Self-similar bumps and wiggles: Isolating the evolution of the BAO peak with power-law initial conditions

Abstract

Motivated by cosmological surveys that demand accurate theoretical modeling of the baryon acoustic oscillation (BAO) feature in galaxy clustering, we analyze N-body simulations in which a BAO-like gaussian bump modulates the linear theory correlation function ξL(r) = (r0/r) n+3 of an underlying self-similar model with initial power spectrum P (k) = Ak n . These simulations test physical and analytic descriptions of BAO evolution far beyond the range of most studies, since we consider a range of underlying power spectra (n = −0.5, −1, −1.5) and evolve simulations to large effective correlation amplitudes (equivalent to σ8 = 4 − 12 for r bao = 100h −1 Mpc). In all cases, non-linear evolution flattens and broadens the BAO bump in ξ(r) while approximately preserving its area. This evolution resembles a "diffusion" process in which the bump width σ bao is the quadrature sum of the linear theory width and a length proportional to the rms relative displacement Σpair(r bao ) of particle pairs separated by r bao . For n = −0.5 and n = −1, we find no detectable shift of the location of the BAO peak, but the peak in the n = −1.5 model shifts steadily to smaller scales, following r peak /r bao = 1 − 1.08(r0/r bao )1.5 . The perturbation theory scheme of McDonald (2007) [1] and, to a lesser extent, standard 1-loop perturbation theory are fairly successful at explaining the non-linear evolution of the fourier power spectrum of our models. Analytic models also explain why the ξ(r) peak shifts much more for n = −1.5 than for n ≥ −1, though no ab initio model we have examined reproduces all of our numerical results. Simulations with L box = 10r bao and L box = 20r bao yield consistent results for ξ(r) at the BAO scale, provided one corrects for the integral constraint imposed by the uniform density box.

On the renormalization of the effective field theory of large scale structures

“…The EFToLSS provides a good fit in the dispalyed range. In the bottom panel, for n = −1.5 we compare with the simulations of [8]. In this case SPT is finite and so we show its prediction as a dashed blue line.…”

“…Now that we have made these cautionary remarks, we can move on and discuss how (3.6) compares with simulations. We use the fitting formulae given in equations A2 of [8] (for n = −1.5, −1) and in 22 of [9] (for n = −1). It would be nice in the future to consider other cases as well.…”

Observational probes of cosmic acceleration

“…The corresponding effect in the power spectrum is the decreased amplitude of the wiggles at higher wavenumber. Roughly speaking, one can think of the width of the evolved ξ(r) peak as the quadrature sum of the initial width and the rms pairwise displacement Σ NL (see Orban and Weinberg 2011, who examine idealized BAO models numerically and analytically). Equivalently, the oscillations in P (k) are damped by a factor exp(−k 2 Σ 2 NL ).…”

Cosmological perturbation theory as a tool for estimating box-scale effects inN-body simulations

“…Regarding the right-hand column in Fig. 5, it should be reiterated that the simulation results presented there are significantly more precise for k k nl than previously-published non-linear fits from either [28] or [25]. A close look at these plots indicate that the Widrow et al [28] fit is a few percent too low near k ∼ k nl /10, and that the Orban & Weinberg fit is likewise a few percent too low at k ∼ 2 k nl but otherwise the agreement is typically within the measured 2σ error bars.…”

“…This choice highlights the self-similar shape of the non-linear power spectrum in the lefthand panels where the y-axes present ∆ 2 (k)/∆ 2 L (k) where ∆ 2 L (k) is the linear theory model for the power-law power spectrum. The right-hand panels highlight the accuracy of the Orban and Weinberg [25] and Widrow et al [28] fitting functions. To the extent that the measurements from each output lie along the same locus of points, this is strong evidence for the essential accuracy of the simulation ensemble 7 in spite of any number of possible sources of error (e.g.…”