Cosmic Strings as Dynamical Dark Energy: Novel Constraints

Cosmic strings, topological defects predicted by high-energy theories, may contribute to the late-time expansion of the Universe, effectively mimicking dynamical dark energy. We investigate four phenomenological extensions of the $\Lambda$CDM model involving a residual string network: (i) a non-relativistic component with positive energy density (Model~1), (ii) a velocity-dependent extension (Model~2), (iii) a non-relativistic string network with energy density allowed to take both positive and negative values (Model~3), and (iv) a general scenario with free energy and velocity parameters (Model~4). These models are constrained using \textit{Planck} CMB data, SDSS or DESI baryon acoustic oscillations, and Type Ia supernovae observations. Models~1 and~2 yield strong upper bounds on the string density, for example, $\Omega_{\mathrm{s}} < 0.00901$ at 95\% CL from the CMB+DESI+DESY5 combination for Model~2, and mildly shift the inferred value of $H_0$ upward, though they are not favored by Bayesian evidence. For the same combination, the bulk velocity is bound as $v_{\mathrm{s}} < 0.569$. Models~3 and~4 exhibit a consistent preference for slightly negative values of $\Omega_{\mathrm{s}}$, with CMB-only data yielding $\Omega_{\mathrm{s}} = -0.038^{+0.029}_{-0.022}$ and $v_{\mathrm{s}}< 0.574$ in Model~4, and a best-fit improvement of $\Delta \chi^2 = -6.07$. However, these improvements are not sufficient to overcome the Occam penalty, and the Bayesian evidence continues to favor $\Lambda$CDM. These findings demonstrate the power of current data to constrain exotic energy components and encourage further exploration of string-inspired extensions to $\Lambda$CDM, particularly those involving negative-tension networks.