Power Spectra in Global Defect Theories of Cosmic Structure Formation

TL;DR

The paper tackles the challenge of predicting perturbation power spectra in defect-based cosmologies, where full linear response is needed due to decoherence from the defect sources. It introduces a practical pipeline that first measures unequal time correlators (UETCs) of the defect stress-energy and then expresses these correlators as a convergent eigenvector product expansion, $C(k,\tau,\tau') = \sum_i \lambda^i v^i(k,\tau) v^i(k,\tau')$, enabling rapid, high-precision propagation of perturbations through a Boltzmann solver. The method handles the matter-radiation transition by diagonalizing at multiple epoch ratios $\tau/\tau^*$, producing a compact set of eigenvectors that interpolate between regimes, with typically the largest 15 eigenvectors providing sufficient accuracy. Applying the approach to global strings, monopoles, textures, and non-topological textures yields a CMB spectrum where vector modes dominate up to $l\sim100$ and results in COBE-normalized $\sigma_8$ values around $0.21$–$0.26\,h$, underscoring a tension with current data and suggesting these defect theories are not favored by observations.

Abstract

An efficient technique for computing perturbation power spectra in field ordering theories of cosmic structure formation is introduced, enabling computations to be carried out with unprecedented precision. Large scale simulations are used to measure unequal time correlators of the source stress energy, taking advantage of scaling during matter and radiation domination, and causality, to make optimal use of the available dynamic range. The correlators are then re-expressed in terms of a sum of eigenvector products, a representation which we argue is optimal, enabling the computation of the final power spectra to be performed at high accuracy. Microwave anisotropy and matter perturbation power spectra for global strings, monopoles, textures and non-topological textures are presented and compared with recent observations.

Figures (4)

• Figure 1: Angular power spectrum of anisotropies generated by the scalar component of the source stress energy for global strings. The upper curve shows the total spectrum, the lower ones contributions from individual eigenvectors. This Figure illustrates decoherence: each eigenvector individually produces an oscillatory $C_l$ spectrum, but these oscillations all cancel in the sum.
• Figure 2: The contributions to the total power from scalar, vector and tensor components.
• Figure 3: Comparison of defect model predictions to current experimental data. All models were COBE normalised at $l=10$.
• Figure 4: Matter power spectra computed from the Boltzmann code summed over the eigenmodes. The upper curve shows the standard cold dark matter (sCDM) power spectrum. The defects generally have more power on small scales than large scales relative to the adiabatic sCDM model. The data points show the mass power spectrum as inferred from the galaxy distribution peacock.