Small-Angle CMB Temperature Anisotropies Induced by Cosmic Strings

TL;DR

This work generates realistic arcminute-scale CMB maps from a network of Nambu-Goto cosmic strings in a FLRW universe, producing 84 independent realizations to study non-Gaussian signatures and the observability of string effects. Using a small-angle approximation and a two-stage light-cone approach, the authors extract the one-point PDF, the angular power spectrum, and a gradient-based string tracer, finding a power-law spectrum with $\ell(\ell+1)C_\ell \propto \ell^{-p}$ where $p=0.889^{+0.001}_{-0.090}$, and a potential dominance of string-induced fluctuations at small scales for $G U$ above a few $\times 10^{-7}$. They demonstrate that the normalized gradient magnitude $|\nabla\Theta|$ traces string paths on the past light cone and highlights cusps and kinks, suggesting that arcminute experiments like ACT could place stringent constraints on $G U$ via non-Gaussian estimators applied to temperature or gradient maps. The study carefully accounts for secondary anisotropies (tSZ, OV, nonlinear kSZ) and instrumental beam effects, while acknowledging limitations from point-source modeling; future extensions include polarization (B-modes) and gravitational-wave considerations from cusps.

Abstract

We use Nambu-Goto numerical simulations to compute the cosmic microwave background (CMB) temperature anisotropies induced at arcminute angular scales by a network of cosmic strings in a Friedmann-Lemaitre-Robertson-Walker (FLRW) expanding universe. We generate 84 statistically independent maps on a 7.2 degree field of view, which we use to derive basic statistical estimators such as the one-point distribution and two-point correlation functions. At high multipoles, the mean angular power spectrum of string-induced CMB temperature anisotropies can be described by a power law slowly decaying as \ell^{-p}, with p=0.889 (+0.001,-0.090) (including only systematic errors). Such a behavior suggests that a nonvanishing string contribution to the overall CMB anisotropies may become the dominant source of fluctuations at small angular scales. We therefore discuss how well the temperature gradient magnitude operator can trace strings in the context of a typical arcminute diffraction-limited experiment. Including both the thermal and nonlinear kinetic Sunyaev-Zel'dovich effects, the Ostriker-Vishniac effect, and the currently favored adiabatic primary anisotropies, we find that, on such a map, strings should be ``eye visible,'' with at least of order ten distinctive string features observable on a 7.2 degree gradient map, for tensions U down to GU \simeq 2 x 10^{-7} (in Planck units). This suggests that, with upcoming experiments such as the Atacama Cosmology Telescope (ACT), optimal non-Gaussian, string-devoted statistical estimators applied to small-angle CMB temperature or gradient maps may put stringent constraints on a possible cosmic string contribution to the CMB anisotropies.

Figures (9)

• Figure 1: String-induced CMB temperature fluctuations on a $7.2^\circ$ field with a (unrealistic) resolution of $\theta_\mathrm{res}=0.42'$ ($1024$ pixels). The upper left image shows the fluctuations induced in between the last scattering surface and the redshift $z=36$, while the upper right map represents the anisotropies produced by strings between $z=36$ and $z=0.3$. Because of their cosmological scaling, most of the long strings intercept our past light cone close to the last scattering surface. The overall string-induced fluctuations are plotted in the bottom left panel. As can be seen in the bottom right image, the edges in the temperature patterns of the other maps can be identified to strings intercepting our past light cone. Note that active regions corresponding to string intersection and loop formation events lead to the bright spots in these maps. Some of these spots are associated with $\Theta > 80\,G U$ and saturate the color scale (see Sec. \ref{['sec:stats']}).
• Figure 2: Influence of the nonscaling structures on the computed CMB temperature maps. $\Theta_\mathrm{all}$ (respectively, $\Theta_\mathrm{inf}$) refers to the CMB fluctuations that would be obtained by keeping (respectively, removing) all loops present in the numerical simulations, including the spurious ones coming from the relaxation of the numerical initial conditions. The left (respectively, right) panel shows the deviation induced by the presence (respectively, absence) of these structures with respect to the reference temperature map shown in the bottom left corner of Fig. \ref{['fig:dtsplit']}. We use these maps in Sec. \ref{['sec:stats']} to estimate the systematic errors induced by the presence of nonscaling structures in the cosmic string simulations.
• Figure 3: The left panel shows the probability distribution function of the CMB temperature fluctuations induced by cosmic strings (solid line). The dotted and dashed curves quantify the systematic errors coming from the string simulations. Each of these one-point functions is averaged over $84$ independent realizations. The dash-dotted curve represents the best Gaussian fit. Deviations from Gaussianity are clearly apparent in the tails of the distribution, as well as from the slight skewness. The right panel shows the probability distribution function of the CMB temperature fluctuations that would have been induced by the nonscaling structures, as defined in Sec. \ref{['sec:robust']}. Once again, the dash-dotted curve represents the best Gaussian fit. A slight positive skewness may be observed, suggesting that the negative skewness observed in the left panel is the result of the loop formation mechanism.
• Figure 4:
• Figure 5: Normalized gradient magnitude of the string-induced temperature anisotropies shown in Fig. \ref{['fig:dtsplit']} (bottom left panel). A logarithmic scale has been used to enhance the contrast by preventing the bright spots from saturating the color scale. Such a map reproduces the string path on our past light cone and enhances the active string regions (see Fig. \ref{['fig:dtsplit']}).