Simulations Of Cosmic Strings Research Articles

Scaling solutions of wiggly cosmic strings

Cosmic strings may have formed in the early universe due to the Kibble mechanism. While string networks are usually modeled as being of Nambu-Goto type, this description is understood to be a convenient approximation, which neglects the typically expected presence of additional degrees of freedom on the string worldsheet. Previous simulations of cosmic strings in expanding universes have established beyond doubt the existence of a significant amount of short-wavelength propagation modes (commonly called wiggles) on the strings, and a wiggly string extension of the canonical velocity-dependent one-scale model has been recently developed. Here we improve the physical interpretation of this model, by studying the possible asymptotic scaling solutions of this model, and in particular how they are affected by the expansion of the universe and the available energy loss or transfer mechanisms -- e.g., the production of loops and wiggles. In addition to the Nambu-Goto solution, to which the wiggly model reduces in the appropriate limit, we find that there are also solutions where the amount of wiggliness can grow as the network evolves or, for specific expansion rates, become a constant. Our results show that full scaling of the network, including the wiggliness, is much more likely in the matter era than in the radiation era, which is in agreement with numerical simulation results.

Abelian-Higgs cosmic string evolution with CUDA

Topological defects form at cosmological phase transitions by the Kibble mechanism, with cosmic strings—one-dimensional defects—being the most studied example. A rigorous analysis of their astrophysical consequences is limited by the availability of accurate numerical simulations, and therefore by hardware resources and computation time. Improving the speed and efficiency of existing codes is therefore important. All current cosmic string simulations were performed on Central Processing Units. In previous work we presented a General Purpose Graphics Processing Unit implementation of the evolution of cosmological domain wall networks. Here we discuss an analogous implementation for local Abelian-Higgs string networks. We discuss the implementation algorithm (including the discretisation used and how to calculate network averaged quantities) and then showcase its performance and current bottlenecks. We validate the code by directly comparing our results for the canonical scaling properties of the networks in the radiation and matter eras with those in the literature, finding very good agreement. We finally highlight possible directions for improving the scalability of the code.

New CMB constraints for Abelian Higgs cosmic strings

We present cosmic microwave background (CMB) power spectra from recent numerical simulations of cosmic strings in the Abelian Higgs model and compare them to CMB power spectra measured by Planck. We obtain revised constraints on the cosmic string tension parameter Gμ. For example, in the ΛCDM model with the addition of strings and no primordial tensor perturbations, we find Gμ < 2.0 × 10−7 at 95% confidence, about 20% lower than the value obtained from previous simulations, which had 1/64 of the spatial volume. The increased computational volume also makes it possible to simulate fully the physical equations of motion, in which the string cores shrink in comoving coordinates. We find however that this, and the larger dynamic range, changes the amplitude of the power spectra by only about 10%. The main cause of the stronger constraints on Gμ is instead an improved treatment of the string evolution across the radiation-matter transition.

CMB power spectrum of Nambu-Goto cosmic strings

We improve predictions of the cosmic microwave background (CMB) power spectrum induced by cosmic strings by using source terms obtained from Nambu-Goto network simulations in an expanding universe. We use three high-resolution cosmic string simulations that cover the entire period from recombination until late-time $\Lambda$ domination to calculate unequal time correlators (UETCs) for scalar, vector and tensor components of the cosmic-string energy-momentum tensor. We calculate the CMB angular power spectrum from strings in two ways. First, to aid comparison with previous work, we fit our simulated UETCs to those obtained from different parameter combinations from the unconnected segment model and then calculate the CMB power spectra using these parameters to represent the string network. Second and more accurately, we decompose the UETCs into their corresponding eigenvalues and eigenvectors and input them directly into an Einstein-Boltzmann solver to calculate the power spectrum for each of the three simulation time periods. We combine the three simulations together, using each of them in its relevant redshift range and we obtain overall power spectra in temperature and polarisation channels. Finally, we use the power spectra obtained with the latest Planck and BICEP2 likelihoods to obtain constraints on the cosmic string tension.

Constraints on the Nambu-Goto cosmic string contribution to the CMB power spectrum in light of new temperature and polarisation data

Cosmic strings generate vector and tensor modes in the B-channel of polarisation, as well as the usual temperature power spectrum and E-mode polarisation spectrum. We use the power spectrum obtained from high-resolution Nambu-Goto cosmic string simulations together with the Planck and BICEP2 likelihoods to explore the degeneracies appearing between cosmic strings and other cosmological parameters in different inflationary scenarios, as well as the constraints that can be imposed on cosmic strings in each of these situations. In standard ΛCDM, the Planck likelihood yields an upper limit Gμ<1.49 × 10−7 (95% confidence). We also analyse the possibility of explaining the BB power spectrum signal recently detected by the BICEP2 probe. We find that cosmic strings alone are able to explain only part of the B-mode polarisation signal. Apart from the standard ΛCDM model, we look at the following non-minimal parameters: the running of the spectral index, non-zero tensor-to-scalar ratio, additional degrees of freedom (Neff) and sterile neutrinos. We find that in both Planck and BICEP2 scenarios adding Neff induces degeneracies between cosmic strings and Neff and other ΛCDM parameters. With Neff a larger contribution from cosmic strings is allowed, even favoured, but after combining with large-scale structure data, such as BAOs, strings remain strongly constrained.

Improving cosmic string network simulations

In real-time lattice simulations of cosmic strings in the Abelian Higgs model, the broken translational invariance introduces lattice artifacts; relativistic strings therefore decelerate and radiate. We introduce two different methods to construct a moving string on the lattice, and study in detail the lattice effects on moving strings. We find that there are two types of lattice artifact: there is an effective maximum speed with which a moving string can be placed on the lattice, and a moving string also slows down, with the deceleration approximately proportional to the exponential of the velocity. To mitigate this, we introduce and study an improved discretization, based on the tree-level L\uscher-Weisz action, which is found to reduce the deceleration by an order of magnitude, and to increase the string speed limit by an amount equivalent to halving the lattice spacing. The improved algorithm is expected to be very useful for 3D simulations of cosmic strings in the early Universe, where one wishes to simulate as large a volume as possible.

Large parallel cosmic string simulations: New results on loop production

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 nonscaling 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.

Cosmic string induced CMB maps

We compute maps of CMB temperature fluctuations seeded by cosmic strings using high resolution simulations of cosmic strings in a Friedmann-Robertson-Walker universe. We create full-sky, 18\ifmmode^\circ\else\textdegree\fi{} and 3\ifmmode^\circ\else\textdegree\fi{} CMB maps, including the relevant string contribution at each resolution from before recombination to today. We extract the angular power spectrum from these maps, demonstrating the importance of recombination effects. We briefly discuss the probability density function of the pixel temperatures, their skewness, and kurtosis.

CMB temperature bispectrum induced by cosmic strings

The cosmic microwave background (CMB) bispectrum of the temperature anisotropies induced by a network of cosmic strings is derived for small angular scales, under the assumption that the principal cause of temperature fluctuations is the Gott-Kaiser-Stebbins effect. We provide analytical expressions for all isosceles triangle configurations in Fourier space. Their overall amplitude is amplified as the inverse cube of the angle and diverges for flat triangles. The isosceles configurations generically lead to a negative bispectrum with a power-law decay ${\ensuremath{\ell}}^{\ensuremath{-}6}$ for large multipole $\ensuremath{\ell}$. However, collapsed triangles are found to be associated with a positive bispectrum whereas the squeezed triangles still exhibit negative values. We then compare our analytical estimates to a direct computation of the bispectrum from a set of 300 statistically independent temperature maps obtained from Nambu-Goto cosmic string simulations in a Friedmann-Lema\^{\i}tre-Robertson-Walker universe. We find good agreement for the overall amplitude, the power-law behavior, and the angle dependency of the various triangle configurations. At $\ensuremath{\ell}\ensuremath{\sim}500$ the cosmic string Gott-Kaiser-Stebbins effect contributes approximately the same equilateral CMB bispectrum amplitude as an inflationary model with $|{f}_{\mathrm{NL}}^{\mathrm{loc}}|\ensuremath{\simeq}{10}^{3}$, if the strings contribute about 10% of the temperature power spectrum at $\ensuremath{\ell}=10$. Current bounds on ${f}_{\mathrm{NL}}$ are not derived using cosmic string bispectrum templates, and so our ${f}_{\mathrm{NL}}$ estimate cannot be used to derive bounds on strings. However it does suggest that string bispectrum templates should be included in the search of CMB non-Gaussianities.

Vortex Loop Distribution Near a Superfluid Phase Transition

The distribution of thermally excited vortex loops near a superfluid phase transition is calculated. The number density of loops with a given perimeter is found to change from an exponential decay with increasing perimeter to algebraic decay as Tcis approached from below, in agreement with recent simulations of cosmic strings and of the high-Tcsuperconducting transition in zero field. The total line density is calculated and compared with the simulations. A different viewpoint of the Kibble-Zurek scenario for rapidly quenched transitions is proposed, and the role of vortices above the transition temperature is briefly discussed.

Scaling and small-scale structure in cosmic string networks

We examine the scaling properties of an evolving network of strings in Minkowski spacetime and study the evolution of length scales in terms of a three-scale model proposed by Austin, Copeland, and Kibble (ACK). We find good qualitative and some quantitative agreement between the model and our simulations. We also investigate small-scale structure by altering the minimum allowed size for loop production ${E}_{c}.$ Certain quantities depend significantly on this parameter: for example, the scaling density can vary by a factor of 2 or more with increasing ${E}_{c}.$ Small-scale structure as defined by ACK disappears if no restrictions are placed on loop production, and the fractal dimension of the string changes smoothly from 2 to 1 as the resolution scale is decreased. Loops are nearly all produced at the lattice cutoff. We suggest that the lattice cutoff should be interpreted as corresponding to the string width, and that in a real network loops are actually produced with this size. This leads to a radically different string scenario, with particle production rather than gravitational radiation being the dominant mode of energy dissipation. At the very least, a better understanding of the discretization effects in all simulations of cosmic strings is called for.