PX., Li, ZX. & Yu, HW. Determining H 0 using a model-independent method. Front. Phys. 12, 129801 (2017). https://doi.org/10.1007/s11467-016-0599-9
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DOI: https://doi.org/10.1007/s11467-016-0599-9