The Scalar, Vector and Tensor Contributions to CMB anisotropies from Cosmic Defects

TL;DR

This work analyzes how cosmic defects generate CMB anisotropies through scalar, vector, and tensor perturbations under causality, scaling, and statistical isotropy. Using both incoherent and coherent models of the unequal time correlators, the authors show that vector and tensor contributions are non-negligible at large angular scales, and that they can suppress the scalar Doppler peaks by lowering the scalar normalization. A key analytical result is the robust ratio of stress components at small $k$, $ abla \,\langle|\\Theta^S|^2\\rangle : \langle|\\Theta^V|^2\\rangle : \langle|\\Theta^T|^2\\rangle = 3:2:4$, which translates into a large-angle C_l ratio of $C_l^{scalar} : C_l^{V} : C_l^{T} \approx 1.46 : 1 : 0.29$ under the adopted approximations. Together with numerical and coherent-model comparisons, the paper provides a physically transparent explanation for the observed balance between scalar, vector, and tensor contributions and highlights the minimal role of subhorizon structure for shaping the large-angle CMB. This work informs how defect models might be constrained by CMB observations and clarifies the mechanisms by which vector and tensor modes influence Doppler-peak amplitudes.

Abstract

Recent work has emphasised the importance of vector and tensor contributions to the large scale microwave anisotropy fluctuations produced by cosmic defects. In this paper we provide a general discussion of these contributions, and how their magnitude is constrained by the fundamental assumptions of causality, scaling, and statistical isotropy. We discuss an analytic model which illustrates and explains how the ratios of isotropic and anisotropic scalar, vector and tensor microwave anisotropies are determined. This provides a check of the results from large scale numerical simulations, confirming the numerical finding that vector and tensor modes provide substantial contributions to the large angle anisotropies. This leads to a suppression of the scalar normalisation and consequently of the Doppler peaks.

Figures (5)

• Figure 1: The contributions to the total anisotropy power spectrum from scalar, vector and tensor components, in the theories of global strings, monopoles, texture and nontopological texture (taken from ref. [1]).
• Figure 2: The importance of the long wavelength modes in the anisotropy power spectra from cosmic textures. The power spectra due to scalar (dotted), vector (dashed) and tensor (long-dashed) components of the sources are compared to those where the source stress energy components $\Theta_{00}$ and $\Theta^S$ as well as the vector and tensor stresses are set zero for all $k\tau>5$. The upper curves show the full spectra, the lower ones the results where the cutoff is imposed.
• Figure 3: As in Figure 2 but for global strings.
• Figure 4: Tensor anisotropy power spectrum as computed in the analytical model presented here.
• Figure 5: Angular power spectrum of anisotropies generated by a simple coherent model of scaling sources, correctly incorporating the superhorizon constraints on the relative importance of the anisotropic stress $\Theta^S$, vector $\Theta^V$ and tensor $\Theta^T$ perturbations to the source stress tensor.