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E. P. S. Shellard

Publications and source records attributed to E. P. S. Shellard.

At least 73 records · Page 4Linked to original sources
arXiv2007

Primordial non-Gaussianity and the CMB bispectrum

We present a new formalism, together with efficient numerical methods, to directly calculate the CMB bispectrum today from a given primordial bispectrum using the full linear radiation transfer functions. Unlike previous analyses which have assumed simple separable ansatze for the bispectrum, this work applies to a primordial bispectrum of almost arbitrary functional form, for which there may have been both horizon-crossing and superhorizon contributions. We employ adaptive methods on a hierarchical triangular grid and we establish their accuracy by direct comparison with an exact analytic solution, valid on large angular scales. We demonstrate that we can calculate the full CMB bispectrum to greater than 1% precision out to multipoles l<1800 on reasonable computational timescales. We plot the bispectrum for both the superhorizon ('local') and horizon-crossing ('equilateral') asymptotic limits, illustrating its oscillatory nature which is analogous to the CMB power spectrum.

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arXiv2006

Non-linear perturbations in multiple-field inflation

We develop a non-linear framework for describing long-wavelength perturbations in multiple-field inflation. The basic variables describing inhomogeneities are defined in a non-perturbative manner, are invariant under changes of time slicing on large scales and include both matter and metric perturbations. They are combinations of spatial gradients generalising the gauge-invariant variables of linear theory. Dynamical equations are derived and supplemented with stochastic source terms which provide the long-wavelength initial conditions determined from short-wavelength modes. Solutions can be readily obtained via numerical simulations or analytic perturbative expansions. The latter are much simpler than the usual second-order perturbation theory. Applications are given in a companion paper.

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arXiv2006

Large non-Gaussianity in multiple-field inflation

We investigate non-Gaussianity in general multiple-field inflation using the formalism we developed in earlier papers. We use a perturbative expansion of the non-linear equations to calculate the three-point correlator of the curvature perturbation analytically. We derive a general expression that involves only a time integral over background and linear perturbation quantities. We work out this expression explicitly for the two-field slow-roll case, and find that non-Gaussianity can be orders of magnitude larger than in the single-field case. In particular, the bispectrum divided by the square of the power spectrum can easily be of O(1-10), depending on the model. Our result also shows the explicit momentum dependence of the bispectrum. This conclusion of large non-Gaussianity is confirmed in a semi-analytic slow-roll investigation of a simple quadratic two-field model.

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arXiv2005

Effect of Reconnection Probability on Cosmic (Super)string Network Density

We perform numerical simulations of cosmic string evolution with intercommuting probability $P$ in the range $5\times 10^{-3}\le P\le 1$, both in the matter and radiation eras, using a modified version of the Allen-Shellard code. We find that the dependence of the scaling density on $P$ is significantly different than the suggested $ρ\propto P^{-1}$ form. In particular, for probabilities greater than $P\simeq 0.1$, $ρ(1/P)$ is approximately flat, but for $P$ less than this value it is well-fitted by a power-law with exponent $0.6^{+0.15}_{-0.12}$. This shows that the enhancement of string densities due to a small intercommuting probability is much less prominent than initially anticipated. We interpret the flat part of $ρ(1/P)$ in terms of multiple opportunities for string reconnections during one crossing time, due to small-scale wiggles. We also propose a two-scale model incorporating the key physical mechanisms, which satisfactorily fits our results over the whole range of $P$ covered by the simulations.

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arXiv2005

Fractal Properties and Small-scale Structure of Cosmic String Networks

We present results from a detailed numerical study of the small-scale and loop production properties of cosmic string networks, based on the largest and highest resolution string simulations to date. We investigate the non-trivial fractal properties of cosmic strings, in particular, the fractal dimension and renormalised string mass per unit length, and we also study velocity correlations. We demonstrate important differences between string networks in flat (Minkowski) spacetime and the two very similar expanding cases. For high resolution matter era network simulations, we provide strong evidence that small-scale structure has converged to `scaling' on all dynamical lengthscales, without the need for other radiative damping mechanisms. We also discuss preliminary evidence that the dominant loop production size is also approaching scaling.

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arXiv2005

Non-linear inflationary perturbations

We present a method by which cosmological perturbations can be quantitatively studied in single and multi-field inflationary models beyond linear perturbation theory. A non-linear generalization of the gauge-invariant Sasaki-Mukhanov variables is used in a long-wavelength approximation. These generalized variables remain invariant under time slicing changes on long wavelengths. The equations they obey are relatively simple and can be formulated for a number of time slicing choices. Initial conditions are set after horizon crossing and the subsequent evolution is fully non-linear. We briefly discuss how these methods can be implemented numerically in the study of non-Gaussian signatures from specific inflationary models.

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arXiv2005

Simple route to non-Gaussianity in inflation

We present a simple way to calculate non-Gaussianity in inflation using fully non-linear equations on long wavelengths with stochastic sources to take into account the short-wavelength quantum fluctuations. Our formalism includes both scalar metric and matter perturbations, combining them into variables which are invariant under changes of time slicing in the long-wavelength limit. We illustrate this method with a perturbative calculation in the single-field slow-roll case. We also introduce a convenient choice of variables to graphically present the full momentum dependence of the three-point correlator.

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arXiv2005

Cycloops: Dark Matter or a Monopole Problem for Brane Inflation?

We consider cosmic loop production by long string interactions in cosmological models with compact extra dimensions. In the case that the compact manifold is not simply connected, we focus on the possibility of loops wrapping around non-trivial cycles and becoming topologically trapped. Such loops, denoted cycloops, behave like matter in the radiation era, posing a potential monopole problem. We calculate the number distribution and the energy density of these objects as functions of cosmic time and use them to study cosmological constraints imposed on simple brane inflation models. For typical choices of parameters we find that to avoid cycloop domination before the matter-radiation transition, the strings must be unacceptably light, namely $Gμ<10^{-18}$, unless some mechanism to dilute the cycloops is provided. By exploring the full parameter space however, we are able to find models with $Gμ\sim 10^{-14}$, which is marginally consistent with brane inflation. In such models the cycloop could provide an interesting dark matter candidate.

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arXiv2005

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.

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arXiv2004

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.

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arXiv2003

The Separate Universe Approach and the Evolution of Nonlinear Superhorizon Cosmological Perturbations

In this letter we review the separate universe approach for cosmological perturbations and point out that it is essentially the lowest order approximation to a gradient expansion. Using this approach, one can study the nonlinear evolution of inhomogeneous spacetimes and find the conditions under which the long wavlength curvature perturbation can vary with time. When there is one degree of freedom or a well-defined equation of state the nonlinear long wavelength curvature perturbation remains constant. With more degrees of freedom it can vary and this variation is determined by the non-adiabatic pressure perturbation, exactly as in linear theory. We identify combinations of spatial vectors characterizing the curvature perturbation which are invariant under a change of time hypersurfaces.

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arXiv2003

Large Angle CMB Fluctuations from Cosmic Strings with a Comological Constant

In this paper, we present results for large-angle CMB anisotropies generated from high resolution simulations of cosmic string networks in a range of flat FRW universes with a cosmological constant. Using an ensemble of all-sky maps, we compare with the COBE data to infer a normalization (or upper bound) on the string linear energy density $μ$. For a flat matter-dominated model ($Ω_{M}=1$) we find $Gμ/c^2 \approx 0.7\times 10^{-6}$, which is lower than previous constraints probably because of the more accurate inclusion of string small-scale structure. For a cosmological constant within an observationally acceptable range, we find a relatively weak dependence with $Gμ/c^2$ less than 10% higher.

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arXiv2003

Topological defects: A problem for cyclic universes?

We study the behaviour of cosmic string networks in contracting universes, and discuss some of their possible consequences. We note that there is a fundamental time asymmetry between defect network evolution for an expanding universe and a contracting universe. A string network with negligible loop production and small-scale structure will asymptotically behave during the collapse phase as a radiation fluid. In realistic networks these two effects are important, making this solution only approximate. We derive new scaling solutions describing this effect, and test them against high-resolution numerical simulations. A string network in a contracting universe, together with the gravitational radiation background it has generated, can significantly affect the dynamics of the universe both locally and globally. The network can be an important source of radiation, entropy and inhomogeneity. We discuss the possible implications of these findings for bouncing and cyclic cosmological models.

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arXiv2003

Vorton Existence and Stability

We present the first concrete evidence for the classical stability of vortons, circular cosmic string loops stabilized by the angular momentum of the charge and current trapped on the string. We begin by summarizing what is known about vorton solutions and, in particular, their analytic stability with respect to a range of radial and nonradial perturbations. We then discuss numerical results of vorton simulations in a full 3D field theory, that is, Witten's original bosonic superconducting string model with a modified potential term. For specific parameter values, these simulations demonstrate the long-term stability of sufficiently large vorton solutions created with an elliptical initial ansatz.

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arXiv2003

On the Behaviour and Stability of Superconducting Currents

We present analytic and numerical results for the evolution of currents on superconducting strings in the classical $U(1) \times U(1)$ model. We derive an energy functional for the currents and charges on these strings, establishing rigorously that minima should exist in this model for loops of finite size (vortons) if both charge and current are present on the worldsheet. We then study the stability of the currents on these strings, and we find an analytic criterion for the onset of instability (in the neutral limit). This limit specifies a lower maximal current than previous heuristic estimates. We conclude with a discussion of the evolution of loops towards their final vorton state in the model under consideration.

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arXiv2002

Topological Defects in Contracting Universes

We study the behaviour and consequences of cosmic string networks in contracting universes. They approximately behave during the collapse phase as a radiation fluids. Scaling solutions describing this are derived and tested against high-resolution numerical simulations. A string network in a contracting universe, together with the gravitational radiation it generates, can affect the dynamics of the universe both locally and globally, and be an important source of radiation, entropy and inhomogeneity. We discuss possible implications for bouncing and cyclic models.

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arXiv2002

Causal perturbation theory in general FRW cosmologies II: superhorizon behaviour and initial conditions

We describe how causality and energy-momentum conservation constrain the superhorizon behaviour of perturbation variables in a general FRW spacetime. The effect of intrinsic curvature upon the horizon scale is discussed and `white noise' results for the power spectra of generic `causally-seeded' superhorizon perturbations are obtained. We present a detailed derivation of the superhorizon energy density power spectrum for curved universes, and provide elegant mathematical arguments for a curved universe analogue of the Bessel function addition theorem. This yields physical insight into both the familiar $k^4$ result for flat space and the $K \not= 0$ case: curvature effects are seen to be evident from as early as half the curvature scale. We consider the implications of these results for the physically and numerically significant issue of setting consistent initial conditions.

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