Resumming Cosmological Perturbations via the Lagrangian Picture: One-loop Results in Real Space and in Redshift Space

TL;DR

This work introduces a Lagrangian perturbation theory (LPT)–based resummation for nonlinear cosmological perturbations, deriving a tractable power spectrum that naturally incorporates infinite Eulerian perturbation terms via an exponential damping factor. The authors compute both real-space and redshift-space clustering, showing that the formalism accurately captures BAO features and nonlinear smoothing, and extends to redshift-space distortions with analytic kernels and cumulants. The 1-loop real-space and redshift-space results outperform standard 1-loop SPT and align well with N-body simulations across BAO scales, while maintaining computational efficiency. This framework provides a robust analytic tool for interpreting redshift surveys and constraining cosmological parameters, including dark energy and curvature, with BAO measurements.

Abstract

We develop a new approach to study the nonlinear evolution in the large-scale structure of the Universe both in real space and in redshift space, extending the standard perturbation theory of gravitational instability. Infinite series of terms in standard Eulerian perturbation theory are resummed as a result of our starting from a Lagrangian description of perturbations. Delicate nonlinear effects on scales of the baryon acoustic oscillations are more accurately described by our method than the standard one. Our approach differs from other resummation techniques recently proposed, such as the renormalized perturbation theory, etc., in that we use simple techniques and thus resulting equations are undemanding to evaluate, and in that our approach is capable of quantifying the nonlinear effects in redshift space. The power spectrum and correlation function of our approach are in good agreement with numerical simulations in literature on scales of baryon acoustic oscillations. Especially, nonlinear effects on the baryon acoustic peak of the correlation function are accurately described both in real space and in redshift space. Our approach provides a unique opportunity to analytically investigate the nonlinear effects on baryon acoustic scales in observable redshift space, which is requisite in constraining the nature of dark energy, the curvature of the Universe, etc., by redshift surveys.

Figures (12)

• Figure 1: Diagrammatic representations of $C^{(11)}_{ij}(\bm{p})$ (a), $C^{(22)}_{ij}(\bm{p})$ (b), $C^{(13)}_{ij}(\bm{p})$ (c), and $C^{(112)}_{ijk}(\bm{p}_1,\bm{p}_2,\bm{p}_3)$ (d).
• Figure 2: Diagrams for our resummed power spectrum of Eq. (\ref{['eq:1-27']}).
• Figure 3: Two-loop bubble diagrams (see text).
• Figure 4: Comparison of power spectra by different approximations at redshifts $z=0, 1, 2, 4$ (from upper to lower lines). Black (solid) line: this work; red (dotted) line: linear theory; green (dashed) line: 1-loop SPT. Two nonlinear scales $k_{\rm NL}$, $k_{\rm NL}/2$ in each redshift are indicated by arrows.
• Figure 5: Nonlinear evolution of the baryon acoustic oscillations in real space for various redshifts, $z = 0$ (top left), $0.5$ (center left), $1$ (bottom left), $2$ (top right), $3$ (center right), $4$ (bottom right). Each power spectrum is divided by a smoothed, no-wiggle linear power spectrum $P_{\rm nw}(k)$EH99. Black (solid) line: this work; red (dotted) line: linear theory; green (dashed) line: 1-loop SPT. The validity range $k < k_{\rm NL}/2$, where our result is expected to be accurate within a few percent, is indicated by arrows.