WIMP Dark Matter and the QCD Equation of State

Weakly Interacting Massive Particles (WIMPs) of mass m freeze out at a temperature T_f ~ m/25, i.e. in the range 400 MeV -- 40 GeV for a particle in the typical mass range 10 -- 1000 GeV. The WIMP relic density, which depends on the effective number of relativistic degrees of freedom at T_f, may be measured to better than 1% by Planck, warranting comparable theoretical precision. Recent theoretical and experimental advances in the understanding of high temperature QCD show that the quark gluon plasma departs significantly from ideal behaviour up to temperatures of several GeV, necessitating an improvement of the cosmological equation of state over those currently used. We discuss how this increases the relic density by approximately 1.5 -- 3.5% in benchmark mSUGRA models, with an uncertainly in the QCD corrections of 0.5 -- 1 %. We point out what further work is required to achieve a theoretical accuracy comparable with the expected observational precision, and speculate that the effective number of degrees of freedom at T_f may become measurable in the foreseeable future.Comment: 4pp, 2figs. More info including Matlab scripts used to generate equation of state curves at http://www.pact.cpes.sussex.ac.uk/arXiv/hep-ph/0501232

Correlations in Cosmic String Networks

We investigate scaling and correlations of the energy and momentum in an evolving network of cosmic strings in Minkowski space. These quantities are of great interest, as they must be understood before accurate predictions for the power spectra of the perturbations in the matter and radiation in the early Universe can be made. We argue that Minkowski space provides a reasonable approximation to a Friedmann background for string dynamics and we use our results to construct a simple model of the network, in which it is considered to consist of randomly placed segments moving with random velocities. This model works well in accounting for features of the two-time correlation functions, and even better for the power spectra.Comment: 20pp Plain LaTeX, 11 EPS figures, uses epsf.st

Where are the Hedgehogs in Nematics?

In experiments which take a liquid crystal rapidly from the isotropic to the nematic phase, a dense tangle of defects is formed. In nematics, there are in principle both line and point defects (``hedgehogs''), but no point defects are observed until the defect network has coarsened appreciably. In this letter the expected density of point defects is shown to be extremely low, approximately $10^{-8}$ per initially correlated domain, as result of the topology (specifically, the homology) of the order parameter space.Comment: 6 pages, latex, 1 figure (self-unpacking PostScript)

Large Radius Hagedorn Regime in String Gas Cosmology

We calculate the equation of state of a gas of strings at high density in a large toroidal universe, and use it to determine the cosmological evolution of background metric and dilaton fields in the entire large radius Hagedorn regime, (ln S)^{1/d} << R << S^{1/d} (with S the total entropy). The pressure in this regime is not vanishing but of O(1), while the equation of state is proportional to volume, which makes our solutions significantly different from previously published approximate solutions. For example, we are able to calculate the duration of the high-density "Hagedorn" phase, which increases exponentially with increasing entropy, S. We go on to discuss the difficulties of the scenario, quantifying the problems of establishing thermal equilibrium and producing a large but not too weakly-coupled universe.Comment: 12 pages, 4 figures, more details presented in string thermodynamics section, to be published in Physical Review

Anti-Proton Evolution in Little Bangs and Big Bang

The abundances of anti-protons and protons are considered within momentum-integrated Boltzmann equations describing Little Bangs, i.e., fireballs created in relativistic heavy-ion collisions. Despite of a large anti-proton annihilation cross section we find a small drop of the ratio of anti-protons to protons from 170 MeV (chemical freeze-out temperature) till 100 MeV (kinetic freeze-out temperature) for CERN-SPS and BNL-RHIC energies thus corroborating the solution of the previously exposed "ani-proton puzzle". In contrast, the Big Bang evolves so slowly that the anti-baryons are kept for a long time in equilibrium resulting in an exceedingly small fraction. The adiabatic path of cosmic matter in the phase diagram of strongly interacting matter is mapped out

Numerical simulations of string networks in the Abelian-Higgs model

We present the results of a field theory simulation of networks of strings in the Abelian Higgs model. Starting from a random initial configuration we show that the resulting vortex tangle approaches a self-similar regime in which the length density of lines of zeros of $\phi$ reduces as $t^{-2}$. We demonstrate that the network loses energy directly into scalar and gauge radiation. These results support a recent claim that particle production, and not gravitational radiation, is the dominant energy loss mechanism for cosmic strings. This means that cosmic strings in Grand Unified Theories are severely constrained by high energy cosmic ray fluxes: either they are ruled out, or an implausibly small fraction of their energy ends up in quarks and leptons.Comment: 4pp RevTeX, 3 eps figures, clarifications and new results included, to be published in Phys. Rev. Let

Defect formation and local gauge invariance

We propose a new mechanism for formation of topological defects in a U(1) model with a local gauge symmetry. This mechanism leads to definite predictions, which are qualitatively different from those of the Kibble-Zurek mechanism of global theories. We confirm these predictions in numerical simulations, and they can also be tested in superconductor experiments. We believe that the mechanism generalizes to more complicated theories.Comment: REVTeX, 4 pages, 2 figures. The explicit form of the Hamiltonian and the equations of motion added. To appear in PRL (http://prl.aps.org/

Cosmic Necklaces and Ultrahigh Energy Cosmic Rays

Cosmic necklaces are hybrid topological defects consisting of monopoles and strings, with two strings attached to each monopole. We argue that the cosmological evolution of necklaces may significantly differ from that of cosmic strings. The typical velocity of necklaces can be much smaller than the speed of light, and the characteristic scale of the network much smaller than the horizon. We estimate the flux of high-energy protons produced by monopole annihilation in the decaying closed loops. For some reasonable values of the parameters it is comparable to the observed flux of ultrahigh-energy cosmic rays.Comment: 10 pages, Revtex, 1 figur

Cosmic String Formation from Correlated Fields

We simulate the formation of cosmic strings at the zeros of a complex Gaussian field with a power spectrum $P(k) \propto k^n$, specifically addressing the issue of the fraction of length in infinite strings. We make two improvements over previous simulations: we include a non-zero random background field in our box to simulate the effect of long-wavelength modes, and we examine the effects of smoothing the field on small scales. The inclusion of the background field significantly reduces the fraction of length in infinite strings for $n < -2$. Our results are consistent with the possibility that infinite strings disappear at some $n = n_c$ in the range $-3 \le n_c < -2.2$, although we cannot rule out $n_c = -3$, in which case infinite strings would disappear only at the point where the mean string density goes to zero. We present an analytic argument which suggests the latter case. Smoothing on small scales eliminates closed loops on the order of the lattice cell size and leads to a ``lattice-free" estimate of the infinite string fraction. As expected, this fraction depends on the type of window function used for smoothing.Comment: 24 pages, latex, 10 figures, submitted to Phys Rev

The evolution of a network of cosmic string loops

We set up and analyse a model for the non-equilibrium evolution of a network of cosmic strings initially containing only loops and no infinite strings. Due to this particular initial condition, our analytical approach differs significantly from existing ones. We describe the average properties of the network in terms of the distribution function n(l,t) dl, the average number of loops per unit volume with physical length between l and l + dl at time t. The dynamical processes which change the length of loops are then estimated and an equation, which we call the `rate equation', is derived for (dn/dt). In a non-expanding universe, the loops should reach the equilibrium distribution predicted by string statistical mechanics. Analysis of the rate equation gives results consistent with this. We then study the rate equation in an expanding universe and suggest that three different final states are possible for the evolving loop network, each of which may well be realised for some initial conditions. If the initial energy density in loops in the radiation era is low, then the loops rapidly disappear. For large initial energy densities, we expect that either infinite strings are formed or that the loops tend towards a scaling solution in the radiation era and then rapidly disappear in the matter era. Such a scenario may be relevant given recent work highlighting the problems with structure formation from the standard cosmic string scenario.Comment: LaTeX, 27 pages, 10 figures included as .eps file