Stable nonsingular cosmologies in beyond Horndeski theory and disformal transformations

Abstract

In this paper, we collect, systemize and generalize the existing results for relations between general Horndeski theories and beyond Horndeski theories via disformal transformations of metric. We focus on those subclasses of beyond Horndeski theories which are disformally related to Horndeski theories and derive additional transformation rules relating the Lagrangian functions of these two theories. Then we demonstrate that some of these transformation rules become singular at some moments(s) once one constructs a nonsingular cosmological solution in beyond Horndeski theory that is free from ghost, gradient instabilities and strong gravity regime during the entire evolution of the system. The key issue here is that such solutions are banned in Horndeski theory due to the existing no-go theorem. The proof of singular behavior of disformal relations in this case resolves the apparent contradiction between the fact that Horndeski and beyond Horndeski theories were initially implied to be related via healthy field redefinition and at the same time these theories describe different physics in the context of nonsingular cosmologies.