How does non-linear dynamics affect the baryon acoustic oscillation?

Abstract

We study the non-linear behavior of the baryon acoustic oscillation in the power spectrum and the correlation function by decomposing the dark matter perturbations into the short- and long-wavelength modes. The evolution of the dark matter fluctuations can be described as a global coordinate transformation caused by the long-wavelength displacement vector acting on short-wavelength matter perturbation undergoing non-linear growth. Using this feature, we investigate the well known cancellation of the high-$k$ solutions in the standard perturbation theory. While the standard perturbation theory naturally satisfies the cancellation of the high-$k$ solutions, some of the recently proposed improved perturbation theories do not guarantee the cancellation. We show that this cancellation clarifies the success of the standard perturbation theory at the 2-loop order in describing the amplitude of the non-linear power spectrum even at high-$k$ regions.We propose an extension of the standard 2-loop level perturbation theory model of the non-linear power spectrum that more accurately models the non-linear evolution of the baryon acoustic oscillation than the standard perturbation theory. The model consists of simple and intuitive parts: the non-linear evolution of the smoothed power spectrum without the baryon acoustic oscillations and the non-linear evolution of the baryon acoustic oscillations due to the large-scale velocity of dark matter and due to the gravitational attraction between dark matter particles. Our extended model predicts the smoothing parameter of the baryon acoustic oscillation peak at $z=0.35$ as $\sim 7.7\ {\rm Mpc}/h$ and describes the small non-linear shift in the peak position due to the galaxy random motions.

Figures (8)

• Figure 1: The exact solutions of $P_{22}$ and $P_{13}$ [eq. \ref{['corrections:1loop']}] and the high-$k$ solutions without the short-wavelength modes $P_{\rm 22,high-k}$ and $P_{\rm 13,high-k}$ [eq. \ref{['ap_P1loop']}] are plotted as the red and black solid lines, respectively. The black dashed line denotes the no-wiggle high-$k$ solution for $P_{22}$ [eq. \ref{['each_ap_1loop_nw']}].
• Figure 2: The exact solutions for $P_{15}$, $P_{24}$, $P_{33a}$ and $P_{33b}$ [eq. \ref{['corrections:2loop']}], their high-$k$ solutions [eq. \ref{['ap_P2loop']}], and the no-wiggle high-$k$ solutions for $P_{24}$ and $P_{33b}$ [eq. \ref{['each_ap_2loop_nw_1loop']}] are plotted as the red solid, black solid, and black dashed lines, respectively. The fractional differences defined as ${\rm Diff. [\%]}\equiv (P_{\rm exact}- P_{\rm high\mathchar'-k})*100/P_{\rm lin}^{\rm nw}$ are also plotted as the black solid lines, where the no-wiggle linear power spectrum $P_{\rm lin}^{\rm nw}$ is presented in Eisenstein:1997ik. For $P_{24}$ and $P_{33b}$, the fractional differences between the exact solutions and the no-wiggle high-$k$ solutions are plotted as the black dashed lines.
• Figure 3: The theoretical predictions at the 2-loop level (SPT [eq. \ref{['S_2loop']}], modified SPT [eq. \ref{['main_2']}], Reg PT [eq. \ref{['Ex_RegPT_2loop']}], LRT [eq. \ref{['LRT:2loop']}]) and the $N$-body simulation results are plotted as the red solid, red dashed, orange solid, blue solid lines, and the green symbols at $z=1.0$ and $z=0.35$.
• Figure 4: The exact an approximated 1- and 2-loop correction terms $P_{\rm 1\mathchar'-loo}$, $P_{\rm 2\mathchar'-loop}$, and $P_{\rm 1\mathchar'-loop} + P_{2\mathchar'-loop}$ are plotted as the orange, blue, and red solid (dashed) lines.
• Figure 5: The various predictions of the evolution of BAO are plotted. The linear, 1-loop, and 2-loop corrections to BAO given in eq. \ref{['BAO_l12']} are plotted as the black dashed, orange solid, purple solid lines. The BAO behavior in the modified linear model (the second term in eq. \ref{['modified_linear']}) and our result (the second line in eq. \ref{['main_2']}) are plotted by the blue and red solid lines, respectively.