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

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.

💡 Research Summary

The paper addresses the Trans‑Planckian Censorship Conjecture (TCC), which imposes extremely stringent limits on single‑field slow‑roll inflation (inflationary energy density below ~10¹⁰ GeV and a tensor‑to‑scalar ratio r < 10⁻³⁰). The authors propose a two‑stage inflationary scenario that evades these limits while remaining compatible with current observations.

The key innovation is to generalize the kinetic sector of a single scalar field by imposing the relation
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