Constant roll inflation and Finsler geometry: exploring anisotropic universe with scalar factor parametrization

Abstract

In this paper, we investigate the concept of cosmological constant-roll inflation within the framework of Finslerian space-time. We approach the theory of cosmic evolution using Finsler geometry, incorporating the parametrization of the anisotropic parameter by the scalar factor a(t) by ηt=at-n\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\eta \\left( t \\right) =a\\left( t \\right) ^{-n}$$\\end{document}, where n is any real number. Our exploration mainly focuses on constant roll inflation, The analytical expression for Hubble parameter is found by using constant roll condition, and we derive crucial cosmological parameters such as scalar factor a(t), scalar spectral index (ns)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(n_{s})$$\\end{document}, and tensor-to-scalar ratio (r) for the inflationary universe. By using the analytical expressions for slow-roll parameters and the number of e-folds number we have found the values of ns\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n_{s}$$\\end{document} and r. Further, we identify the range of α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} values for which the theoretical values of spectral indices align with the observed Planck’s data. This work significantly contributes to our understanding of inflationary dynamics within the context of Finsler geometry.