# Trans-Planckian quantum corrections and inflationary vacuum fluctuations of non-minimally coupled scalar fields

## TL;DR

This paper investigates how trans-Planckian physics influences inflationary vacuum fluctuations and primordial density perturbations, showing that UV effects can significantly modify the inflationary potential under certain conditions.

## Contribution

It introduces a method to incorporate trans-Planckian corrections into the inflationary potential using non-minimally coupled scalar fields and adiabatic regularization.

## Key findings

- UV effects are embedded in the effective potential during inflation.
- Trans-Planckian corrections can significantly alter the inflationary potential.
- Derived a constraint on UV scale: _{UV} bb H/g^{1/2}.

## Abstract

In the present paper we discuss how trans-Planckian physics affects inflationary vacuum fluctuations and primordial density perturbations. The trans-Planckian problem during inflation has been widely discussed in literature, but it is still under debate. We reconsider this problem by using the two-point correlation function of the non-minimally coupled scalar fields and constructing the effective potential with the adiabatic (WKB) regularization or approximation. First, we clearly show that the cut-off divergence of the quantum fluctuations does not drastically change during inflation under reasonable assumptions and the corrections can be embedded in standard effective potential. Thus, the UV effects on the primordial density perturbation are well translated into the effective potential. Then, we find out the modified effective potential from the inflationary fluctuations and show how the trans-Planckian or UV corrections change the potential during inflation. We clearly show that the new physics strongly affects the inflation potential during inflation and we obtain a inflationary constraint $\Lambda_{\rm UV} \ll H/g^{1/2}$ where $g$ is the interaction coupling at the UV scale $\Lambda_{\rm UV}$.