Some remarks on nonminimal coupling of the inflaton

摘要

The nonminimal coupling of the inflaton is known to alleviate the smallness of the quartic coupling λ in the chaotic inflation with φ~4 potential. A large ξ is required to obtain the cosmic microwave background (CMB) power spectrum while a small value ~ 1/6 seems to be preferred from spectral index. There are issues related to conformal transformations, choice of frame and natural value(s) of ξ for a given potential. We revisit some of these issues and invoke field theoretic arguments (which exist in different context and have not been employed previously in the context of inflation) in order to address the same. A rather strong and general conclusion reached, based on the requirements of renormalizability and finiteness of specific matrix elements in a quantum theory, is that it is generically not possible to eliminate the nonminimal coupling by going from the Jordan to the Einstein frame via conformal transformations. We also comment on Higgs inflation.