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We analyze the shapes of cosmic string loops found in large-scale simulations of an expanding-universe string network. The simulation does not include gravitational back reaction, but we model that process by smoothing the loop using Lorentzian convolution. We find that loops at formation consist of generally straight segments separated by kinks. We do not see cusps or any cusp-like structure at the scale of the entire loop, although we do see very small regions of string that move with large Lorentz boosts. However, smoothing of the string almost always introduces two cusps on each loop. The smoothing process does not lead to any significant fragmentation of loops that were in non-self-intersecting trajectories before smoothing.
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Observational effects of cosmic string loops depend on how loops are distributed in space. Chernoff cite{Chernoff} has argued that loops can be gravitationally captured in galaxies and that for sufficiently small values of $Gmu$ their distribution follows that of dark matter, independently of the loops length. We re-analyze this issue using the spherical model of galaxy formation with full account taken of the gravitational rocket effect -- loop accelerated motion due to asymmetric emission of gravitational waves. We find that only loops greater than a certain size are captured and that the number of captured loops is orders of magnitude smaller than estimated by Chernoff.
Using recent simulation results, we provide the mass and speed spectrum of cosmic string loops. This is the quantity of primary interest for many phenomenological signatures of cosmic strings, and it can be accurately predicted using recently acquired detailed knowledge of the loop production function. We emphasize that gravitational smoothing of long strings does not play any role in determining the total number of existing loops. We derive a bound on the string tension imposed by recent constraints on the stochastic gravitational wave background from pulsar timing arrays, finding $Gmu leq 2.8times 10^{-9}$. We also provide a derivation of the Boltzmann equation for cosmic string loops in the language of differential forms.
We examine the effects of cosmic strings on structure formation and on the ionization history of the universe. While Gaussian perturbations from inflation are known to provide the dominant contribution to the large scale structure of the universe, density perturbations due to strings are highly non-Gaussian and can produce nonlinear structures at very early times. This could lead to early star formation and reionization of the universe. We improve on earlier studies of these effects by accounting for high loop velocities and for the filamentary shape of the resulting halos. We find that for string energy scales Gmu > 10^{-7} the effect of strings on the CMB temperature and polarization power spectra can be significant and is likely to be detectable by the Planck satellite. We mention shortcomings of the standard cosmological model of galaxy formation which may be remedied with the addition of cosmic strings, and comment on other possible observational implications of early structure formation by strings.
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.
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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