[Paper Review] Cosmic String Wake Detection using 3D Ridgelet Transformations

Samuel Laliberte, Robert Brandenberger+1 more|arXiv (Cornell University)|Jul 25, 2018

Astrophysics and Cosmic Phenomena22 references3 citations

TL;DR

This paper proposes using 3D ridgelet transformations to detect cosmic string wakes in N-body simulations of dark matter distributions. By analyzing ridgelet coefficients across spatial and angular parameters, the method identifies planar overdensities from cosmic strings, achieving a 6.8σ detection significance for a string with tension $G\mu = 10^{-7}$ at redshift $z = 10$, demonstrating high sensitivity to non-Gaussian signals in position space.

ABSTRACT

Three-dimensional ridgelet statistics are used to search for the signals of cosmic string wakes in the distribution of dark matter. We compare N-body simulations of the dark matter distribution in cosmological models with and without a cosmic string wake, assuming that the dominant sources of fluctuations are those predicted in the standard $Λ$CDM model. Cosmic string wakes lead to overdense regions with planar topology, and hence three-dimensional ridgelet statistics are a promising analysis tool. The string signal is easier identifiable for larger string tensions and at higher redshift. We find that a wake produced by a string of tension $Gμ= 10^{-7}$ (a value slightly lower than the best current robust upper bound) can be detected at $6 \, σ$ confidence level at a cosmological redshift $z = 10$.

Motivation & Objective

• To detect cosmic string wakes in 3D dark matter distributions using a position-space statistical method.
• To overcome limitations of Fourier-based techniques by exploiting the planar, non-Gaussian topology of cosmic string wakes.
• To determine the lowest redshift at which a cosmic string signal with $G\mu = 10^{-7}$ remains detectable in cosmological simulations.
• To validate the effectiveness of 3D ridgelet transformations as a robust tool for identifying weak, structured signals in nonlinear density fields.
• To provide a foundation for applying this method to real weak lensing or 21 cm surveys targeting high-redshift cosmic string signatures.

Proposed method

• Applying 3D ridgelet transforms to N-body simulation outputs with and without added cosmic string wakes to extract spatial-scale and angular-scale features.
• Fixing the scale parameter $a = a_{\text{max}}$ and position parameter $b = 0$ $h^{-1}\text{Mpc}$ based on prior analysis to optimize detection of planar structures.
• Computing ridgelet coefficients $\mathcal{R}_{\rho}$ over a grid of 50² orientations $(\theta_1, \theta_2) \in [0, \pi) \times [0, \pi)$ to map signal strength across angular parameters.
• Comparing mean ridgelet coefficients between simulation boxes with and without wakes to identify statistically significant deviations.
• Using the standard deviation of coefficient means to define a 6σ detection threshold for signal significance.
• Analyzing the spatial and angular distribution of ridgelet maxima to confirm that peaks correspond to the presence of a wake.

Experimental results

Research questions

• RQ1 Can 3D ridgelet transformations detect cosmic string wakes in 3D dark matter distributions at high redshift?
• RQ2 At what redshift does the signal of a cosmic string wake with $G\mu = 10^{-7}$ become statistically indistinguishable from $\Lambda$CDM fluctuations?
• RQ3 How does the ridgelet method compare to Fourier-based or wavelet-based techniques in detecting non-Gaussian, planar structures?
• RQ4 What are the optimal ridgelet parameters ($a$, $b$, $\theta_1$, $\theta_2$) for maximizing detection sensitivity to cosmic string wakes?
• RQ5 Does the method remain effective when the wake signal is swamped by nonlinear $\Lambda$CDM density fluctuations at lower redshifts?

Key findings

• A cosmic string wake with $G\mu = 10^{-7}$ produces a detectable signal at $z = 10$ with a confidence level of $6.8 \pm 0.9\,\sigma$ using 3D ridgelet analysis.
• The ridgelet coefficient maximum occurs at $b_{\text{max}} = (-4 \pm 4) \times 10^{-3}\,h^{-1}\text{Mpc}$, confirming $b = 0$ as an optimal fixed parameter for detection.
• The signal is most prominent at $\theta_1 = \theta_2 = \pi/2$, where the ridgelet coefficients exhibit a clear, localized maximum only in the presence of a wake.
• The method successfully distinguishes wake-affected simulation boxes from control boxes without wakes, as confirmed by visual and statistical comparison in Figure 14.
• The detection significance remains high at $z = 10$ due to the relative dominance of the wake's planar structure over nonlinear $\Lambda$CDM fluctuations.
• Higher-resolution simulations are expected to extend the detectable redshift range slightly below $z = 10$, though current resolution limits detection to $z \geq 10$.