# Non-standard hierarchies of the runnings of the spectral index in inflation

## TL;DR

This paper explores non-standard hierarchies of the spectral index runnings in inflation, proposing multi-field models with non-canonical kinetic terms and alternative scenarios like variable speed of light and quantum gravity effects.

## Contribution

It introduces a minimal two-field inflation model with non-canonical kinetic structure to generate large, non-standard hierarchies of spectral index runnings, and discusses alternative theoretical scenarios.

## Key findings

- Multi-field models can produce large non-standard runnings.
- Non-canonical kinetic terms are key to realizing these hierarchies.
- Alternative scenarios like variable speed of light also impact spectral index runnings.

## Abstract

Recent analyses of cosmic microwave background surveys have revealed hints that there may be a non-trivial running of the running of the spectral index. If future experiments were to confirm these hints, it would prove a powerful discriminator of inflationary models, ruling out simple single field models. We discuss how isocurvature perturbations in multi-field models can be invoked to generate large runnings in a non-standard hierarchy, and find that a minimal model capable of practically realising this would be a two-field model with a non-canonical kinetic structure. We also consider alternative scenarios such as variable speed of light models and canonical quantum gravity effects and their implications for runnings of the spectral index.