Constructing a cosmological model-independent Hubble diagram of type Ia supernovae with cosmic chronometers

TL;DR

This paper develops a model-independent method to construct Hubble diagrams of type Ia supernovae using cosmic chronometers, employing Gaussian processes and non-parametric smoothing to reconstruct the Hubble parameter from galaxy age data.

Contribution

It introduces a novel approach combining Gaussian processes and smoothing techniques to calibrate supernova luminosities without assuming a specific cosmological model.

Findings

Non-parametric smoothing yields H0 values consistent with local measurements.

Gaussian process reconstructions are sensitive to prior mean functions.

Both methods enable cosmology-independent supernova calibration.

Abstract

We apply two methods, namely the Gaussian processes and the non-parametric smoothing procedure, to reconstruct the Hubble parameter $H(z)$ as a function of redshift from 15 measurements of the expansion rate obtained from age estimates of passively evolving galaxies. These reconstructions enable us to derive the luminosity distance to a certain redshift $z$, calibrate the light-curve fitting parameters accounting for the (unknown) intrinsic magnitude of type Ia supernova (SNe Ia) and construct cosmological model-independent Hubble diagrams of SNe Ia. In order to test the compatibility between the reconstructed functions of $H(z)$, we perform a statistical analysis considering the latest SNe Ia sample, the so-called JLA compilation. We find that, for the Gaussian processes, the reconstructed functions of Hubble parameter versus redshift, and thus the following analysis on SNe Ia calibrations and cosmological implications, are sensitive to prior mean functions. However, for the non-parametric smoothing method, the reconstructed functions are not dependent on initial guess models, and consistently require high values of $H_0$, which are in excellent agreement with recent measurements of this quantity from Cepheids and other local distance indicators.