Impact of the small-scale structure on the Stochastic Background of Gravitational Waves from cosmic strings

Author(s)

Abstract

Numerical simulations and analytical models suggest that infinite cosmic strings produce cosmic string loops of all sizes with a given power-law. Precise estimations of the power-law exponent are still matter of debate while numerical simulations do not incorporate all the radiation and back-reaction effects expected to affect the network at small scales. Previously it has been shown, using a Boltzmann approach, that depending on the steepness of the loop production function and the gravitational back-reaction scale, a so-called Extra Population of Small Loops (EPSL) can be generated in the loop number density. We propose a framework to study the influence of this extra population of small loops on the Stochastic Background of Gravitational Waves (SBGW). We show that this extra population can have a significant signature at frequencies higher than H0(Γ Gμ)−1 where Γ is of order 50 and H0 is the Hubble constant. We propose a complete classification of the Gravitational Wave (GW) power spectra expected from cosmic strings into four classes, including the model of Blanco-Pillado, Olum and Shlaer and the model of Lorenz, Ringeval and Sakellariadou. Finally we show that given the uncertainties on the Polchinski-Rocha exponents, two hybrid classes of GW power spectrum can be considered giving very different predictions for the SBGW.

Figures

: Radiation era

: Matter era

The decomposition of the \gls{lnd} into two populations, the \gls{slnd} and the \gls{epsl} for $\chi=0.2$ and $G\mu = 10^{-13}$ in the radiation era. The infrared cutoff is set to $\gammai = 0.1$.

Impact of the extra population of small loops onto the \gls{sbgw} in the parameter space $\chir,\chim$ for $G\mu=10^{-13}$. In the blue region, the high frequency plateau for $\OmegaGW$ is dominated by the extra population of small loops produced during radiation era. In the red region, the spectrum presents a peak around $\uHo {\gammac^{(m)}}^{-1}$ produced by the \gls{epsl} during the matter era. Outside those regions, the population of small loops can be neglected.

: $G\mu = 10^{-13}$, $\chir = 0.5$, $\chim = 0.655$

: $G\mu = 10^{-13}$, $\chir = 0.2$, $\chim = 0.295$

: $G\mu = 10^{-13}$, $\chir = 0.45$, $\chim = 0.295$

: $G\mu = 10^{-13}$, $\chir = 0.2$, $\chim = 0.45$

: LIGO/Virgo, sensitivity of $\OmegaGW=10^{-7}$ taken at $f=20$ Hz

: LIGO/Virgo constraints on $G\mu$ at $\chim=0.295$. The orange region is excluded giving non-convex constraints on $G\mu$ for a given model.

: PTA, sensitivity of $\OmegaGW=10^{-12}$ taken at $f=2\times 10^{-9}$ Hz

: LISA, sensitivity of $\OmegaGW=10^{-13}$ taken at $f=10^{-2}$ Hz