A Non-parametric Reconstruction of the Hubble Parameter $H(z)$ Based on Radial Basis Function Neural Networks

Abstract

Accurately measuring the Hubble parameter is vital for understanding the expansion history and properties of the universe. In this paper, we propose a new method that supplements the covariance between redshift pairs to improve the reconstruction of the Hubble parameter using the OHD dataset. Our approach utilizes a cosmological model-independent radial basis function neural network (RBFNN) to describe the Hubble parameter as a function of redshift effectively. Our experiments show that this method results in a reconstructed Hubble parameter of $H_0=67.1\pm 9.7\mathrm{km}{\mathrm{s}}^{-1}\mathrm{Mp}{\mathrm{c}}^{-1}$ , which is more noise-resistant and fits better with the $\Lambda$CDM model at high redshifts. Providing the covariance between redshift pairs in subsequent observations will significantly improve the reliability and accuracy of Hubble parametric data reconstruction. Future applications of this method could help overcome the limitations of previous methods and lead to new advances in our understanding of the universe.

arXiv comment10 pages, 2 tables, 5 figures. Matches the published version

References in corpus (29)

• A 2.4% Determination of the Local Value of the Hubble Constant
• In the Realm of the Hubble tension $-$ a Review of Solutions
• Constraints on the redshift dependence of the dark energy potential
• Tensions between the Early and the Late Universe
• A 6% measurement of the Hubble parameter at $z\sim 0.45$: direct evidence of the epoch of cosmic re-acceleration
• Cosmic Chronometers: Constraining the Equation of State of Dark Energy. I: H(z) Measurements
• Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z$\sim$2
• Two new diagnostics of dark energy
• Age-dating Luminous Red Galaxies observed with the Southern African Large Telescope
• Measurements of the Hubble Constant: Tensions in Perspective
• Constraints on the equation of state of dark energy and the Hubble constant from stellar ages and the CMB
• New constraints on cosmological parameters and neutrino properties using the expansion rate of the Universe to z~1.75
• Setting the Stage for Cosmic Chronometers. II. Impact of Stellar Population Synthesis Models Systematics and Full Covariance Matrix
• $H_0$ from cosmic chronometers and Type Ia supernovae, with Gaussian Processes and the novel Weighted Polynomial Regression method
• A litmus test for Lambda
• Model independent tests of the standard cosmological model
• Power of Observational Hubble Parameter Data: a Figure of Merit Exploration
• New Observational $H(z)$ Data from Full-Spectrum Fitting of Cosmic Chronometers in the LEGA-C Survey
• Reconstructing Functions and Estimating Parameters with Artificial Neural Networks: A Test with the Hubble Parameter and SNe Ia
• Neural Network Reconstruction of Late-Time Cosmology and Null Tests
• Reconstructing teleparallel gravity with cosmic structure growth and expansion rate data
• Hubble parameter reconstruction from a principal component analysis: minimizing the bias
• Towards a model-independent reconstruction approach for late-time Hubble data
• Nonparametric reconstruction of the cosmic expansion with local regression smoothing and simulation extrapolation
• Influence of the Bounds of the Hyperparameters on the Reconstruction of Hubble Constant with Gaussian Process
• Likelihood-free Cosmological Constraints with Artificial Neural Networks: An Application on Hubble Parameters and SNe Ia
• Reconstruction of late-time cosmology using Principal Component Analysis
• Cosmic expansion history from SNe Ia data via information field theory -- the charm code
• Test of Artificial Neural Networks in Likelihood-free Cosmological Constraints: A Comparison of IMNN and DAE

Cited by in corpus (7)

• The CosmoVerse White Paper: Addressing observational tensions in cosmology with systematics and fundamental physics
• LADDER: Revisiting the Cosmic Distance Ladder with Deep Learning Approaches and Exploring its Applications
• Gamma-Ray Bursts Calibrated from the Observational $H(z)$ Data in Artificial Neural Network Framework
• Gamma-Ray Bursts Calibrated by Using Artificial Neural Networks from the Pantheon+ Sample
• Estimating Cosmological Parameters and Reconstructing Hubble Constant with Artificial Neural Networks: A Test with covariance matrix and mock H(z)
• FLRW Kinematic-Induced Measurement of the Hubble Constant from Cosmic Chronometer and Redshift Drift Observations
• Constraining the Hubble Constant with a Simulated Full Covariance Matrix Using Neural Networks