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 $M_B$ 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 $\mu(z)$. Consequently, the degeneracy between the absolute magnitude and the Hubble constant $H_0$, 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 $M_B(z) = M_B + \delta M_B(z)$ 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 $M_B = -19.22\pm0.20$, and for the GP we get $M_B = -19.25\pm0.39$ as a mean for the full distribution when using the sound horizon from late time measurements. These estimations provide a $1\,\sigma$ possibility of a nuisance parameter presence $\delta M_B(z)$ 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.