usepackage[polutonikogreek,english]{babel}

foreignlanguage{polutonikogreek}{...}

documentclass[11pt, english, ...]

documentclass[11pt, english, greek.polutoniko, ...]

textgreek{...}

usepackage{fontspec}

The fontspec package requires either XeTeX or LuaTeX.
You must change your typesetting engine to, e.g., "xelatex" or
"lualatex"instead of plain "latex" or "pdflatex".

documentclass[11pt, english, singlespacing, headsepline, ]{MastersDoctoralThesis}

documentclass{article}
usepackage[utf8]{inputenc}

usepackage{textgreek}

begin{document}

{textgreekfont Πάτερ ἡμῶν ὁ ἐν τοῖς οὐρανοῖς}

{textgreekfontcatcode`~=12 P'ater <hm~wn <o >en to~is o>urano~is}

end{document}

PassOptionsToPackage{greek.polutoniko, main=english}{babel}
documentclass[11pt, english, singlespacing, headsepline]{MastersDoctoralThesis}
usepackage[utf8]{inputenc}

begin{document}
Cosmos in Greek is textgreek{Κόσμος}
end{document}