Large Angle CMB Fluctuations from Cosmic Strings with a Comological Constant

TL;DR

This work investigates whether a cosmological constant alters the large-angle CMB fluctuations seeded by cosmic strings and how this affects the COBE-derived normalization. The authors perform high-resolution Allen–Shellard string-network simulations in flat FRW universes with varying $\Omega_\Lambda$, generate all-sky maps, and compute COBE-normalized angular power spectra using a pixelized, FFT-based harmonic approach. They find a scale-invariant plateau at $\ell\lesssim 20$ and deduce a COBE normalization of $G\mu/c^2 \approx (0.695 + 0.012/(1-\Omega_\Lambda)) \times 10^{-6}$, with $\Omega_\Lambda=0$ giving $\sim 0.70\times 10^{-6}$ and larger $\Omega_\Lambda$ yielding modest increases. The cosmological constant has a relatively small effect (e.g., $\sim 6\%$ increase for $\Omega_\Lambda=0.7$) because late-time vacuum domination modestly dampens string velocities, a result that refines the allowed string tension and informs models where strings arise (e.g., brane inflation).

Abstract

In this paper, we present results for large-angle CMB anisotropies generated from high resolution simulations of cosmic string networks in a range of flat FRW universes with a cosmological constant. Using an ensemble of all-sky maps, we compare with the COBE data to infer a normalization (or upper bound) on the string linear energy density $μ$. For a flat matter-dominated model ($Ω_{M}=1$) we find $Gμ/c^2 \approx 0.7\times 10^{-6}$, which is lower than previous constraints probably because of the more accurate inclusion of string small-scale structure. For a cosmological constant within an observationally acceptable range, we find a relatively weak dependence with $Gμ/c^2$ less than 10% higher.

Figures (5)

• Figure 1: All-sky string-induced maps for a flat FRW Universe with $\Omega_{\Lambda} = 0$ and. $0.7$
• Figure 2: Individual power spectra for the $\Omega_{\Lambda} = 0$ run in blue with the average in red.
• Figure 3: Average power spectra for each run.
• Figure 4: Average rms long string velocity for the last half of the string network simulations for $\Omega_\Lambda = 0$ (red), $\Omega_\Lambda = 0.4$ (green), $\Omega_\Lambda = 0.7$ (blue) and $\Omega_\Lambda = 0.85$ (black). Even the extremal $\Lambda$-model shows only a relatively small 11% decline in the average string velocity by the present day. (Relative conformal time is plotted with $\eta_0 = 0.5$.)
• Figure 5: String linear energy density obtained from the COBE normalisation. The solid line is the curve (\ref{['gmu_eq']}).