Time-Sliced Perturbation Theory II: Baryon Acoustic Oscillations and Infrared Resummation

TL;DR

The paper develops a systematic, diagrammatic resummation of infrared non-linear effects in BAO physics using Time-Sliced Perturbation Theory (TSPT) with a wiggly-smooth decomposition of the power spectrum. It identifies IR-enhanced diagrams, formulates robust power-counting, and performs leading- and next-to-leading-order resummations for the power spectrum and bispectrum, including hard-loop corrections. The approach yields accurate BAO broadening and a quantifiable BAO peak shift, showing strong agreement with N-body data and improving over standard perturbation theory without ad hoc parameters. The framework provides a clear route to higher-order corrections and extensions to more general observables and cosmologies.

Abstract

We use time-sliced perturbation theory (TSPT) to give an accurate description of the infrared non-linear effects affecting the baryonic acoustic oscillations (BAO) present in the distribution of matter at very large scales. In TSPT this can be done via a systematic resummation that has a simple diagrammatic representation and does not involve uncontrollable approximations. We discuss the power counting rules and derive explicit expressions for the resummed matter power spectrum up to next-to leading order and the bispectrum at the leading order. The two-point correlation function agrees well with N-body data at BAO scales. The systematic approach also allows to reliably assess the shift of the baryon acoustic peak due to non-linear effects.

Figures (8)

• Figure 1: Matter two-point correlation function $\xi(x)$ at redshift $z=0$. The thin (thick) blue solid line shows the infrared-resummed result obtained in TSPT at leading order (next-to-leading order). At BAO scales the perturbative expansion within the TSPT framework converges well and agrees with $N$-body results from large-scale numerical simulations Kim:2011ab (red dot-dashed line). For comparison, we also show the linear (black dashed) and SPT 1-loop (black dotted) results.
• Figure 2: Example of TSPT Feynman rules.
• Figure 3: Ratio of oscillatory (wiggly) part $P_w$ of the linear power spectrum to the smooth part $P_s$ obtained using two separation prescriptions. The $\Lambda$CDM cosmological parameters have been chosen as in Kim:2011ab. The solid curve corresponds to the decomposition used in numerical computations in Sec. \ref{['sec:pract']}. The alternative decomposition (dashed curve) is used for cross-checks.
• Figure 4: Example of Feynman rules for wiggly and smooth elements.
• Figure 5: Dependence of the BAO damping factor $\Sigma^2$ on the separation scale $k_S$. Dashed curves show the limiting cases discussed in the text.