Cosmic String Evolution in Higher Dimensions

We obtain the equations of motion for cosmic strings in extensions of the 3+1 FRW model with extra dimensions. From these we derive a generalisation of the Velocity-dependent One-Scale (VOS) model for cosmic string network evolution which we apply, first, to a higher-dimensional isotropic $D+1$ FRW model and, second, to a 3+1 FRW model with static flat extra dimensions. In the former case the string network does not achieve a scaling regime because of the diminishing rate of string intersections ($D>3$), but this can be avoided in the latter case by considering compact, small extra dimensions, for which there is a reduced but still appreciable string intercommuting probability. We note that the velocity components lying in the three expanding dimensions are Hubble-damped, whereas those in the static extra dimensions are only very weakly damped. This leads to the pathological possibility, in principle, that string motion in the three infinite dimensions can come to a halt preventing the strings from intersecting, with the result that scaling is not achieved and the strings irreversibly dominate the early universe. We note criteria by which this can be avoided, notably if the spatial structure of the network becomes essentially three-dimensional, as is expected for string networks produced in brane inflation. Applying our model to a brane inflation setting, we find scaling solutions in which the effective 3D string motion does not necessarily stop, but it is slowed down because of the excitations trapped in the extra dimensions. These effects are likely to influence cosmic string network evolution for a long period after formation and we discuss their more general implications.Comment: 23 pages, 8 figures. Minor updates and notational clarification

Effects of Inflation on a Cosmic String Loop Population

We study the evolution of simple cosmic string loop solutions in an inflationary universe. We show, for the particular case of circular loops, that periodic solutions do exist in a de Sitter universe, below a critical loop radius $R_c H=1/2$. On the other hand, larger loops freeze in comoving coordinates, and we explicitly show that they can survive more $e$-foldings of inflation than point-like objects. We discuss the implications of these findings for the survival of realistic cosmic string loops during inflation, and for the general characteristics of post-inflationary cosmic string networks. We also consider the analogous solutions for domain walls, in which case the critical radius is $R_c H=2/3$.Comment: 5 pages, 5 figures, accepted for publication in Physical Review

Unified model for vortex-string network evolution

We describe and numerically test the velocity-dependent one-scale (VOS) string evolution model, a simple analytic approach describing a string network with the averaged correlation length and velocity. We show that it accurately reproduces the large-scale behaviour (in particular the scaling laws) of numerical simulations of both Goto-Nambu and field theory string networks. We explicitly demonstrate the relation between the high-energy physics approach and the damped and non-relativistic limits which are relevant for condensed matter physics. We also reproduce experimental results in this context and show that the vortex-string density is significantly reduced by loop production, an effect not included in the usual `coarse-grained' approach.Comment: 5 pages; v2: cosmetic changes, version to appear in PR

Cosmological Perturbations from Cosmic Strings

Some aspects of the theory of cosmological perturbations from cosmic strings and other topological defects are outlined, with particular reference to a simple example: a spatially flat CDM-dominated universe. The conserved energy-momentum pseudo-tensor is introduced, and the equation for the density perturbation derived from it. It is shown how the scaling hypothesis for defect evolution results in a Harrison-Zel'dovich spectrum for wavelengths well inside the horizon.Comment: LaTeX, 6pp. From Proceedings of `Trends in Astroparticle Physics', Stockholm, Sweden 22-25 September 1994, edited by L. Bergstr\"om, P. Carlson, P.O. Hulth and H. Snellman (to be published in Nucl.~Phys~B, Proceedings Supplements Section

Axion Cosmology Revisited

The misalignment mechanism for axion production depends on the temperature-dependent axion mass. The latter has recently been determined within the interacting instanton liquid model (IILM), and provides for the first time a well-motivated axion mass for all temperatures. We reexamine the constraints placed on the axion parameter space in the light of this new mass function. We find an accurate and updated constraint f_a \le 2.8(\pm2)\times 10^{11}\units{GeV} or m_a \ge 21(\pm2) \units{\mu eV} from the misalignment mechanism in the classic axion window (thermal scenario). However, this is superseded by axion string radiation which leads to f_a \lesssim 3.2^{+4}_{-2} \times 10^{10} \units{GeV} or m_a \gtrsim 0.20 ^{+0.2}_{-0.1} \units{meV}. In this analysis, we take care to precisely compute the effective degrees of freedom and, to fill a gap in the literature, we present accurate fitting formulas. We solve the evolution equations exactly, and find that analytic results used to date generally underestimate the full numerical solution by a factor 2-3. In the inflationary scenario, axions induce isocurvature fluctuations and constrain the allowed inflationary scale $H_I$. Taking anharmonic effects into account, we show that these bounds are actually weaker than previously computed. Considering the fine-tuning issue of the misalignment angle in the whole of the anthropic window, we derive new bounds which open up the inflationary window near $\theta_a \to \pi$. In particular, we find that inflationary dark matter axions can have masses as high as 0.01--1\units{meV}, covering the whole thermal axion range, with values of $H_I$ up to $10^9$GeV. Quantum fluctuations during inflation exclude dominant dark matter axions with masses above $m_a\lesssim 1$meV.Comment: 42 pages, 12 figures, version as accepted by Phys.Rev.

Spectrum of radiation from axion strings

In the wide variety of axion cosmologies in which axion strings form, their radiative decay is the dominant mechanism for the production of axions, imposing a tight constraint on the axion mass. Here, we focus on the mechanism by which axions are produced in this scenario and, in particular, the key issue of the axion spectrum emitted by an evolving network of strings.Comment: to be published in the proceedings of the 5th IFT Workshop on Axion

Analytic Results for the Gravitational Radiation from a Class of Cosmic String Loops

Cosmic string loops are defined by a pair of periodic functions ${\bf a}$ and ${\bf b}$, which trace out unit-length closed curves in three-dimensional space. We consider a particular class of loops, for which ${\bf a}$ lies along a line and ${\bf b}$ lies in the plane orthogonal to that line. For this class of cosmic string loops one may give a simple analytic expression for the power $\gamma$ radiated in gravitational waves. We evaluate $\gamma$ exactly in closed form for several special cases: (1) ${\bf b}$ a circle traversed $M$ times; (2) ${\bf b}$ a regular polygon with $N$ sides and interior vertex angle $\pi-2\pi M/N$; (3) ${\bf b}$ an isosceles triangle with semi-angle $\theta$. We prove that case (1) with $M=1$ is the absolute minimum of $\gamma$ within our special class of loops, and identify all the stationary points of $\gamma$ in this class.Comment: 15 pages, RevTex 3.0, 7 figures available via anonymous ftp from directory pub/pcasper at alpha1.csd.uwm.edu, WISC-MILW-94-TH-1

Gravitational waveforms from the evaporating ACO cosmic string loop

The linearly polarized gravitational waveforms from a certain type of rotating, evaporating cosmic string - the Allen-Casper-Ottewill loop - are constructed and plotted over the lifetime of the loop. The formulas for the waveforms are simple and exact, and describe waves which attenuate self-similarly, with the amplitude and period of the waves falling off linearly with time.Comment: 30 pages, 16 figure

Waveforms for Gravitational Radiation from Cosmic String Loops

We obtain general formulae for the plus- and cross- polarized waveforms of gravitational radiation emitted by a cosmic string loop in transverse, traceless (synchronous, harmonic) gauge. These equations are then specialized to the case of piecewise linear loops, and it is shown that the general waveform for such a loop is a piecewise linear function. We give several simple examples of the waveforms from such loops. We also discuss the relation between the gravitational radiation by a smooth loop and by a piecewise linear approximation to it.Comment: 16 pages, 6 figures, Revte