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We determine the distribution of cosmic string loops directly from simulations, rather than determining the loop production function and inferring the loop distribution from that. For a wide range of loop lengths, the results agree well with a power law exponent -2.5 in the radiation era and -2 in the matter era, the universal result for any loop production function that does not diverge at small scales. Our results extend those of Ringeval, Sakellariadou, and Bouchet: we are able to run for 15 times longer in conformal time and simulate a volume 300-2400 times larger. At the times they reached, our simulation is in general agreement with the more negative exponents they found, -2.6 and -2.4. However, our simulations show that this was a transient regime; at later times the exponents decline to the values above. This provides further evidence against models with a rapid divergence of the loop density at small scales, such as ``model 3 used to analyze LIGO data and predict LISA sensitivity.
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Using a new parallel computing technique, we have run the largest cosmic string simulations ever performed. Our results confirm the existence of a long transient period where a non-scaling distribution of small loops is produced at lengths depending on the initial correlation scale. As time passes, this initial population gives way to the true scaling regime, where loops of size approximately equal to one-twentieth the horizon distance become a significant component. We observe similar behavior in matter and radiation eras, as well as in flat space. In the matter era, the scaling population of large loops becomes the dominant component; we expect this to eventually happen in the other eras as well.
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