Cosmic microwave background in a non-Archimedean world

Abstract

The universe begins its expansion from dimensions below the Planck scale, where the uncertainty principle reigns. If at these dimensions the Archimedean geometry is useless, the p-adic non-Archimedean world creates an environment conducive to phenomenological modeling. The standard description of the cosmological density contrast is made by the Fourier decomposition of plane waves in the field of p-adic numbers Qp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {Q}_p$$\\end{document}. The coupling of the primordial perturbations is done by coupling the phases. Since the phases are the stars of this article, we represent them in the hue-saturation-brightness color space both in R\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {R}$$\\end{document} and in Qp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {Q}_p$$\\end{document}. If the primordial perturbations interact weakly with each other, with their growth they become important enough from an energetic point of view to gravitationally interact with each other. We identify the coupling using the phase gradient operator, and extract the coupled points from the spectrum. We use pseudoentropy for the quantitative analysis of the information generated by the phases.