Baryon Acoustic Oscillations in 2D: Modeling Redshift-space Power Spectrum from Perturbation Theory

TL;DR

The paper addresses the difficulty of extracting BAO information from redshift-space galaxy clustering due to non-linear gravitational clustering and redshift distortions. It develops an improved perturbation-theory framework that keeps non-linear density–velocity couplings through non-trivial A(k,μ) and B(k,μ) corrections derived from the exact redshift-space expression, and validates the approach against N-body simulations. It demonstrates that existing perturbation theory and phenomenological models bias cosmological inferences by up to a few percent, while the new model achieves near-percent accuracy for the monopole and quadrupole and reduces biases in the distance and growth-rate parameters. The results support using this enhanced redshift-space template to constrain dark energy and modified gravity from anisotropic BAOs in current and future surveys, with caveats about further improvements in bispectrum modeling and galaxy bias.

Abstract

We present an improved prescription for matter power spectrum in redshift space taking a proper account of both the non-linear gravitational clustering and redshift distortion, which are of particular importance for accurately modeling baryon acoustic oscillations (BAOs). Contrary to the models of redshift distortion phenomenologically introduced but frequently used in the literature, the new model includes the corrections arising from the non-linear coupling between the density and velocity fields associated with two competitive effects of redshift distortion, i.e., Kaiser and Finger-of-God effects. Based on the improved treatment of perturbation theory for gravitational clustering, we compare our model predictions with monopole and quadrupole power spectra of N-body simulations, and an excellent agreement is achieved over the scales of BAOs. Potential impacts on constraining dark energy and modified gravity from the redshift-space power spectrum are also investigated based on the Fisher-matrix formalism. We find that the existing phenomenological models of redshift distortion produce a systematic error on measurements of the angular diameter distance and Hubble parameter by 1~2%, and the growth rate parameter by ~5%, which would become non-negligible for future galaxy surveys. Correctly modeling redshift distortion is thus essential, and the new prescription of redshift-space power spectrum including the non-linear corrections can be used as an accurate theoretical template for anisotropic BAOs.

Figures (10)

• Figure 1: Ratio of power spectra to smoothed reference spectra in redshift space, $P_\ell^{\rm (S)}(k)/P_{\ell,{\rm no\hbox{-}wiggle}}^{\rm (S)}(k)$. N-body results are taken from the wmap5 simulations of Ref. Taruya:2009ir. The reference spectrum $P_{\ell,{\rm no\hbox{-}wiggle}}^{\rm (S)}$ is calculated from the no-wiggle approximation of the linear transfer function, and the linear theory of the Kaiser effect is taken into account. Short dashed and dot-dashed lines respectively indicate the results of one-loop PT and Lagrangian PT calculations for redshift-space power spectrum (Eqs. (\ref{['eq:Pk_SPT']}) and (\ref{['eq:Pk_LPT']})).
• Figure 2: Same as in Fig. \ref{['fig:ratio_pk_red_PT']}, but we here plot the results of phenomenological model predictions. The three different predictions depicted as solid, dashed, dot-dashed lines are based on the phenomenological model of redshift distortion (\ref{['eq:model_Psk']}) with various choices of Kaiser and Finger-of-God terms (Eqs.(\ref{['eq:model_Kaiser']}) and (\ref{['eq:model_FoG']})). Left panel shows the monopole power spectra ($\ell=0$), and the right panel shows the quadrupole spectra ($\ell=2$). In all cases, one-dimensional velocity dispersion $\sigma_{\rm v}$ was determined by fitting the predictions to the N-body simulations. In each panel, vertical arrow indicates the maximum wavenumber $k_{1\%}$ for improved PT prediction including up to the second-order Born approximation (see Eq. (\ref{['eq:k_limit']}) for definition).
• Figure 3: Redshift evolution of velocity dispersion $\sigma_{\rm v}$ determined by fitting the predictions of monopole and quadrupole power spectra to the N-body results. While the solid lines represent the linear theory prediction, the symbols indicate the results obtained by fitting models of redshift distortion with various choices of Kaiser and damping terms (see Fig. \ref{['fig:ratio_pk_red_phenom']}).
• Figure 4: Contributions of power spectrum corrections coming from the $A$ and $B$ terms divided by the smooth reference power spectrum, $P^{\rm(S)}_{\ell,{\rm corr}}(k)/P^{\rm(S)}_{\ell,{\rm no\hbox{-}wiggle}}(k)$ (Eq. (\ref{['eq:pkred_corr']})). We adopt the Gaussian form of the damping function $D_{\rm FoG}$ with $\sigma_{\rm v}$ computed from linear theory (see Eq.(\ref{['eq:sigmav_lin']})). Left and right panels respectively show the monopole and quadrupole power spectra at redshifts $z=3$ and $1$.
• Figure 5: Same as in Fig. \ref{['fig:ratio_pk_red_phenom']}, but we here adopt new model of redshift distortion (\ref{['eq:new_model']}). Solid and dashed lines represent the predictions for which the spectra $P_{\delta\delta}$, $P_{\delta \theta}$ and $P_{\theta\theta}$ are obtained from the improved PT including the correction up to the second-order Born correction, and one-loop calculations of the standard PT, respectively. In both cases, the corrections $A$ and $B$ given in Eqs. (\ref{['eq:A_term']}) and (\ref{['eq:B_term']}) are calculated from standard PT results (see Appendix \ref{['appendix:PT_calc_correction']}). The vertical arrows indicate the maximum wavenumber $k_{1\%}$ defined in Eq. (\ref{['eq:k_limit']}), for standard PT and improved PT (from left to right).