Testing cosmological models with the brightness profile of distant galaxies

The goal of this work is to use observed galaxy surface brightness profiles at high redshifts to determine, among a few candidates, the cosmological model best suited to interpret these observations. Theoretical predictions of galactic surface brightness profiles are compared to observational data in two cosmological models, Λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Lambda $\end{document}CDM and Einstein-de Sitter, to calculate the evolutionary effects of different spacetime geometries in these profiles in order to try to find out if the available data is capable of indicating the cosmology that most adequately represents actual galactic brightness profiles observations. Starting from the connection between the angular diameter distance and the galactic surface brightness as advanced by Ellis and Perry (Mon. Not. R. Astron. Soc. 187:357, 1979), we derived scaling relations using data from the Virgo galactic cluster in order to obtain theoretical predictions of the galactic surface brightness modeled by the Sérsic profile at redshift values equal to a sample of galaxies in the range 1.5≲z≲2.3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$1.5 \lesssim z \lesssim 2.3$\end{document} composed by a subset of Szomoru’s et al. (Astrophys. J. 749:121, 2012) observations. We then calculated the difference between theory and observation in order to determine the changes required in the effective radius and effective surface brightness so that the observed galaxies may evolve to have features similar to the Virgo cluster ones. Our results show that within the data uncertainties of this particular subset of galaxies it is not possible to distinguish which of the two cosmological models used here predicts theoretical curves in better agreement with the observed ones, that is, one cannot identify a clear and detectable difference in galactic evolution incurred by the galaxies of our sample when applying each cosmology. We also concluded that the Sérsic index n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$n$\end{document} does not seem to play a significant effect in the evolution of these galaxies. Further developments of the methodology employed here to test cosmological models are also discussed.