we then need to find the residues on the variable
χ 2 = (m B ,i − mtB ,i )−
(m B , j − mtB , j )
ij
(1 Mpc) H 0
[1] Adam G. Riess, Stefano Casertano, Wenlong Yuan, Lucas M. Macri, Dan Scolnic,
Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the hubble constant and stronger evidence for physics beyond
CDM, Astrophys. J. 876 (1) (2019) 85.
[2] Kenneth C. Wong, et al., H0LiCOW XIII. A 2.4% measurement of H 0 from lensed
quasars: 5.3σ tension between early and late-Universe probes, 7.2019.
[3] M.J. Reid, J.A. Braatz, J.J. Condon, L.J. Greenhill, C. Henkel, K.Y. Lo, The megamaser cosmology project: I. VLBI observations of UGC 3789, Astrophys. J. 695
(2009) 287–291.
[4] Wendy L. Freedman, et al., The Carnegie-Chicago Hubble Program. VIII. An Independent Determination of the Hubble Constant Based on the Tip of the Red
Giant Branch, 7.2019.
[5] N. Aghanim, et al., Planck 2018 results. VI. Cosmological parameters, 7.2018.
[6] Jose Luis Bernal, Licia Verde, Adam G. Riess, The trouble with H 0 , J. Cosmol.
Astropart. Phys. 10 (2016) 019.
[7] Adam G. Riess, The expansion of the Universe is faster than expected, Nature
Rev. Phys. 2 (1) (2019) 10–12.
[8] Antonio De Felice, Andreas Doll, Shinji Mukohyama, A theory of type-II minimally modified gravity, J. Cosmol. Astropart. Phys. 09 (2020) 034.
[9] Andrew R. Liddle, Information criteria for astrophysical model selection, Mon.
Not. R. Astron. Soc. 377 (2007) L74–L78.
[10] N. Aghanim, et al., Planck 2018 results. V. CMB power spectra and likelihoods,
2019.
[11] Florian Beutler, Chris Blake, Matthew Colless, D. Heath Jones, Lister StaveleySmith, Lachlan Campbell, Quentin Parker, Will Saunders, Fred Watson, The 6dF
galaxy survey: baryon acoustic oscillations and the local hubble constant, Mon.
Not. R. Astron. Soc. 416 (2011) 3017–3032.
[12] Ashley J. Ross, Lado Samushia, Cullan Howlett, Will J. Percival, Angela Burden,
Marc Manera, The clustering of the SDSS DR7 main galaxy sample – I. A 4 per
cent distance measure at z = 0.15, Mon. Not. R. Astron. Soc. 449 (1) (2015)
835–847.
[13] Shadab Alam, et al., The clustering of galaxies in the completed SDSS-III baryon
oscillation spectroscopic survey: cosmological analysis of the DR12 galaxy sample, Mon. Not. R. Astron. Soc. 470 (3) (2017) 2617–2652.
[14] D.M. Scolnic, et al., The complete light-curve sample of spectroscopically confirmed SNe ia from Pan-STARRS1 and cosmological constraints from the combined pantheon sample, Astrophys. J. 859 (2) (2018) 101.
[15] David Camarena, Valerio Marra, Local determination of the Hubble constant
and the deceleration parameter, Phys. Rev. Res. 2 (1) (2020) 013028.
[16] Giampaolo Benevento, Wayne Hu, Marco Raveri, Can late dark energy transitions raise the Hubble constant?, Phys. Rev. D 101 (10) (2020) 103517.
[17] N. Aghanim, et al., Planck intermediate results. LI. Features in the cosmic microwave background temperature power spectrum and shifts in cosmological
parameters, Astron. Astrophys. 607 (2017) A95.
[18] Pavel Motloch, Wayne Hu, Lensinglike tensions in the Planck legacy release,
Phys. Rev. D 101 (8) (2020) 083515.
[19] Diego Blas, Julien Lesgourgues, Thomas Tram, The cosmic linear anisotropy
solving system (CLASS) II: approximation schemes, J. Cosmol. Astropart. Phys.
1107 (2011) 034.
[20] Masroor C. Pookkillath, Antonio De Felice, Shinji Mukohyama, Baryon physics
and tight coupling approximation in Boltzmann codes, Universe 6 (2020) 6.
[21] Benjamin Audren, Julien Lesgourgues, Karim Benabed, Simon Prunet, Conservative constraints on early cosmology: an illustration of the Monte python
cosmological parameter inference code, J. Cosmol. Astropart. Phys. 1302 (2013)
001.
[22] Thejs Brinckmann, Julien Lesgourgues, MontePython 3: boosted MCMC sampler
and other features, Phys. Dark Universe 24 (2019) 100260.
[23] Antony Lewis, GetDist: a Python package for analysing Monte Carlo samples,
10.2019.
[24] Balakrishna S. Haridasu, Matteo Viel, Nicola Vittorio, Sources of H 0 -tensions in
dark energy scenarios, 12.2020.
[25] Adam G. Riess, Stefano Casertano, Wenlong Yuan, J. Bradley Bowers, Lucas
Macri, Joel C. Zinn, Dan Scolnic, Cosmic Distances Calibrated to 1% Precision
with Gaia EDR3 Parallaxes and Hubble Space Telescope Photometry of 75 Milky
Way Cepheids Confirm Tension with LambdaCDM, 12.2020.
[26] Ryan E. Keeley, Shahab Joudaki, Manoj Kaplinghat, David Kirkby, Implications
of a transition in the dark energy equation of state for the H 0 and σ8 tensions,
J. Cosmol. Astropart. Phys. 12 (2019) 035.
[27] Kyriakos Vattis, Savvas M. Koushiappas, Abraham Loeb, Dark matter decaying
in the late Universe can relieve the H0 tension, Phys. Rev. D 99 (12) (2019)
121302.
[28] Gongjun Choi, Motoo Suzuki, Tsutomu T. Yanagida, Quintessence axion dark
energy and a solution to the Hubble tension, Phys. Lett. B 805 (2020) 135408.
= W i − M B + 5 log10
−
ij
(1 Mpc) H 0
W j − M B + 5 log10
(A.6)
Now consider
d¯ L ≡ (1 + z)
z
dz
E ( z )
(A.7)
so that
d¯ L =
dz d¯ L
dN dz
= d¯ L +
(1 + z)2
E ( z)
(A.8)
where we have used
dz
dN
= 1+ z,
(A.9)
considering N = ln(a0 /a) = ln(1 + z). Now we can solve for d¯ L ( z),
given the initial conditions d¯ L (0) = 0 = z(0).
Once we have the quantities d¯ L for any data-redshift, we have
W i so that we are able to find
S 0 ≡ V T − 1 V ,
S1 ≡ W
−1
(A.10)
V,
(A.11)
where V i = 1 and i j is the covariance matrix.
Finally, the mean value and the variance of H 0loc can be determined by the log-normal distribution
H 0loc = e μln + 2 σln ,
H 0loc
(A.12) ...
論文の公開元へ
