A unified cosmographic reconstruction of the Hubble expansion: Bayesian constraints on dark energy and modified-gravity diagnostics
- 1Department of Mathematics, Bengaluru City University , Bengaluru 560001, Karnataka ,
- 2Department of Mathematics, Nrupathunga University , Bengaluru 560001, Karnataka ,
- 3Department of P.G. Studies and Research in Mathematics, Kuvempu University , Shankaraghatta, Shivamogga 577451, Karnataka ,
Abstract
We introduce the adaptive expansion-index parametrization, a compact and physically regularized representation of late-time expansion histories, and present it as the central methodological contribution of this work. Rather than parametrizing H(z), q(z), or w(z) directly, we model the logarithmic expansion index ϵ (z)≡ dln H/ dln (1+z)=1+q(z) with a three-parameter saturating profile that interpolates smoothly between a matter-like regime at high redshift and a de Sitter attractor in the future. The model integrates analytically to E(z)=[((1+z)3ν +κ)/(1+κ)]ϵ m/(3ν) and contains spatially flat Lambda cold dark matter (ΛCDM) exactly as the interior point (ϵ m,ν)=(3/2,1), so that departures from the concordance model are tested within a nested parameter space. By construction, the expansion rate is positive, finite-time future singularities are absent, the transition redshift is analytic, and the deceleration, jerk, snap and lerk parameters follow from an exact recursion. Because the ansatz encodes assumptions of smoothness, monotonicity, a single transition, and regular asymptotics, the reconstruction is parametric rather than model-independent, and its parameters are best read as coordinates within this representation. We constrain the model with 34 cosmic-chronometer measurements, 13 DESI DR2 BAO distance ratios with full covariance, and Pantheon+ supernovae with SH0ES calibration, treating the sound horizon rd as free. We find no statistically compelling departure from ΛCDM, while the H0 discrepancy persists as a shift in rd. Quantities tied to high-redshift, asymptotic, or extrapolated behaviour, including the cosmic age, higher-order cosmography, the effective dark-energy equation of state, and illustrative f(T), f(Q) and f(R) reconstructions, are more parametrization-dependent and are presented as applications of the framework.
Related
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- Hierarchical Gaussian-process reconstruction of late-time expansion with DESI BAO and compressed Planck priors
BibTeX
@article{k2026unified,
title = {{A unified cosmographic reconstruction of the Hubble expansion: Bayesian constraints on dark energy and modified-gravity diagnostics}},
author = {Thippeswamy K. R. and Laxmi Nirani and Narasimhamurthy S. K.},
journal = {Monthly Notices of the Royal Astronomical Society},
year = {2026},
month = oct,
doi = {10.1093/mnras/stag1872},
url = {https://academic.oup.com/mnras/article/doi/10.1093/mnras/stag1872/8965445},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - A unified cosmographic reconstruction of the Hubble expansion: Bayesian constraints on dark energy and modified-gravity diagnostics
AU - Thippeswamy K. R.
AU - Laxmi Nirani
AU - Narasimhamurthy S. K.
PY - 2026
DA - 2026/10/21
JO - Monthly Notices of the Royal Astronomical Society
DO - 10.1093/mnras/stag1872
UR - https://academic.oup.com/mnras/article/doi/10.1093/mnras/stag1872/8965445
AB - We introduce the adaptive expansion-index parametrization, a compact and physically regularized representation of late-time expansion histories, and present it as the central methodological contribution of this work. Rather than parametrizing H(z), q(z), or w(z) directly, we model the logarithmic expansion index ϵ (z)≡ dln H/ dln (1+z)=1+q(z) with a three-parameter saturating profile that interpolates smoothly between a matter-like regime at high redshift and a de Sitter attractor in the future. The model integrates analytically to E(z)=[((1+z)^3ν +κ)/(1+κ)]^ϵ _m/(3ν) and contains spatially flat Lambda cold dark matter (ΛCDM) exactly as the interior point (ϵ _m,ν)=(3/2,1), so that departures from the concordance model are tested within a nested parameter space. By construction, the expansion rate is positive, finite-time future singularities are absent, the transition redshift is analytic, and the deceleration, jerk, snap and lerk parameters follow from an exact recursion. Because the ansatz encodes assumptions of smoothness, monotonicity, a single transition, and regular asymptotics, the reconstruction is parametric rather than model-independent, and its parameters are best read as coordinates within this representation. We constrain the model with 34 cosmic-chronometer measurements, 13 DESI DR2 BAO distance ratios with full covariance, and Pantheon^+ supernovae with SH0ES calibration, treating the sound horizon r_d as free. We find no statistically compelling departure from ΛCDM, while the H_0 discrepancy persists as a shift in r_d. Quantities tied to high-redshift, asymptotic, or extrapolated behaviour, including the cosmic age, higher-order cosmography, the effective dark-energy equation of state, and illustrative f(T), f(Q) and f(R) reconstructions, are more parametrization-dependent and are presented as applications of the framework.
SN - 0035-8711
SN - 1365-2966
ER -