CMB anisotropies from cosmic (super)strings in light of ACT DR6

Abstract

We present updated constraints on cosmic string and superstring parameters derived from Cosmic Microwave Background (CMB) anisotropies. The constraints are obtained via Markov Chain Monte Carlo (MCMC) analyses of the full \textit{Planck} temperature and polarization data combined with the Atacama Cosmology Telescope (ACT) Data Release 6 (DR6). For ordinary cosmic strings, we constrain the string tension $Gμ$, the string wiggliness parameter $α$, and the self-chopping efficiency $\tilde{c}$. For cosmic superstrings, we constrain the fundamental string tension $Gμ_F$, the string coupling $g_s$, and a parameter $w$ describing the volume of the compact extra dimensions. In both cases, we find significantly tighter bounds on the string tension compared to previous analyses, obtaining $2σ$ upper limits of $Gμ< 3.66\times10^{-8}$ and $Gμ_F < 1.38\times10^{-8}$. We also discuss the significant prior-dependence of these results. The computational pipeline used in this work, including a modified version of \texttt{CAMB} capable of computing CMB anisotropies sourced by any active network described via unequal-time correlators, is released publicly as \texttt{CAMBactive} \cite{Raidal_CAMBactive_CAMB_extension_2026}.

Figures (7)

• Figure 1: ACT DR6 and Planck PR3 combined TT (top), EE (middle), and TE (bottom) power spectra. The solid black curve shows the ACT and Planck best-fit $\Lambda$CDM model, while the dashed red curve shows cosmic strings from the USM model (Sec. \ref{['sec:USM']}) with $G\mu = 10^{-7}$, $\alpha = 1.9$, and $\tilde{c} = 0.23$.
• Figure 2: Cosmic string anisotropy spectra calculated from UETCs with different grid resolutions. The first column shows the high-resolution "true" spectrum, the chosen lower resolution spectrum and the CV noise. The second column shows the difference between the two spectra and the CV noise, while the third column gives the SNR at each multipole and the total SNR. The spectra are calculated using $G\mu=8\times 10^{-8}$. Only the TT and EE modes are shown; the remaining modes contribute subdominantly to the total SNR.
• Figure 3: Fan plots showing the distribution of emulator errors from the true spectrum with respect to the cosmic variance error. The cosmological and string parameter values used are selected from MCMC chains and represent physical scenarios.
• Figure 4: Marginalized posterior distributions for the ordinary cosmic string parameters $\{G\mu, \alpha, \tilde{c}\}$. In each panel, we compare the constraints from Planck CamSpec PR4 (red) and Planck PR3 + ACT DR6 (blue). The left column shows the results under uninformative flat priors, highlighting the prior volume effect between linear (a) and log (c) parametrizations. The right column shows the results with physically-motivated Gaussian priors on $\alpha$ and $\tilde{c}$.
• Figure 5: Marginalized posterior distributions for the fundamental cosmic superstring parameters $\{G\mu_F, \alpha, \tilde{c}, g_s, w\}$. We compare results from Planck CamSpec PR4 (red) and Planck PR3 + ACT DR6 (blue). The left column (a, c) employs uninformative flat priors on $\alpha,\tilde{c}$, whereas the right column (b, d) applies physically-motivated Gaussian priors on $\alpha$ and $\tilde{c}$. While the string coupling $g_s$, effective wiggliness $\alpha$ and extra dimension volume parameter $w$ remain largely unconstrained across all cases, their inclusion modifies the shape of the tension contours.