Cosmic String Loops Research Articles

Cosmic string loop collapse in full general relativity

We present the first fully general relativistic dynamical simulations of Abelian Higgs cosmic strings using 3+1D numerical relativity. Focusing on cosmic string loops, we show that they collapse due to their tension and can either (i) unwind and disperse or (ii) form a black hole, depending on their tension $G\mu$ and initial radius. We show that these results can be predicted using an approximate formula derived using the hoop conjecture, and argue that it is independent of field interactions. We extract the gravitational waveform produced in the black hole formation case and show that it is dominated by the $l=2$ and $m=0$ mode. We also compute the total gravitational wave energy emitted during such a collapse, being $0.5\pm 0.2~ \%$ of the initial total cosmic string loop mass, for a string tension of $G\mu=1.6\times 10^{-2}$ and radius $R=100~M_{pl}^{-1}$. We use our results to put a bound on the production rate of planar cosmic strings loops as $N \lesssim 10^{-2}~\mathrm{Gpc}^{-3}~\mathrm{yr}^{-1}$.

Signature of inflation in the stochastic gravitational wave background generated by cosmic string networks

A cosmic string network created during an inflationary stage in the early Universe - here defined as i-string network - is expected to enter a transient stretching regime during inflation, in which its characteristic length is stretched to scales much larger than the Hubble radius, before attaining a standard evolution once the network re-enters the Hubble volume after inflation. During the stretching regime, the production of cosmic string loops and consequent emission of gravitational radiation are significantly suppressed. Here, we compute the power spectrum of the stochastic gravitational wave background generated by i-string networks using the velocity-dependent one scale model to describe the network dynamics, and demonstrate that this regime introduces a high-frequency signature on an otherwise standard spectrum of the stochastic gravitational wave background generated by cosmic strings. We argue that, if observed by current or forthcoming experiments, this signature would provide strong evidence for i-strings and, therefore, for (primordial) inflation. We also develop a simple single-parameter algorithm for the computation of the stochastic gravitational wave background generated by i-strings from that of a standard cosmic string network, which may be useful in the determination of the observational constraints to be obtained by current and forthcoming gravitational wave experiments.

Constraints on cosmic strings using data from the first Advanced LIGO observing run

Cosmic strings are topological defects which can be formed in GUT-scale phase transitions in the early universe. They are also predicted to form in the context of string theory. The main mechanism for a network of Nambu-Goto cosmic strings to lose energy is through the production of loops and the subsequent emission of gravitational waves, thus offering an experimental signature for the existence of cosmic strings. Here we report on the analysis conducted to specifically search for gravitational-wave bursts from cosmic string loops in the data of Advanced LIGO 2015-2016 observing run (O1). No evidence of such signals was found in the data, and as a result we set upper limits on the cosmic string parameters for three recent loop distribution models. In this paper, we initially derive constraints on the string tension $G\mu$ and the intercommutation probability, using not only the burst analysis performed on the O1 data set, but also results from the previously published LIGO stochastic O1 analysis, pulsar timing arrays, cosmic microwave background and Big-Bang nucleosynthesis experiments. We show that these data sets are complementary in that they probe gravitational waves produced by cosmic string loops during very different epochs. Finally, we show that the data sets exclude large parts of the parameter space of the three loop distribution models we consider.

Superconducting cosmic string loops as sources for fast radio bursts

The cusp burst radiation of superconducting cosmic string (SCS) loops is thought to be a possible origin of observed fast radio bursts with the model-predicted radiation spectrum and the redshift- and energy-dependent event rate, we fit the observational redshift and energy distributions of 21 Parkes fast radio bursts and constrain the model parameters. It is found that the model can basically be consistent with the observations, if the current on the SCS loops has a present value of $\ensuremath{\sim}{10}^{16}{\ensuremath{\mu}}_{17}^{9/10}\text{ }\text{ }\mathrm{esu}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$ and evolves with redshift as an empirical power law $\ensuremath{\sim}(1+z{)}^{\ensuremath{-}1.3}$, where ${\ensuremath{\mu}}_{17}=\ensuremath{\mu}/{10}^{17}\text{ }\text{ }\mathrm{g}\text{ }{\mathrm{cm}}^{\ensuremath{-}1}$ is the string tension. This current evolution may provide a clue to probe the evolution of the cosmic magnetic fields and the gathering of the SCS loops to galaxy clusters.

Stochastic gravitational waves from cosmic string loops in scaling

If cosmic strings are formed in the early universe, their associated loops emit gravitational waves during the whole cosmic history and contribute to the stochastic gravitational wave background at all frequencies. We provide a new estimate of the stochastic gravitational wave spectrum by considering a realistic cosmological loop distribution, in scaling, as it can be inferred from Nambu-Goto numerical simulations. Our result takes into account various effects neglected so far. We include both gravitational wave emission and backreaction effects on the loop distribution and show that they produce two distinct features in the spectrum. Concerning the string microstructure, in addition to the presence of cusps and kinks, we show that gravitational wave bursts created by the collision of kinks could dominate the signal for wiggly strings, a situation which may be favoured in the light of recent numerical simulations. In view of these new results, we propose four prototypical scenarios, within the margin of the remaining theoretical uncertainties, for which we derive the corresponding signal and estimate the constraints on the string tension put by both the LIGO and European Pulsar Timing Array (EPTA) observations. The less constrained of these scenarios is shown to have a string tension GU ≤ 7.2 × 10−11, at 95% of confidence. Smooth loops carrying two cusps per oscillation verify the two-sigma bound GU ≤ 1.0 × 10−11 while the most constrained of all scenarios describes very kinky loops and satisfies GU ≤ 6.7× 10−14 at 95% of confidence.

Gravitational Smoothing of Kinks on Cosmic String Loops.

We analyze the effect of gravitational backreaction on cosmic string loops with kinks, which is an important determinant of the shape, and thus the potential observability, of string loops which may exist in the Universe today. Kinks are not rounded off, but may be straightened out. This means that backreaction will only cause loops with kinks to develop cusps after some potentially large fraction of their lifetimes. In some loops, symmetries prevent even this process, so that the loop evaporates in a self-similar fashion and the kinks are unchanged. As an example, we discuss backreaction on the rectangular Garfinkle-Vachaspati loop.

Gravitational backreaction on piecewise linear cosmic string loops

We calculate the metric and affine connection due to a piecewise linear cosmic string loop, and the effect of gravitational back reaction for the Garfinkle-Vachaspati loop with four straight segments. As expected, back reaction reduces the size of the loop, in accord with the energy going into gravitational waves. The "square" (maximally symmetric) loop evaporates without changing shape, but for all other loops in this class, the kinks become less sharp and segments between kinks become curved. If the loop is close to the square case, it will evaporate before its kinks are significantly changed, if it is far from square, the opening out of the kinks is much faster than evaporation of the loop.

Dynamical behavior and Jacobi stability analysis of wound strings

We numerically solve the equations of motion (EOM) for two models of circular cosmic string loops with windings in a simply connected internal space. Since the windings cannot be topologically stabilized, stability must be achieved (if at all) dynamically. As toy models for realistic compactifications, we consider windings on a small section of $\mathbb{R}^2$, which is valid as an approximation to any simply connected internal manifold if the winding radius is sufficiently small, and windings on an $S^2$ of constant radius $\mathcal{R}$. We then use Kosambi-Cartan-Chern (KCC) theory to analyze the Jacobi stability of the string equations and determine bounds on the physical parameters that ensure dynamical stability of the windings. We find that, for the same initial conditions, the curvature and topology of the internal space have nontrivial effects on the microscopic behavior of the string in the higher dimensions, but that the macroscopic behavior is remarkably insensitive to the details of the motion in the compact space. This suggests that higher-dimensional signatures may be extremely difficult to detect in the effective $(3+1)$-dimensional dynamics of strings compactified on an internal space, even if configurations with nontrivial windings persist over long time periods.

Cosmic Strings and The Origins of Globular Clusters

Background: Globular clusters are galactic structures whose origin is not well understood. In this paper we propose that their origin may be found in the accretions formed around cosmic string loops.
 Methods: To test this hypothesis we derived the mass distribution that would be associated with the ac- cretions and compared it to the observed mass distribution of globular clusters in our galaxy. Our derived distribution left us one free parameter (cosmic string tension) which we varied to optimize the fit. Once optimized, we compared the shape of the distribution and the number density that our model predicted with empirical observations. Later, we derived how velocity effects would alter the shape of this distribution.
 Results: We achieved significant agreement between our model and observed values. Furthermore, the op- timal tension corresponds to particle physics theories that have not been ruled out. Our analysis further suggests that globular clusters form around slowly moving (< 3% the speed of light) cosmic string loops; any model with significantly faster cosmic string loops would contradict our hypothesis.
 Limitations: Our results were obtained by using numerous approximations (such as the Zel’dovich approx- imation) and thus should be treated as an order of magnitude estimation. Our data was also limited to observed globular clusters within the Milky Way, limiting our sample size to approximately 120 globular clusters.
 Conclusions: We managed to obtain strong agreement between our model and observed globular clusters, suggesting that they may be seeded by cosmic string loops. This also serves to explain many other charac- teristics of globular clusters, such as age, density and location. The analyses used in this report can also be used when considering the formation of other accretion objects, such as ultra-compact-minihalos.

Cosmic Microwave Background spectral distortions from cosmic string loops

Cosmic string loops contain cusps which decay by emitting bursts of particles. A significant fraction of the released energy is in the form of photons. These photons are injected non-thermally and can hence cause spectral distortions of the Cosmic Microwave Background (CMB). Under the assumption that cusps are robust against gravitational back-reaction, we compute the fractional energy density released as photons in the redshift interval where such non-thermal photon injection causes CMB spectral distortions. Whereas current constraints on such spectral distortions are not strong enough to constrain the string tension, future missions such as the PIXIE experiment will be able to provide limits which rule out a range of string tensions between G μ ∼ 10−15 and G μ ∼ 10−12, thus ruling out particle physics models yielding these kind of intermediate-scale cosmic strings.

Large scale CMB anomalies from thawing cosmic strings

Cosmic strings formed during inflation are expected to be either diluted over super-Hubble distances, i.e., invisible today, or to have crossed our past light cone very recently. We discuss the latter situation in which a few strings imprint their signature in the Cosmic Microwave Background (CMB) Anisotropies after recombination. Being almost frozen in the Hubble flow, these strings are quasi static and evade almost all of the previously derived constraints on their tension while being able to source large scale anisotropies in the CMB sky. Using a local variance estimator on thousand of numerically simulated Nambu-Goto all sky maps, we compute the expected signal and show that it can mimic a dipole modulation at large angular scales while being negligible at small angles. Interestingly, such a scenario generically produces one cold spot from the thawing of a cosmic string loop. Mixed with anisotropies of inflationary origin, we find that a few strings of tension GU = \U0001d4aa(1) × 10−6 match the amplitude of the dipole modulation reported in the Planck satellite measurements and could be at the origin of other large scale anomalies.

Effects of cosmic string velocities and the origin of globular clusters

With the hypothesis that cosmic string loops act as seeds for globular clusters in mind, we study the role that velocities of these strings will play in determining the mass distribution of globular clusters. Loops with high enough velocities will not form compact and roughly spherical objects and can hence not be the seeds for globular clusters. We compute the expected number density and mass function of globular clusters as a function of both the string tension and the peak loop velocity, and compare the results with the observational data on the mass distribution of globular clusters in our Milky Way. We determine the critical peak string loop velocity above which the agreement between the string loop model for the origin of globular clusters (neglecting loop velocities) and observational data is lost.

Three Duality Symmetries between Photons and Cosmic String Loops, and Macro and Micro Black Holes

We present a review of two thermal duality symmetries between two different kinds of systems: photons and cosmic string loops, and macro black holes and micro black holes, respectively. It also follows a third joint duality symmetry amongst them through thermal equilibrium and stability between macro black holes and photon gas, and micro black holes and string loop gas, respectively. The possible cosmological consequences of these symmetries are discussed.

Cosmic string loop shapes

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.

Thermal duality and thermodynamics of micro black holes

Starting from a generalized black hole entropy with logarithmic area corrections, in this paper we obtain (for positive value of the coefficient of the correction term) a generalized equation of state for black holes with two dual branches. In one of them (the usual one for macro black holes) T ≃ 1/M, with T temperature and M mass. In the other one, for micro black holes, instead, T ≃ M. We compare the equilibrium and stability between macro black holes and electromagnetic radiation in a finite box with reflecting walls, with the dual situation corresponding to micro black holes and cosmic string loops, also in a finite box. In this model, the dual phenomenon of evaporation of unstable macro black holes into a stable gas of electromagnetic radiation would be the condensation of unstable gas of cosmic string loops into stable micro black holes.

Constraints on cosmic strings from ultracompact minihalos

Cosmic strings are expected to form loops. These can act as seeds for accretion of dark matter, leading to the formation of ultracompact minihalos (UCMHs). We perform a detailed study of the accretion of dark matter onto cosmic string loops and compute the resulting mass distribution of UCMHs. We then apply observational limits on the present-day abundance of UCMHs to derive corresponding limits on the cosmic string tension $G\ensuremath{\mu}$. The bounds are strongly dependent upon the assumed distribution of loop velocities and their impacts on UCMH formation. Under the assumption that a loop can move up to a thousand times its own radius and still form a UCMH, we find a limit of $G\ensuremath{\mu}\ensuremath{\le}1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$. We show, in opposition to previous results, that strong limits on the cosmic string tension are not obtainable from UCMHs when more stringent (and realistic) requirements are placed on loop velocities.

Cosmic string loops as the seeds of super-massive black holes

Recent discoveries of super-massive black holes at high redshifts indicate a possible tension with the standard ΛCDM paradigm of early universe cosmology which has difficulties in explaining the origin of the required nonlinear compact seeds which trigger the formation of these super-massive black holes. Here we show that cosmic string loops which result from a scaling solution of strings formed during a phase transition in the very early universe lead to an additional source of compact seeds. The number density of string-induced seeds dominates at high redshifts and can help trigger the formation of the observed super-massive black holes.

Cosmic strings and the origin of globular clusters

We hypothesize that cosmic string loops are the seeds about which globular clusters accrete. Fixing the cosmic string tension by demanding that the peak in the distribution of masses of objects accreting onto string loops agrees with the peak in the observed mass distribution of globular clusters in our Milky Way galaxy, we then compute the expected number density and mass function of globular clusters, and compare with observations. Our hypothesis naturally explains why globular clusters are the oldest and most dense objects in a galaxy, and why they are found in the halo of the galaxy.

Fast radio bursts as electromagnetic radiation from cusps on superconducting cosmic strings

Cosmic strings are topological defects, relicts of the early Universe, which can be formed during phase transitions of fields with spontaneous broken symmetry. There also exists a special class of cosmic strings - superconducting cosmic strings, inside of which the massless charge carriers, so-called zero modes, are presented and can move along the string without any resistance. The superconducting cosmic strings during their relativistic motion through the cosmic plasma could be a powerful source of electromagnetic radiation. The emission of cusps on the superconducting strings is highly beamed and has the nature of bursts. In the present work, it is shown, that the millisecond extragalactic radio bursts, discovered during the last decade, called the fast radio bursts (FRB), with unknown nature, could be explained as radiation from cusps on superconducting cosmic strings. Estimates made for ten FRBs discovered till now show that bursts could be produced by a string with α=ΓGμ/c2∼ 5⋅10-13-10-12, where Γ ∼ 50 is a dimensionless parameter, G is the gravitational constant, c is the speed of light, μ is the mass per unit length of a string, which corresponds to the energy scale of the phase transition η∼1.2⋅1012-1.7⋅1012 GeV. The observed duration, flux and event rate are in a good agreement with the proposed model. In the framework of emission from cusps of superconducting cosmic string loops, probability of FRB detecting is estimated, which is found to be highly close to the probability of detecting, given by observational data.

Implications of fast radio bursts for superconducting cosmic strings

Highly beamed, short-duration electromagnetic bursts could be produced by superconducting cosmic string (SCS) loops oscillating in cosmic magnetic fields. We demonstrated that the basic characteristics of SCS bursts such as the electromagnetic frequency and the energy release could be consistently exhibited in the recently discovered fast radio bursts (FRBs). Moreover, it is first showed that the redshift distribution of the FRBs can also be well accounted for by the SCS burst model. Such agreements between the FRBs and SCS bursts suggest that the FRBs could originate from SCS bursts and thus they could provide an effective probe to study SCSs. The obtained values of model parameters indicate that the loops generating the FRBs have a small length scale and they are mostly formed in the radiation-dominated cosmological epoch.