Probing the gravitational wave background from cosmic strings with LISA

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Cosmic string SGWB curves (all in red) near various relevant values of $G\mu$. The dashed orange curve is the EPTA sensitivity, and the darkest red curve just below is for $G\mu=10^{-10}$. The dash-dotted dark orange curve is the (projected) SKA sensitivity, and the dark red curve just below is for $G\mu=10^{-13}$. The dotted black curve is the LISA PLS; the red curve whose peak passes through it, and the light red curve just below, are for $G\mu=10^{-15}$ and $10^{-17}$ respectively. The $P_n$ are inferred from simulation~\cite{Blanco-Pillado:2017oxo}, and the loop number density is from Model II.

Idem as figure~\ref{fig:fiducialSGWB}, but with $P_n\propto n^{-4/3}$ and using the loop number density from Model III~\cite{Lorenz:2010sm}.

Examples of spectra for several values of $G\mu$ and $\alpha=10^{-1}$ using both the full VOS solution (with {\it VOS} superscript) and assuming the network is always in scaling through eqs.~(\ref{eqn:VOSrad},\ref{eqn:VOSmat}) (with {\it scaling} superscript). The gray area indicates LISA sensitivity.

Examples of spectra with $G\mu=10^{-11}$ assuming a constant number of degrees of freedom (black solid line) and standard cosmology with SM particle content (blue dashed line). The gray area indicates LISA sensitivity.

Examples of spectra with $G\mu=10^{-11}$ in standard cosmology (black solid line) and several spectra in cosmological evolution with $\Delta g_*=100$ new degrees of freedom annihilating at at the range of temperatures of interest for LISA. The gray area indicates LISA sensitivity.

Examples of spectra with $G\mu=10^{-11}$ in standard cosmology (black solid line) and several spectra in cosmological evolution with a period of early matter domination as well as kination ending in the range of temperatures of interest for LISA. The black dashed line indicates LISA sensitivity.

How the SGWB of a loop network (solid blue curves) shifts through the LISA sensitivity band (dotted black curve) as the string tension varies. We assume $P_n\propto n^{-4/3}$ for this figure, but other spectra exhibit similar behavior.

A comparison of the LISA sensitivity curve to the SGWB predicted by all three models using $G\mu=10^{-17}$, $P_n\propto n^{-4/3}$. Models I and II are effectively identical in this regime, due to $\alpha\gg\mathrm{\Gamma} G\mu$. We therefore see that we expect that LISA could only constrain string tensions higher than $G\mu\approx 10^{-17}$.

The stochastic gravitational wave background generated by cosmic string networks with $G\mu=10^{-10}$ and different values of the loop-size parameter $\alpha$. The shaded area represents the LISA sensitivity window. In these plots, we consider only the fundamental mode of emission and we did not include the change in the effective number of degrees of freedom.

The stochastic gravitational wave background generated by cosmic string networks with $\alpha=10^{-1}$ (solid lines) and $\alpha=10^{-5}$ (dash-dotted lines) for different values of $G\mu$. The shaded area represents the LISA sensitivity window. In these plots, we consider only the fundamental mode of emission and we did not include the change in the effective number of degrees of freedom.

The stochastic gravitational wave background generated by cosmic string networks with $G\mu=10^{-10}$ (solid lines) and $G\mu=10^{-12}$ (dash-dotted lines) for different values of the loop-size parameter $\alpha$ in the small-loop regime. The shaded area represents the LISA sensitivity window. In these plots, we consider only the fundamental mode of emission and we did not include the change in the effective number of degrees of freedom.

Projected constraints on $G\mu$ of the LISA mission for cosmic string scenarios characterized by different loop-size parameter $\alpha$ for $n_*=1$ (dashed line) and $n_*=10^5$, with $q=4/3$ (dash-dotted line). The shaded area corresponds to the region of the $(\alpha,G\mu)$ parameter space that will be fully available for exploration with LISA. The dotted line corresponds to scenarios for which $\alpha=\Gamma G\mu$, so that the region above this line corresponds to cosmic string models in which loops are small, while the region bellow corresponds to the large loop regime.