On the Robustness of the Constancy of the Supernova Absolute Magnitude: Non-parametric Reconstruction \& Bayesian approaches

Abstract

In this work, we test the robustness of the constancy of the Supernova absolute magnitude MB using Non-parametric Reconstruction Techniques (NRT). We isolate the luminosity distance parameter dL(z) from the Baryon Acoustic Oscillations (BAO) data set and cancel the expansion part from the observed distance modulus µ(z). Consequently, the degeneracy between the absolute magnitude with the Hubble constant H0, is replaced by a degeneracy with the sound horizon at drag epoch r d . When imposing the r d value, this yields the MB(z) = MB + δMB(z) value from NRT. We perform the respective reconstructions using the model independent Artificial Neural Network (ANN) technique and Gaussian processes (GP) regression. For the ANN we infer MB = −19.22 ± 0.20, and for the GP we get MB = −19.25 ± 0.39 when using the sound horizon from late time measurements. These estimations provide a 1 σ possibility of a nuisance parameter presence δMB(z) at higher redshifts. We also tested different known nuisance models with the Markov Chain Monte Carlo (MCMC) technique which showed a strong preference for the constant model, but it was not possible not single out a best fit nuisance model.

Gaussian Processes and Effective Field Theory of f(T) Gravity under the H 0 Tension

“…Hence, Gaussian processes form a model-independent function reconstruction method without any special physical assumption and parameterization. Therefore, they are widely used in cosmological research to reconstruct physical parameters from observational data sets (Holsclaw et al 2010 Benisty et al 2022).…”

“…The concept of EFT has been widely applied to cosmological studies (Arkani-Hamed et al 2007;Cheung et al 2008;Bloomfield et al 2013;Gleyzes et al 2013;Gubitosi et al 2013;Frusciante & Perenon 2020;Mylova et al 2021;Gong & Mylova 2022), and this approach was developed recently for torsional gravity (Cai et al 2018;Li et al 2018). On the other hand, the Gaussian process regression provides us a reliable way to obtain fitting functions directly from observational data, and it has been widely used to reconstruct nonlinear functions (Holsclaw et al 2010;Seikel & Clarkson 2013;Yang et al 2015;Cai et al 2016a;Wang & Meng 2017;Elizalde & Khurshudyan 2019;Mukherjee & Banerjee 2020;Aljaf et al 2021;Benisty 2021;Bernardo & Levi Said 2021;Jesus et al 2021;Levi Said et al 2021;Rodrigues & Bengaly 2021;von Marttens et al 2021;Benisty et al 2022). With this approach, we are able to analyze Hubble parameter observational data without any special assumption or specific model.…”

The Hubble constant from galaxy cluster scaling-relation and SNe Ia observations: a consistency test

“…For this purpose, we used the scikit-learn module in python [41]. Gaussian Processes (GPs) offer a non-parametric way to model a function and are characterized by the mean function and the kernel function [42,43]. For this work, we select the squared exponential covariance function, which is given by:…”