Parameterizations of the Hubble Constant from the Binned Type Ia Supernova Master Sample: Logarithmic versus Power-law Forms
7 affiliations
- 1National Astronomical Observatory of Japan
- 2The Graduate University for Advanced Studies
- 3Space Science Institute
- 4The University of Burdwan
- 5Cornell University
- 6ENEA
- 7Sapienza University of Rome
Abstract
Motivated by the Hubble tension and the increasing debate about the redshift-dependency in the inferred Hubble constant, we investigate its dependence within the flat ΛCDM framework using a 20 bin analysis of the master Type Ia supernovae (SNe Ia) sample, considering cases with and without very low-redshift data. The main quantity studied is H ₀ ( z )/ H ₀ , where H ₀ is the Hubble constant today, and H ₀ ( z ) is the binned data-driven estimate of the value of H ₀ inferred from the SNe Ia data within redshift intervals at z > 0, such that H ₀ (0) = H ₀ . From the binned analyses, we obtain best-fitting values of H ₀ and Ω m 0 , and employ logarithmic and power-law parameterizations, which are statistically consistent within uncertainties over the redshift range considered. To assess their behavior at earlier epochs, we extrapolate both forms to the cosmic microwave background (CMB) radiation era ( z ≃ 1100), Big Bang nucleosynthesis (BBN, z ∼ 10 ⁹ ), and inflationary scales ( z ∼ 10 ²⁰ ). The reconstructed Hubble constant remains nearly indistinguishable up to the CMB scale, diverges at the few percent to 10% level around BBN, and differs more substantially when extrapolated to inflationary redshifts, although these two regimes lie beyond the direct observational constraints. A distinct asymptotic behavior emerges at very-high redshift: the logarithmic form exhibits a vanishing behavior of H ₀ at finite z , while the power-law form approaches zero asymptotically as z → ∞ . In future studies, independent high-redshift observations and extensions beyond ΛCDM, such as f ( R )-modified gravity, could allow a comparative study of the two parameterizations beyond the SNe Ia regime and their high- z physical implications.
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BibTeX
@article{dainotti2026parameterizations,
title = {{Parameterizations of the Hubble Constant from the Binned Type Ia Supernova Master Sample: Logarithmic versus Power-law Forms}},
author = {Maria Giovanna Dainotti and Avik Banerjee and André LeClair and Giovanni Montani},
journal = {The Astrophysical Journal},
year = {2026},
month = oct,
doi = {10.3847/1538-4357/ae9c32},
url = {https://iopscience.iop.org/article/10.3847/1538-4357/ae9c32},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Parameterizations of the Hubble Constant from the Binned Type Ia Supernova Master Sample: Logarithmic versus Power-law Forms
AU - Maria Giovanna Dainotti
AU - Avik Banerjee
AU - André LeClair
AU - Giovanni Montani
PY - 2026
DA - 2026/10/09
JO - The Astrophysical Journal
DO - 10.3847/1538-4357/ae9c32
UR - https://iopscience.iop.org/article/10.3847/1538-4357/ae9c32
AB - Motivated by the Hubble tension and the increasing debate about the redshift-dependency in the inferred Hubble constant, we investigate its dependence within the flat ΛCDM framework using a 20 bin analysis of the master Type Ia supernovae (SNe Ia) sample, considering cases with and without very low-redshift data. The main quantity studied is H ₀ ( z )/ H ₀ , where H ₀ is the Hubble constant today, and H ₀ ( z ) is the binned data-driven estimate of the value of H ₀ inferred from the SNe Ia data within redshift intervals at z > 0, such that H ₀ (0) = H ₀ . From the binned analyses, we obtain best-fitting values of H ₀ and Ω m 0 , and employ logarithmic and power-law parameterizations, which are statistically consistent within uncertainties over the redshift range considered. To assess their behavior at earlier epochs, we extrapolate both forms to the cosmic microwave background (CMB) radiation era ( z ≃ 1100), Big Bang nucleosynthesis (BBN, z ∼ 10 ⁹ ), and inflationary scales ( z ∼ 10 ²⁰ ). The reconstructed Hubble constant remains nearly indistinguishable up to the CMB scale, diverges at the few percent to 10% level around BBN, and differs more substantially when extrapolated to inflationary redshifts, although these two regimes lie beyond the direct observational constraints. A distinct asymptotic behavior emerges at very-high redshift: the logarithmic form exhibits a vanishing behavior of H ₀ at finite z , while the power-law form approaches zero asymptotically as z → ∞ . In future studies, independent high-redshift observations and extensions beyond ΛCDM, such as f ( R )-modified gravity, could allow a comparative study of the two parameterizations beyond the SNe Ia regime and their high- z physical implications.
SN - 0004-637X
SN - 1538-4357
ER -