arXiv subjects

Mark Hindmarsh

Publications and source records attributed to Mark Hindmarsh.

At least 127 records · Page 7Linked to original sources

arXiv2002

MHD inverse cascade in the early Universe

We have carried out numerical simulations of freely decaying magnetohydrodynamic (MHD) turbulence in three dimensions, which can be applied to the evolution of stochastic magnetic fields in the early Universe. For helical magnetic fields an inverse cascade effect is observed in which magnetic helicity and energy is transfered from smaller scales to larger scales, accompanied by power law growth in the characteristic length scale of the magnetic field. The magnetic field quickly reaches a scaling regime with self-similar evolution, and power law behaviour at high wavenumbers. We also find power law decay in the magnetic and kinematic energies.

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arXiv2001

Sphalerons in Two Higgs Doublet Theories

We undertake a comprehensive investigation of the properties of the sphaleron in electroweak theories with two Higgs doublets. We do this in as model-independent a way as possible: by exploring the physical parameter space described by the masses and mixing angles of the Higgs particles. If there is a large split in the masses of the neutral Higgs particles, there can be several sphaleron solutions, distinguished by their properties under parity and the behaviour of the Higgs field at the origin. In general, these solutions appear in parity conjugate pairs and are not spherically symmetric, although the departure from spherical symmetry is small. Including CP violation in the Higgs potential can change the energy of the sphaleron by up to 14 percent for a given set of Higgs masses, with significant implications for the baryogenesis bound on the mass of the lightest Higgs.

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arXiv2001

Sphalerons with Two Higgs Doublets

We report on work studying the properties of the sphaleron in models of the electroweak interactions with two Higgs doublets in as model-independent a way as possible: by exploring the physical parameter space described by the masses and mixing angles of the Higgs particles. If one of the Higgs particles is heavy, there can be several sphaleron solutions, distinguished by their properties under parity and the behaviour of the Higgs field at the origin. In general, these solutions are not spherically symmetric, although the departure from spherical symmetry is small.

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arXiv1999

Magnetic fields in the early universe in the string approach to MHD

There is a reformulation of magnetohydrodynamics in which the fundamental dynamical quantities are the positions and velocities of the lines of magnetic flux in the plasma, which turn out to obey equations of motion very much like ideal strings. We use this approach to study the evolution of a primordial magnetic field generated during the radiation-dominated era in the early Universe. Causality dictates that the field lines form a tangled random network, and the string-like equations of motion, plus the assumption of perfect reconnection, inevitably lead to a self-similar solution for the magnetic field power spectrum. We present the predicted form of the power spectrum, and discuss insights gained from the string approximation, in particular the implications for the existence or not of an inverse cascade.

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arXiv1999

Structure formation with strings plus inflation: a new paradigm

Recent developments in inflation model building, based on supersymmetry, have produced compelling models in which strings are produced at the end of inflation. In such models the cosmological perturbations are seeded both by the defects and by the quantum fluctuations. We show that such models produce qualitatively new and desirable predictions for CMB anisotropies and the CDM power spectrum. This remark should put an end to the long term animosity between defect and inflationary scenarios of structure formation.

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arXiv1998

Constraints on Axion Models from $K^+\toπ^+ a$

We explore a new class of axion models in which some, but not all, of the left-handed quarks have a Peccei-Quinn symmetry. These models are potentially afflicted by flavour changing neutral currents. We derive the bounds on the Peccei-Quinn symmetry-breaking scale from bounds on the $K^+\to π^+ a$ branching ratio, showing that in some cases they are even stronger than the astrophysical ones, but still not strong enough to kill off the models.

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arXiv1998

Sphalerons with CP-Violating Higgs Potentials

We investigate the effect on the sphaleron in the two Higgs doublet electroweak theory of including CP violation in the Higgs potential. To have better control over the relation between the sphaleron energy and the physical quantities in the theory, we show how to parametrize the Higgs potential in terms of physical masses and mixing angles, one of which causes CP violation. By altering this CP violating angle (and keeping the other physical quantities fixed) the sphaleron energy increases by up to 10%. We also calculate the static minimum energy path between adjacent vacua as a function of Chern-Simons number, using the method of gradient flow. The only effect CP violation has on the barrier is the change in height. As a by-product of our work on parametrization of the potential, we demonstrate that CP violation in the Higgs sector favours nearly degenerate light Higgs masses.

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arXiv1998

CMB and LSS Power Spectra From Local Cosmic String Seeded Struture Formation

We evaluate the two point functions of the stress energy from the largest string simulations carried out so far. The two point functions are used to calculate the cosmic microwave background (CMB) and cold dark matter (CDM) power spectra from local cosmic string models for structure formation. We find that our spectra differ significantly from those previously calculated for both global and local defects. We find a higher Doppler peak at $l=400-600$ and a less severe bias problem than for global defects. Spectra were obtained for a variety of network energy-decay mechanisms.

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arXiv1998

CMB and density fluctuations from strings plus inflation

In cosmological models where local cosmic strings are formed at the end of a period of inflation, the perturbations are seeded both by the defects and by the quantum fluctuations. In a subset of these models, for example those based on $D$-term inflation, the amplitudes are similar. Using our recent calculations of structure formation with cosmic strings, we point out that in a flat cosmology with zero cosmological constant and 5% baryonic component, strings plus inflation fits the observational data much better than each component individually. The large-angle CMB spectrum is mildly tilted, for Harrison-Zeldovich inflationary fluctuations. It then rises to a thick Doppler bump, covering $\ell=200-600$, modulated by soft secondary undulations. The standard CDM anti-biasing problem is cured, giving place to a slightly biased scenario of galaxy formation.

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arXiv1998

The power spectra of CMB and density fluctuations seeded by local cosmic strings

We compute the power spectra in the cosmic microwave background and cold dark matter (CDM) fluctuations seeded by strings, using the largest string simulations performed so far to evaluate the two-point functions of their stress energy tensor. We find that local strings differ from global defects in that the scalar components of the stress-energy tensor dominate over vector and tensor components. This result has far reaching consequences. We find that cosmic strings exhibit a single Doppler peak of acceptable height at high $\ell$. They also seem to have a less severe bias problem than global defects, although the CDM power spectrum in the ``standard'' cosmology (flat geometry, zero cosmological constant, 5% baryonic component) is the wrong shape to fit large scale structure data.

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arXiv1998

Constraints on Axion Models

Two particular classes of axion models are presented, each one yielding a lower bound on the axion decay constant, based though on different considerations. In the first class only some, and not all, of the right-handed quarks have PQ charges, whereas in the second one the left-handed sector of the same quarks is taken into account as well. In the first case we find that bounds coming from astrophysics are significantly relaxed compared with those for the DFSZ. As for the second class, the astrophysical constraints proved to be less severe (with one exception), than those coming from FCNC processes.

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arXiv1998

Cosmic Strings - Dead Again?

I report on recent numerical simulations of the simplest field theory with cosmic string solutions, the Abelian Higgs model. We find that random networks of string quickly converge to a scaling solution in which the network scale length $ξ$ increases linearly with time. There are very few loops with sizes less than $ξ$, and the strings are smooth, showing no signs of ``small scale structure''. We claim that particle production is the dominant energy-loss mechanism, not gravitational radiation as previously thought. For strings in Grand Unified Models, stringent constraints can be placed from cosmic ray observations on the string tension $μ$: we estimate $Gμ< 10^{-9}$, three orders of magnitude lower than the constraint from Cosmic Microwave Background fluctuations.

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arXiv1998

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 $ϕ$ 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.

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arXiv1997

Ordering Dynamics of Topological Defect Networks

I report on some work in progress on the dynamics of extended objects in field theories after a rapid phase transition, as is relevant in the early Universe. An analytic technique, originally introduced to approximate the dynamics of topological defects in condensed matter systems, is extended to cover relativistic objects. An exact formula for the area density of domain walls in $D$ dimensions is derived.

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arXiv1997

Constraints on Variant Axion Models

A particular class of variant axion models with two higgs doublets and a singlet is studied. In these models the axion couples either to the $u$-quark or $t$-quark or both, but not to $b$, $c$, $s$, or $d$. When the axion couples to only one quark the models possess the desirable feature of having no domain wall problem, which makes them viable candidates for a cosmological axion string scenario. We calculate the axion couplings to leptons, photons and nucleons, and the astrophysical constraints on the axion decay constant $v_a$ are investigated and compared to the DFSZ axion model. We find that the most restrictive lower bound on $v_a$, that from SN1987a, is lowered by up to a factor of about 30, depending on the model and also the ratio of the vacuum expectation values of the higgs doublets. For scenarios with axionic strings, the allowed window for $v_a$ in the $u$ quark model can be more than two orders of magnitude. For inflationary scenarios, the cosmological upper bound on $v_a/N$, where $N$ is the QCD anomaly factor, is unaffected: however, the variant models have $N$ either 3 or 6 times smaller than the DFSZ model.

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arXiv1997

Magnetic Fields from Phase Transitions

The generation of primordial magnetic fields from cosmological phase transitions is discussed, paying particular attention to the electroweak transition and to the various definitions of the `average' field that have been put forward. It is emphasised that only the volume average has dynamical significance as a seed for galactic dynamos. On rather general grounds of causality and energy conservation, it is shown that, in the absence of MHD effects that transfer power in the magnetic field from small to large scales, processes occurring at the electroweak transition cannot generate fields stronger than $10^{-20}$ Gauss on a scale of 0.5 Mpc. However, it is implausible that this upper bound could ever be reached, as it would require all the energy in the Universe to be turned into a magnetic field coherent at the horizon scale. Non-linear MHD effects seem therefore to be necessary if the electroweak transition is to create a primordial seed field.

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arXiv1997

The Thermodynamics of Cosmic String densities in U(1) Scalar Field Theory

We present a full characterization of the phase transition in U(1) scalar field theory and of the associated vortex string thermodynamics in 3D. We show that phase transitions in the string densities exist and measure their critical exponents, both for the long string and the short loops. Evidence for a natural separation between these two string populations is presented. In particular our results strongly indicate that an infinite string population will only exist above the critical temperature. Canonical initial conditions for cosmic string evolution are show to correspond to the infinite temperature limit of the theory.

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arXiv1997

On the instability of the one-texture universe

The one-texture universe, introduced by Davis in 1987, is a homogeneous mapping of a scalar field with an $S^3$ vacuum into a closed universe. It has long been known to mathematicians that such solutions, although static, are unstable. We show by explicit construction that there is only one unstable mode, corresponding to collapse of the texture towards a single point, in the case where gravitational backreaction is neglected. We discuss the instability timescale in both static and expanding space-times; in the latter case it is of order of the present age of the universe, suggesting that, though unstable, the one-texture universe could survive to the present. The cosmic microwave background constrains the initial magnitude of this unstable perturbation to be less than of order 10^{-3}.

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