Phases of New Physics in the BAO Spectrum

TL;DR

This paper addresses the challenge of using large-scale structure data in the presence of nonlinear gravitational evolution by identifying a robust observable: the phase of the BAO spectrum. The authors provide three complementary justifications for phase protection: (i) a phase shift maps to a sign change in the real-space correlation function near the BAO scale, which nonlinear dynamics cannot generate; (ii) an explicit all-orders perturbative calculation confirms that nonlinearities alter only the amplitude and frequency of BAO features, not their phase; (iii) a nonperturbative argument based on causality and analyticity of the linear response extends the phase protection beyond perturbation theory. The results imply that late-time BAO-phase measurements can reliably probe early-universe physics, including extra light species characterized by a phase-shifting parameter such as $\beta$, with significant implications for constraints on $N_{\rm eff}$. The work motivates incorporating BAO phase information into future galaxy surveys to improve sensitivity to new physics, potentially rivaling upcoming CMB constraints through LSS data alone.

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.

Figures (3)

• Figure 1: Plot of the BAO spectrum $P^{\rm w}(k)$ for varying number of relativistic species $N_{\rm eff}$. The no-wiggle spectrum $P^{\rm nw}(k)$ has been divided out Hamann:2010pwfuture. The photon and baryon densities have been kept fixed, while the dark matter density has been adjusted to keep matter-radiation equality invariant. The wavenumbers $k$ have been rescaled to remove the effect of $N_{\rm eff}$ on the BAO frequency. The amplitudes of the spectra have been normalized at the peak near $k=0.2\, h {\rm Mpc}^{-1}$ which removes the effect of $N_{\rm eff}$ on the amplitude of the oscillations (and some of the effect on the damping envelope). What remains visible is mostly the phase shift of the spectra.
• Figure 2: Plot of the sine (red) and cosine (blue) contributions to the correlation function (\ref{['equ:Xiw']}) for a toy model with power law index $n=-1.8$ at large $k$. The model includes the effects of Silk damping and a simple parameterization for the turnover of the power spectrum at low $k$. The dashed lines correspond to the same models with the broadband spectrum taken to be the exact $\Lambda$CDM spectrum. Both sets of curves are more realistic than the pure power-law spectra in (\ref{['eq:powerlaw']}). We see qualitatively similar results for the resulting contributions to the correlation function.
• Figure 3: Illustration of the domain of integration of ${\vec{q}}$ for fixed ${\vec{k}}$. We divide the ${\vec{q}}$-plane into two regions: I) $p \equiv |{\vec{k}}-{\vec{q}} | > k_s$ (outside the blue circle) and II) $p< \Lambda < k$ (inside the red circle). These regimes are considered in §\ref{['sec:short']} and §\ref{['sec:long']}, respectively. In the overlap region, $k_s< p < \Lambda$, both treatments apply.