A Remedy of the Trans-Planckian Censorship Problem with Smooth Slow-roll to Power-law Inflation Transitions in Scalar Field Theory

Abstract: It is known that if the standard slow-roll inflation is followed by a power-law inflationary regime, then the trans-Planckian modes may be safely be contained in the Hubble horizon and never exit it during inflation. In this work we investigate how to realize a smooth transition between a slow-roll and a power-law inflationary regime in the context of single scalar field inflation. As we show it is possible to realize such a smooth transition by generalizing the kinetic energy of single scalar field in the form $\dotφ^2=β(φ)V(φ)$, where $β(φ)$ is some appropriate function of the scalar field. Using two distinct approaches we show that it is possible to realize a smooth transition from a slow-roll to a power-law inflationary regime, and the two approaches produce identical results regarding the slow-roll regime. Also we show that the slow-roll regime is quite short, about $N\sim 30$ $e$-foldings, with the flatness and horizon problems being solved with the synergistic effect of the two inflationary patches. The slow-roll era is found to be compatible with the Atacama Cosmology Telescope data.