# Low-Scale D-term Inflation and the Relaxion

## TL;DR

This paper proposes a low-scale inflation model driven by a D-term from a new gauge symmetry, which naturally integrates the relaxion mechanism to address the supersymmetric hierarchy problem and explains soft mass scales up to 10^6 GeV.

## Contribution

It introduces a novel low-scale D-term inflation model that incorporates the relaxion mechanism within supersymmetry, compatible with Planck data and explaining soft mass scales.

## Key findings

- Achieves a low Hubble scale of inflation consistent with observations.
- Demonstrates the relaxion can scan soft masses up to 10^6 GeV.
- Provides a natural framework linking inflation and supersymmetry breaking.

## Abstract

We present a dynamical cosmological solution that simultaneously accounts for the early inflationary stage of the Universe and solves the supersymmetric little hierarchy problem via the relaxion mechanism. First, we consider an inflationary potential arising from the $D$-term of a new $U(1)$ gauge symmetry with a Fayet--Iliopolous term, that is independent of the relaxion. A technically natural, small $U(1)$ gauge coupling, $g\lesssim 10^{-8}$, allows for a low Hubble scale of inflation, $H_I\lesssim 10^5$ GeV, which is shown to be consistent with Planck data. This feature is then used to realize a supersymmetric two-field relaxion mechanism, where the second field is identified as the inflaton provided that $H_I\lesssim 10$ GeV. The inflaton controls the relaxion barrier height allowing the relaxion to evolve in the early Universe and scan the supersymmetric soft masses. After electroweak symmetry is broken, the relaxion settles at a local supersymmetry-breaking minimum with a range of $F$-term values that can naturally explain supersymmetric soft mass scales up to $10^6$ GeV.