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

TL;DR

The paper addresses the trans-Planckian censorship problem (TCC) in slow-roll inflation by proposing a smooth transition to a power-law inflationary tail within a single scalar field framework. It introduces a kinetic-energy ansatz $\dot{\phi}^2=\beta(\phi)V(\phi)$ with a carefully chosen $\beta(\phi)$ (e.g., $\beta(\phi)=\gamma/(\delta+\lambda\kappa\phi)$) that interpolates between $\beta\approx0$ during slow-roll and $\beta\approx\text{const}=\beta$ in the tail, yielding two inflationary patches. The slow-roll phase lasts about $N\sim30$ e-folds and produces $n_s$ and $r$ compatible with ACT and latest BICEP-Keck constraints, while the subsequent power-law tail features an exponential-like potential with $V(\phi)\simeq \mathcal{V}_0 e^{\tilde{\lambda}\phi}$ and a constant equation of state $w_\phi= (\beta-2)/(\beta+2)$, enabling a slower horizon contraction and alleviating TCC concerns. The overall inflationary history can address flatness and horizon problems, with the tail ending via a hybrid waterfall mechanism that yields a finite total duration.

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.

Figures (2)

• Figure 1: The TCC problem resolution in standard slow-roll inflation (blue circles) and in the scenario of a short slow-roll era followed by a power-law inflationary tail (green circles).
• Figure 2: The phenomenology of the slow-roll regime potential (\ref{['approximatepotential1']}) for $\gamma=0.1$ and $N=30$$e$-foldings, with the parameter $\lambda$ chosen in the range $\lambda=[10,100]$. We confront the model with the Planck 2018 likelihood curves, the BICEP/Keck updates on the Planck data and the ACT constraints on the spectral index (purple region). The model is compatible with the ACT data for $\lambda$ in the range $\lambda=[40,100]$.