Equivalence Principle and the Baryon Acoustic Peak

TL;DR

This work analyzes how a long-wavelength density perturbation $\delta_L$ couples to short-distance cosmological statistics near the BAO feature, using the equivalence principle to show a universal long-short interaction. It derives a real-space three-point function and a squeezed-limit bispectrum that capture this coupling in the presence of BAO wiggles, and develops an infrared (IR) resummation framework to sum all orders in the long-mode displacement, significantly improving perturbation theory predictions for the BAO power spectrum. The authors quantify BAO broadening with a scale $\Sigma_\Lambda$ and show how IR resummation yields a dressed correlation function $\tilde{\xi}_g$ and a practical $P̃(k)$ that match simulations and reproduce the observed broadening, with the Zel'dovich approximation emerging naturally from this approach. They also discuss BAO reconstruction as an empirical validation of the underlying long-short coupling and its practical implications for precision cosmology.

Abstract

We study the dominant effect of a long wavelength density perturbation $δ(λ_L)$ on short distance physics. In the non-relativistic limit, the result is a uniform acceleration, fixed by the equivalence principle, and typically has no effect on statistical averages due to translational invariance. This same reasoning has been formalized to obtain a "consistency condition" on the cosmological correlation functions. In the presence of a feature, such as the acoustic peak at $l_{\rm BAO}$, this naive expectation breaks down for $λ_L<l_{\rm BAO}$. We calculate a universal piece of the three-point correlation function in this regime. The same effect is shown to underlie the spread of the acoustic peak, and is calculable to all orders in the long modes. This can be used to improve the result of perturbative calculations - a technique known as "infra-red resummation" - and is explicitly applied to the one-loop calculation of power spectrum. Finally, the success of BAO reconstruction schemes is argued to be another empirical evidence for the validity of the results.

Figures (6)

• Figure 1: Upper panel: The mixed real-momentum space three-point function of equation \ref{['eq:real']} (solid line) and the perturbation theory result (dot-dashed line) as a function of $r$. Both curves are obtained for $q=0.03\;h{\rm Mpc}^{-1}$, and are normalized by $P_{\rm lin}(k_{\rm eq})\xi(2\pi/k_{\rm eq})$. Lower panel: The comparison between the two results when the background (calculated from the featureless power spectrum) is subtracted.
• Figure 2: Upper panel: The bispectrum calculated using equation \ref{['bi']} (solid line) and the tree-level perturbation theory result (dot-dashed line) as a function of $k$, for $q=0.03\;h{\rm Mpc}^{-1}$. Both curves are normalized by $P_{\rm lin}^2(k_{\rm eq})$. Lower panel: The same as above with the smooth background subtracted.
• Figure 3: The acoustic peak in the matter correlation function in linear theory (solid), 1-loop perturbation theory (dashed), and simulation.
• Figure 4: The ratio of various theoretical approximations to the power spectrum to the simulation result. Solid: IR-resummed \ref{['1loop1']}, short-dashed: 1-parameter 1-loop EFT \ref{['1loop2']}, dot-dashed: 0-parameter 1-loop EFT \ref{['1loop2']} with $R=0$, and long-dashed: linear. The gray shaded region on the IR-resummed EFT curve gives the statistical error.
• Figure 5: Various theoretical approximations to the acoustic peak in the correlation function as well as simulation measurements. Solid: linear, dashed: IR-resummed linear, dot-dashed: IR-resummed 1-loop, and dotted: Zel'dovich.