# Many-field Inflation: Universality or Prior Dependence?

## TL;DR

This paper explores how initial condition priors influence observable predictions in many-field inflation models, deriving universal formulas and highlighting prior dependence, especially in quadratic inflation.

## Contribution

It provides analytic expressions linking spectral index predictions to initial condition priors in many-field inflation, using the central limit theorem and horizon crossing approximation.

## Key findings

- Universal predictions depend on prior choices for initial conditions.
- Analytic formulas derived for spectral index in many-field inflation.
- Numerical simulations confirm the validity of the analytic results.

## Abstract

We investigate the observational signatures of many-field inflation and present analytic expressions for the spectral index as a function of the prior. For a given prior we employ the central limit theorem and the horizon crossing approximation to derive universal predictions. These include a specific dependence on the prior choice for initial conditions that has not been seen in previous studies. Our main focus is on quadratic inflation, for which the initial conditions statistics decouple from those of the mass distribution, while other monomials are also briefly discussed. We verify the validity of our calculations by comparing to full numerical simulations with 100 fields using the transport method.