Derivative hierarchy as the origin of kernel-dependent trends in Gaussian process reconstructions of the hubble parameter

Abstract

We perform a model independent reconstruction of the cosmic expansion history using Gaussian Process regression, investigating how the smoothness properties of covariance kernels influence the inferred Hubble parameter. Using 32 cosmic chronometer measurements, we reconstruct $H(z)$ with the Matérn $3/2$, $5/2$, $7/2$, $9/2$, and Squared Exponential kernels, which form a well-defined hierarchy of differentiability. Across this hierarchy, we observe a systematic and monotonic trend in which increasing kernel smoothness is associated with progressively lower reconstructed values of the present-day Hubble constant $H_0$, accompanied by reduced statistical uncertainties. Rather than indicating a statistical preference for a specific kernel, this behaviour reflects the sensitivity of non-parametric reconstructions to the assumed smoothness prior encoded in the covariance function. The same ordering is reflected in descriptive goodness-of-fit statistics and remains stable when incorporating recent DESI DR2 BAO measurements and performing jackknife resampling tests, demonstrating robustness against individual data points and dataset variations. Additional analysis of derivative reconstructions shows that differences in kernel differentiability propagate into the local slope of the expansion history, providing a consistent interpretation of the observed ordering in $H_0$. Our results highlight that kernel smoothness plays an important role in Gaussian Process reconstructions and should be carefully accounted for when interpreting non-parametric cosmological inferences.

Published in Physics Letters B

References in corpus (16)

• The Clustering of the SDSS DR7 Main Galaxy Sample I: A 4 per cent Distance Measure at z=0.15
• DESI 2024 VI: Cosmological Constraints from the Measurements of Baryon Acoustic Oscillations
• Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z$\sim$2
• Gaussian Process Cosmography
• DESI 2024 IV: Baryon Acoustic Oscillations from the Lyman Alpha Forest
• Nonparametric Dark Energy Reconstruction from Supernova Data
• DESI 2024: Reconstructing Dark Energy using Crossing Statistics with DESI DR1 BAO data
• Nonparametric Reconstruction of the Dark Energy Equation of State
• Nonparametric late-time expansion history reconstruction and implications for the Hubble tension in light of recent DESI and type Ia supernovae data
• Using H(z) data as a probe of the concordance model
• Cosmic chronometers to calibrate the ladders and measure the curvature of the Universe. A model-independent study
• Model-independent cosmological inference post DESI DR1 BAO measurements
• Neural Network Reconstruction of $H^{\prime }(z)$ and its application in Teleparallel Gravity
• Non-parametric reconstruction of cosmological observables using Gaussian Processes Regression
• Reconstruction of dark energy using DESI DR2
• Revisiting model-independent constraints on spatial curvature and cosmic ladders calibration: updated and forecast analyses

Cited by in corpus (1)

• Model-independent reconstruction of cosmic thermodynamics and dark energy dynamics