1. Self-similar Bumps and Wiggles: Isolating the Evolution of
the BAO Peak with Power-law Initial Conditions
Chris Orban (OSU) with David Weinberg (OSU)
Simulation Results
Fourier Analysis
Motivation
The galaxy clustering signature from baryon acoustic oscillations (BAO) in the early universe holds valuable information for constraining dark energy
Deeply non-linear regime
Time
How “standard” is this standard ruler?
How does this signature shift or broaden?
BAO bump
Exponential damping of the input “wiggle” spectrum using a diffusion-inspired model does a good job of modeling the simulation results (solid colored lines)
The above shows results from an ensemble of 7 dark-matter-only N-body simulations (rbao / Lbox = 1/20, N=5123, Gadget-2 code).
Image Credit: SDSS
Testing Perturbation Theory
Simplifying the Problem
The bump evolves like an attenuated and broadened gaussian with the area under the bump roughly constant, much like a diffusion process.
Real-space correlation function
Fourier Space
Fourier
Transform!
Fractional shift of BAO scale
30% shift!!!
The SimpleRG scheme from McDonald 2007 does a remarkable job of predicting the quasi-linear power spectrum; standard 1-loop PT less so.
There is an appreciable shift of the BAO peak in the case with the most large scale power (n = -1.5). Other cases show no shift. The Smith et al ansatz (dot-dashed lines on right) for the shift agrees with this trend when ro / rbao is small.
Initial matter power spectrum (right) in correlation space (left) is a power law* times a Gaussian bump (i.e. a BAO-like feature).
Most PT schemes designed for CDM yield divergent predictions for powerlaw cosmologies
For the m = 1.0, = b = k = 0.0 cosmology the full non-linear evolution of the bump should scale with self-similarity, depending only on ro / rbao where ro is defined by (ro) ≡1.
Tests of Self-Similarity
Future Work
In tests where rbao is doubled, so that
rbao / Lbox = 1/10 and rbao / np-1/3 = 50 where np-1/3 is the mean inter-particle spacing, the simulations seem to match the expected self-similar behavior (i.e. matches the results from rbao / Lbox = 1/10 and rbao / np-1/3 = 25 simulations shown in dot dashed lines)
These results agree for all three powerlaws, n = -0.5, -1, -1.5; evidence that N-body simulations robustly predict the evolution of the BAO bump even in these extreme models
Investigate halo clustering / scale–dependent bias
Revisit Sirko 2005 method for running ensembles of simulations
If this self-similarity is violated it is a smoking gun for unwanted numerical effects introduced by the scale of the box or the scale of the initial mean inter-particle spacing.
Acknowledgements
Simulations including a cosmological constant also show self-similarity since outputs at the same ro / rbao are consistent with the m = 1, = 0 simulations.
This work made extensive use of resources at the Ohio Supercomputer Center. CO is supported by the OSU Center for Cosmology and Astro-Particle Physics.
Note: (r) results are self-similar only if an integral-constraint correction is applied!
*A power law in fourier space is also a power law in configuration space, i.e. P(k)  kn (r)  r-(n+3)