1. Simplifying the Problem Tests of Self-Similarity
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
How “standard” is this standard ruler?
How does this signature shift or broaden?
Exponential damping of the input “wiggle” spectrum with one free parameter does a good job of modeling the simulation results
For an n = -1 background power-law slope the “smearing out” of the bump is well-modeled with a broadened and attenuated gaussian
Image Credit: SDSS
Simplifying the Problem
The above shows results from an ensemble of 7 dark-matter-only N-body simulations (Lbox = 2048 h-1Mpc, N=5123, Gadget-2 code)
Real-space correlation function
Fourier Space
Tests of Self-Similarity
Fourier
Transform!
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Adding a second “shift” parameter, , improves agreement at later outputs
We find a 1% shift by z = 0 (RNL /rbao = 0.053)
Initial matter power spectrum (right) in correlation space (left) is a power law* times a Gaussian bump (i.e. a BAO-like feature)
rbao / Lbox = 1 / 20
rbao / Lbox = 1 / 10
Future Directions
In the m = 1.0, = b = k = 0.0 cosmology the full non-linear evolution of the bump should scale with self-similarity
Compare to beyond-1st-order perturbation theory predictions
Explore ICs with different background power laws
Simulations with  ≠ 0.0, m ≠ 1.0
Of the results from the three ensembles of simulations shown here, one maintains self-similarity (top left) while the others do not.
The top two plots have the same initial interparticle separation (i.e. np1/3 = N1/3 /Lbox) but different box sizes, while the bottom plot has a larger interparticle separation than the simulations in the section above this one, but with the same Lbox.
Discrepancies with the Gaussian fit to the simulations in the previous section signal a break-down of self-similar evolution.
The measured shape of the bump should only depend on RNL /rbao where RNL is defined by (RNL) ≡1, and on bao/r bao where bao is the standard-deviation width of the initial bump
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Acknowledgements
If this self-similarity is violated it is a red flag for unwanted numerical effects introduced by the scale of the box or the scale of the initial interparticle spacing
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.
rbao / np1/3 = 100/8
*Typically a power law in fourier space is also a power law in configuration space. Here P(k)  k-1 (r)  r-2