Landscape Poster Template

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, N5123, 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. 2008 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 / scaledependent
  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-(n3)