Hubble parameter reconstruction from a principal component analysis: minimizing the bias

TL;DR

This paper presents a model-independent method using principal component analysis to reconstruct the Hubble parameter from supernova data, effectively reducing bias and aligning with independent measurements.

Contribution

It introduces a bias-suppression technique in PCA-based Hubble parameter reconstruction that does not rely on specific cosmological models or assumptions.

Findings

Successfully suppresses high-redshift bias in PCA components

Reconstructs Hubble parameter with reasonable uncertainty from real data

Results agree with independent galaxy-based measurements

Abstract

A model-independent reconstruction of the cosmic expansion rate is essential to a robust analysis of cosmological observations. Our goal is to demonstrate that current data are able to provide reasonable constraints on the behavior of the Hubble parameter with redshift, independently of any cosmological model or underlying gravity theory. Using type Ia supernova data, we show that it is possible to analytically calculate the Fisher matrix components in a Hubble parameter analysis without assumptions about the energy content of the Universe. We used a principal component analysis to reconstruct the Hubble parameter as a linear combination of the Fisher matrix eigenvectors (principal components). To suppress the bias introduced by the high redshift behavior of the components, we considered the value of the Hubble parameter at high redshift as a free parameter. We first tested our procedure using a mock sample of type Ia supernova observations, we then applied it to the real data compiled by the Sloan Digital Sky Survey (SDSS) group. In the mock sample analysis, we demonstrate that it is possible to drastically suppress the bias introduced by the high redshift behavior of the principal components. Applying our procedure to the real data, we show that it allows us to determine the behavior of the Hubble parameter with reasonable uncertainty, without introducing any ad-hoc parameterizations. Beyond that, our reconstruction agrees with completely independent measurements of the Hubble parameter obtained from red-envelope galaxies.