Redshift-Binned Constraints on the Hubble Constant under $Λ$CDM, CPL, and Padé Cosmography

TL;DR

The paper investigates whether late-time measurements of the Hubble constant show genuine redshift evolution by performing a redshift-binned, multi-probe analysis across eight bins using Pantheon+ SNe Ia, DESI BAO, cosmic chronometers, and megamasers within flat $\Lambda$CDM, CPL, and Padé cosmography. It introduces a Fourier-like parametrization to capture any oscillatory $H_0(z)$ pattern and conducts thorough robustness tests, including alternative binning schemes, single-probe fits, and global versus piecewise-constant parameter configurations. The baseline analysis reveals a mild oscillatory trend with amplitude $A\approx 4.7$ km s$^{-1}$ Mpc$^{-1}$ and marginal significance $N_\sigma\approx 1.7$–$1.9\sigma$, consistent across models, but the trend can be replicated by allowing degeneracies among $H_0$, $\Omega_m$, $M$, and $r_d$ in a fully global fit. The authors conclude that the apparent redshift evolution of $H_0$ is not robust evidence for new physics, but rather an artefact of parameter degeneracies and current data limitations, highlighting the need to control late-time systematics and degeneracies in future analyses.

Abstract

Motivated by recent claims of a possible redshift dependence in late-Universe determinations of the Hubble constant ($H_0$), we test the robustness of this behaviour using multiple cosmological probes. We perform a joint redshift-binned analysis of $H_0$ across eight bins using late-Universe probes -- Pantheon+ SNe~Ia, DESI BAO, cosmic chronometers, and water megamasers -- under three cosmological frameworks: flat $Λ$CDM, CPL, and Padé cosmography. Under a common baseline scheme, all three models show a qualitatively similar, low-amplitude variation in the per-bin $H_0$ estimates. A simple Fourier-like parametrization captures this behaviour, but the amplitude differs from zero only at a marginal significance of about $1.71$--$1.94\,σ$, with similar behaviour observed across all three cosmological frameworks. We then investigate the robustness and possible origin of this feature. Alternative binning schemes preserve its qualitative form, whereas single-probe per-bin fits (SNe-only, CC-only, BAO-only) yield ratios $H_{0,i}/H_{0,\mathrm{global}}$ mostly consistent with unity and do not reproduce the pronounced drift seen in the joint baseline constraints. Finally, by comparing different global versus piecewise-constant configurations for $\{H_0,Ω_m,M,r_d\}$, we find that a baseline-like oscillatory pattern re-emerges only when multiple degenerate parameter combinations are allowed to vary across bins, while it is strongly suppressed when only $H_0$ is bin-dependent. Taken together, these results indicate that the apparent oscillatory behaviour of $H_0(z)$ in late-time arises from known parameter degeneracies and does not constitute robust evidence for a genuine redshift evolution.

Figures (6)

• Figure 1: Per-bin constraints on the Hubble constant $H_0(z)$ from three models under the baseline scheme. Blue squares: flat $\Lambda$CDM; orange triangles: CPL ($w_0w_a$CDM); green circles: Padé $P_{21}$ cosmography. Error bars show 68% credible intervals at the effective redshift $z_{\rm eff}$. Purple and gray shaded bands indicate the SH0ES ($H_0 = 73.04 \pm 1.04$ km s$^{-1}$ Mpc$^{-1}$) Riess2022 and Planck 2018 ($H_0 = 67.4 \pm 0.5$ km s$^{-1}$ Mpc$^{-1}$) Planck2018 results, respectively.
• Figure 2: Fourier-like single-mode fits to the binned $H_0(z)$ obtained in the baseline scheme for the flat $\Lambda$CDM, CPL, and Padé $P_{21}$ models. Solid, dashed, and dash-dotted curves show the best-fitting $H_0^{\mathrm{eff}}(z) = \hat{H}_0 + A \cos(4\pi a)$ for $\Lambda$CDM, CPL, and Padé, respectively. Thin colored dotted lines indicate the individual $1\sigma$ envelopes of each model, while the gray shaded region marks their common $1\sigma$ overlap. The open circles with error bars denote the baseline $\Lambda$CDM bin measurements, plotted for reference.
• Figure 3: Alternative binning scheme results. (a--d) For each binning scheme (A0–A3), the solid curve shows the Fourier-like best-fit trend of $H_0(z)$ and the shaded band indicates its $1\sigma$ credible region; the upper-left annotations list the fitted $(\hat{H}_0, A)$ values. (e) Points-only comparison: each marker is the binned $H_0$ at the effective redshift $z_{\rm eff}$ with a $1\sigma$ error bar; the gray band indicates the global (unbinned) estimate from the same data and model. (f) Consensus region across schemes: the shaded area denotes the Majority overlap (3/4), the black dashed lines mark the Full overlap (4/4), and the solid black curve is the mean of the four fitted trends.
• Figure 4: Per-bin ratios of the Hubble constant, $H_{0,i}/H_{0,\mathrm{global}}$, versus effective redshift $z_{\rm eff}$, for the single-probe binned fits compared with the baseline scheme. Hollow five-point stars denote the baseline scheme; filled circles, squares, and triangles correspond to SNe-only, CC-only, and BAO-only, respectively. Vertical bars show $1\sigma$ uncertainties. The dashed horizontal line marks $H_{0,i}/H_{0,\mathrm{global}} = 1$, i.e. no deviation from each probe's global scale.
• Figure 5: Constraints on piecewise-constant $H_0(z)$ for different parameter configurations. The left panel compares the baseline binned analysis (Baseline) with the case in which all four parameters $\{H_0,\Omega_m,M,r_d\}$ are treated as piecewise-constant (All-para). The right panel shows the configuration in which only $H_0$ varies between bins ($H_0$-only), compared with the All-para case. In both panels, the shaded bands show the $1\sigma$ uncertainty of the corresponding Fourier fits, with colors matching the associated data points.