Palatini Higgs inflation and the refined dS conjecture

The refined de Sitter derivative conjecture provides constraints to potentials that are low energy effective theories of quantum gravity. It can give direct bounds on inflationary scenarios and determine whether the theory is in the Landscape or the Swampland (Cheong et al. in Phys Lett B 789:336–340, 2019). Any inflationary model can be checked by these conditions, and non-minimally coupled scalar field theory is not an exception. We consider the “Palatini Higgs inflation” scenario taking the refined de Sitter derivative conjecture into account. According to the latest cosmological observations from Planck 2018, BICEP2+Keck\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {BICEP2+}Keck$$\end{document} (Ade et al. in Phys Rev Lett 121:221301, 2018; Akrami et al in Planck 2018 results. X. Constraints on inflation, 2018. arXiv:1807.06211 [astro-ph.CO]; Aghanim et al. in Planck 2018 results: VI. Cosmological parameters, 2018. arXiv:1807.06209 [astro-ph.CO]) and the bound of non-minimal coupling parameter ξ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\xi $$\end{document} (Shaposhnikov et al. in arXiv:2001.09088v2; in JCAP 07:064, 2020), we suggest that if the refined dS conjecture does indeed hold, then the Palatini Higgs inflation model cannot be the low energy effective theory of a consistent quantum gravity theory since the two parameters c1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$c_1$$\end{document} and c2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$c_2$$\end{document} are much smaller than order 1, which is inconsistent with the refined dS conjecture. Therefore, we suggest that it is in the “Swampland.”