# Phases of New Physics in the BAO Spectrum

## TL;DR

The paper demonstrates that the phase of the BAO spectrum remains unaffected by nonlinear evolution, making it a reliable indicator for detecting early universe new physics such as additional light species.

## Contribution

It establishes the invariance of the BAO phase against nonlinear effects through multiple theoretical arguments and computations.

## Key findings

- BAO phase is unaffected by nonlinear evolution
- Phase shift corresponds to a sign change in the correlation function
- Measuring BAO phase can reliably probe early universe physics

## Abstract

We show that the phase of the spectrum of baryon acoustic oscillations (BAO) is immune to the effects of nonlinear evolution. This suggests that any new physics that contributes to the initial phase of the BAO spectrum, such as extra light species in the early universe, can be extracted reliably at late times. We provide three arguments in support of our claim: First, we point out that a phase shift of the BAO spectrum maps to a characteristic sign change in the real space correlation function and that this feature cannot be generated or modified by nonlinear dynamics. Second, we confirm this intuition through an explicit computation, valid to all orders in cosmological perturbation theory. Finally, we provide a nonperturbative argument using general analytic properties of the linear response to the initial oscillations. Our result motivates measuring the phase of the BAO spectrum as a robust probe of new physics.