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.
Highlights
The imprint of the baryonic acoustic oscillations (BAO) on the distribution of matter at large scales and at different redshifts gives precise information about the expansion history and constituents of the Universe [1,2,3,4,5]
We develop a systematic approach to describe non-linear effects on the BAO feature in equal-time correlation functions based on time-sliced perturbation theory (TSPT) [24]
In this work we have developed a systematic approach to describe the non-linear evolution of the feature imprinted in the matter correlation functions by baryon acoustic oscillations
Summary
The imprint of the baryonic acoustic oscillations (BAO) on the distribution of matter at large scales and at different redshifts gives precise information about the expansion history and constituents of the Universe [1,2,3,4,5]. Apart from being quantitatively important in order to achieve good agreement with the results of large-scale N -body simulations at BAO scales, these NLO contributions are crucial for a reliable determination of the shift of the BAO peak They are sensitive to the non-dipole corrections and capture deviations from the Zel’dovich approximation. We further find that the difference between the NLO correlation function computed in TSPT and that obtained within the Zel’dovich approximation is about 5% in the region of the BAO peak (see Sec. 7.3) While small, this difference is above the estimated uncertainty in the TSPT calculation and the expected ultimate precision required to analyze the data of future surveys. Appendices A—E contain details of the calculations, whereas in Appendices F, G we present an alternative derivation of IR resummation of the power spectrum in SPT and compare our results with the exact formulas in the Zel’dovich approximation
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