## Author(s)

Auclair, Pierre, Steer, Danièle A., Vachaspati, Tanmay## Abstract

We account for particle emission and gravitational radiation from cosmic string loops to determine their effect on the loop distribution and observational signatures of strings. The effect of particle emission is that the number density of loops no longer scales. This results in a high-frequency cutoff on the stochastic gravitational wave background, but we show that the expected cutoff is outside the range of current and planned detectors. Particle emission from string loops also produces a diffuse gamma-ray background that is sensitive to the presence of kinks and cusps on the loops. However, both for kinks and cusps, and with mild assumptions about particle physics interactions, current diffuse gamma-ray background observations do not constrain Gμ.

## Figures

Loop distribution for kinks in the radiation era, with $\alpha=0.1$ and $\gammad = 10^{-6}$, and at several different epochs. Black solid line: $\gammak=0$ ($t\rightarrow \infty$), the NG loop distribution. Red dash line: $\gammak(t)=10^{-5}\gammad$ (corresponding to $t=10^5 t_k$). Blue dot-dash line $\gammak(t)=\gammad$ (corresponding to $t=t_k$). Green dotted line $\gammak(t)=10^4\gammad$ (corresponding $t=10^{-4}t_k$).

Loop number density $\N=t^4 n$ for kinks [LH panel] and cusps [RH panel], for $G\mu=10^{-17}$. Thus $z_k\sim 10^{12}$ and $z_c \sim 10^{4}$. From bottom to top, the curves show snapshots of the loop distribution at redshifts $z=10^{13}, 10^{11}, 10^{9}, 10^{7}, 10^{5}$, and the black curve is the scaling loop distribution at $z\rightarrow 0$. The loop distributions are supressed for $z\gg z_k$ or $z\gg z_c$.

Loop number density $\N=t^4 n$ for kinks [LH panel] and cusps [RH panel], for $G\mu=10^{-17}$. Thus $z_k\sim 10^{12}$ and $z_c \sim 10^{4}$. From bottom to top, the curves show snapshots of the loop distribution at redshifts $z=10^{13}, 10^{11}, 10^{9}, 10^{7}, 10^{5}$, and the black curve is the scaling loop distribution at $z\rightarrow 0$. The loop distributions are supressed for $z\gg z_k$ or $z\gg z_c$.

SBGW including the backreaction of particle emission on the loop distribution. LH panel: kinks on loops, RH panel: cusps on loop. The spectra are cutoff at high frequency, as indicated by the black vertical lines. $G\mu$ ranges from $10^{-17}$ (lower curve), through $10^{-15}$, $10^{-13}$,$10^{-11}$, $10^{-9}$ and $10^{-7}$ (upper curve). Also plotted are the power-law integrated sensitivity curves from SKA (pink dashed) \cite{Janssen:2014dka}, LISA (yellow dashed) \cite{Caprini:2019pxz}, adv-LIGO (grey dashed) \cite{TheLIGOScientific:2016dpb} and Einstein Telescope (blue dashed) \cite{Punturo:2010zz,Hild:2010id}.

SBGW including the backreaction of particle emission on the loop distribution. LH panel: kinks on loops, RH panel: cusps on loop. The spectra are cutoff at high frequency, as indicated by the black vertical lines. $G\mu$ ranges from $10^{-17}$ (lower curve), through $10^{-15}$, $10^{-13}$,$10^{-11}$, $10^{-9}$ and $10^{-7}$ (upper curve). Also plotted are the power-law integrated sensitivity curves from SKA (pink dashed) \cite{Janssen:2014dka}, LISA (yellow dashed) \cite{Caprini:2019pxz}, adv-LIGO (grey dashed) \cite{TheLIGOScientific:2016dpb} and Einstein Telescope (blue dashed) \cite{Punturo:2010zz,Hild:2010id}.

Contribution of cosmic strings to the Diffuse Gamma-Ray Background. The (blue) horizontal line is the experimental constraint from Fermi-LAT, while the (orange) line is the exact numerical calculation for kinks (LH panel) and cusps (RH panel). On either side of the maxima, the slope and amplitude can be estimated using the results of previous sections. Kinks: for low $G\mu$ the slope is $9/8$ (dashed-green line), and for high $G\mu$ it depends on $\mu^{-2}\log(\mu)$ (dashed-red line). Cusps: For low $G\mu$ the slope is $13/12$ (dashed-green line), and for high $G\mu$ it is $-5/4$ (dashed-red line). The slightly different amplitude between the numerical calculation and the analytical one is because the latter assumes a matter dominated universe, and hence neglects effects of late time acceleration.

Contribution of cosmic strings to the Diffuse Gamma-Ray Background. The (blue) horizontal line is the experimental constraint from Fermi-LAT, while the (orange) line is the exact numerical calculation for kinks (LH panel) and cusps (RH panel). On either side of the maxima, the slope and amplitude can be estimated using the results of previous sections. Kinks: for low $G\mu$ the slope is $9/8$ (dashed-green line), and for high $G\mu$ it depends on $\mu^{-2}\log(\mu)$ (dashed-red line). Cusps: For low $G\mu$ the slope is $13/12$ (dashed-green line), and for high $G\mu$ it is $-5/4$ (dashed-red line). The slightly different amplitude between the numerical calculation and the analytical one is because the latter assumes a matter dominated universe, and hence neglects effects of late time acceleration.