Cosmic Microwave Background Anisotropies from Scaling Seeds: Global Defect Models

TL;DR

This work investigates CMB anisotropies arising from scaling seeds in global defect models, focusing on textures in a spatially flat universe with a cosmological constant. It introduces a gauge-invariant perturbation framework and an unequal-time correlator approach, solving the Einstein–Boltzmann system with a Green's-function-based eigenmode expansion to predict $C_\ell$, matter power, and bulk velocities from seed fluctuations. The main finding is that globally scaling seed models generically suppress acoustic peaks in the CMB and underpredict large-scale mass and velocity fluctuations, with bulk-velocity data providing the strongest constraint against such models, even though current CMB data alone do not conclusively rule them out. The results underscore the tension between these scaling-seed predictions and large-scale structure observations, while highlighting that non-Gaussianity and biasing complicate the interpretation and that peculiar velocities offer a robust avenue for falsification.

Abstract

We investigate the global texture model of structure formation in cosmogonies with non-zero cosmological constant for different values of the Hubble parameter. We find that the absence of significant acoustic peaks and little power on large scales are robust predictions of these models. However, from a careful comparison with data we conclude that at present we cannot safely reject the model on the grounds of present CMB data. Exclusion by means of galaxy correlation data requires assumptions on biasing and statistics. New, very stringent constraints come from peculiar velocities. Investigating the large-N limit, we argue that our main conclusions apply to all global O(N) models of structure formation.

Figures (22)

• Figure 1: The two point correlation function $C_{11}(z,r) = k^4\sqrt{tt'}\langle\Phi_s({\bf k},t)\Phi_s^*({\bf k},t')\rangle$ is shown. Panel (a) represents the result from numerical simulations of the texture model; panel (b) shows the large-$N$ limit. For fixed $r$ the correlator is constant for $z<1$ and then decays. Note also the symmetry under $r\rightarrow 1/r$.
• Figure 2: The same as Fig. \ref{['fig1']} but for $C_{22}(z,r) = k^4\sqrt{tt'}\langle\Psi_s({\bf k},t)\Psi_s^*({\bf k},t')\rangle$.
• Figure 3: The unequal time correlator, $|C_{12}(z,r)| = k^4\sqrt{tt'}|\langle\Phi_s({\bf k},t)\Psi_s^*({\bf k},t')\rangle|$ is shown. Note that the $r\rightarrow 1/r$ symmetry is lost in this case.
• Figure 4: The correlators $C_{ij}(z,1)$ are shown. The solid, dashed and dotted lines represent $C_{22}~,~C_{11}$ and $|C_{12}|$ respectively. Panel (a) is obtained from numerical simulations of the texture model and panel (b) shows the large-$N$ limit. A striking difference is that the large-$N$ value for $|C_{12}|$ is relatively well approximated by the perfectly coherent result $\sqrt{|C_{11}C_{22}|}$ while the texture curve for $|C_{12}|$ lies nearly a factor 10 lower.
• Figure 5: The correlators $C_{ij}(0,r)$ are shown in the same line styles as in Fig. \ref{['fig4']}, but for $z=0$ as function of $r=t'/t$. The stronger decoherence of the texture model is even more evident here.