On the robustness of the constancy of the Supernova absolute magnitude: Non-parametric reconstruction & Bayesian approaches

In this work, we test the robustness of the constancy of the Supernova absolute magnitude M_B using Non-parametric Reconstruction Techniques (NRT). We isolate the luminosity distance parameter d_L(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 and the Hubble constant H₀, is replaced by a degeneracy between M_B and the sound horizon at drag epoch r_d. When imposing the r_d value, this yields the M_B(z) =M_B + δM_B(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 M_B = - 19 . 22 ± 0 . 20 , and for the GP we get M_B = - 19 . 25 ± 0 . 39 as a mean for the full distribution when using the sound horizon from late time measurements. These estimations provide a 1 σ possibility of a nuisance parameter presence δM_B(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.