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In this paper, we discuss about the possibility to enhance thetensor-to-scalar ratio $r$ under the condition of Trans-Planckian censorshipconjecture (TCC), thus $r\sim O(10^{-3})$ could be observable within thesensitivity of future experiments. We make use of the scalar-tensor theorywhere inflaton is nonminimally coupled to gravity. After demonstrating that theTCC condition could be modified in scalar-tensor theory, we show that due tothe effects of modified gravity at the end of inflation, a large $r\simO(10^{-3})$ could be allowed without violating the TCC. Moreover, themodification can give rise to a weak coupling of gravity to the inflationfield. If such an effect has been present as early as inflation starts, itwould imply that in our case, the Universe might have experienced anasymptotically safe period at its early time.

Large $r$ against Trans-Planckian Censorship in Scalar-Tensor Theory?