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

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