Cosmic microwave background anisotropy from wiggly strings

TL;DR

This work addresses how wiggly cosmic strings influence CMBR anisotropy and the matter power spectrum, exploring whether small-scale wiggles can reconcile predictions with observations. It combines a wiggly-string stress-energy model with the one-scale string-network evolution and uses line-of-sight integration via $\text{CMBFAST}$ to predict observables. Key findings show that wiggliness raises the CMB power peak at $l \approx 400$ and can boost small-scale matter power, but a cosmological-constant–dominated model still requires a scale-dependent bias of order $b \approx 1.6$ to $2.4$, with COBE-normalized $G\mu_0$ near $10^{-6}$ to a few $\times10^{-6}$. The work demonstrates that incorporating small-scale structure in strings can improve data compatibility, while also highlighting limitations due to neglect of loops, compensation, and backreaction, pointing to directions for refined string-network modeling.

Abstract

We investigate the effect of wiggly cosmic strings on the cosmic microwave background radiation anisotropy and matter power spectrum by modifying the string network model used by Albrecht et al.. We employ the wiggly equation of state for strings and the one-scale model for the cosmological evolution of certain network characteristics. For the same choice of simulation parameters we compare the results with and without including wiggliness in the model and find that wiggliness together with the accompanying low string velocities lead to a significant peak in the microwave background anisotropy and to an enhancement in the matter power spectrum. For the cosmologies we have investigated (standard CDM, and, CDM plus cosmological constant), and within the limitations of our modeling of the string network, the anisotropy is in reasonable agreement with current observations but the COBE normalized amplitude of density perturbations is lower than what the data suggests. In the case of a cosmological constant and CDM model, a bias factor of about 2 is required.

Figures (15)

• Figure 1: A schematic picture of the string network model. All string segments (depicted by filled circles) are born at an early epoch and then decay at various later times. The segments are labeled by the index $m$ and the decay times are shown as numbers along the $\tau$ axis. In certain cosmologies, it is possible that some string segments never decay.
• Figure 2: The modified model of the string network. All strings that decay at the same (discretized) time in Fig. \ref{['net1']} are consolidated into one string segment and assigned a weight that is the square root of the number of segments that the consolidated segment represents. This works for all segments that decay by the end of the simulation but will miss those segments that do not decay. In the present scheme, the segments that will not have decayed by the end of the simulation are consolidated into one string. The contribution of this surviving segment is the remainder term in the expression for the energy momentum tensor in eq. ( \ref{['modifiedtheta']}).
• Figure 3: The velocity of strings $v$ as a function of the conformal time for $\Omega_{baryons}=.05$, $\Omega_{CDM}=0.95$, $\Omega_{\Lambda}=0$ (dotted line) and $\Omega_{baryons}=.05$, $\Omega_{CDM}=0.25$, $\Omega_{\Lambda}=0.7$ (solid line).
• Figure 4: The length of string segments, $l(\tau)$, divided by $\tau$ as a function of $\tau$ for $\Omega_{baryons}=.05$, $\Omega_{CDM}=0.95$, $\Omega_{\Lambda}=0$ (dotted line) and $\Omega_{baryons}=.05$, $\Omega_{CDM}=0.25$, $\Omega_{\Lambda}=0.7$ (solid line).
• Figure 5: The wiggliness $\alpha$ as a function of the conformal time for $\Omega_{baryons}=.05$, $\Omega_{CDM}=0.95$, $\Omega_{\Lambda}=0$ (dotted line) and $\Omega_{baryons}=.05$, $\Omega_{CDM}=0.25$, $\Omega_{\Lambda}=0.7$ (solid line).