arXiv subjects

William Nelson

Publications and source records attributed to William Nelson.

32 records · Page 2Linked to original sources

arXiv2009

Unstable Anisotropic Loop Quantum Cosmology

We study stability conditions of the full Hamiltonian constraint equation describing the quantum dynamics of the diagonal Bianchi I model in the context of LQC. Our analysis has shown robust evidence of an instability in the explicit implementation of the difference equation, implying important consequences for the correspondence between the full LQG theory and LQC. As a result, one may question the choice of the quantisation approach, the model of lattice refinement, and/or the role of the ambiguity parameters; all these should in principle be dictated by the full LQG theory.

gr-qc↗

arXiv2009

Natural inflation mechanism in asymptotic noncommutative geometry

The possibility of having an inflationary epoch within a noncommutative geometry approach to unifying gravity and the standard model is demonstrated. This inflationary phase occurs without the need to introduce "ad hoc" additional fields or potentials, rather it is a consequence of a nonminimal coupling between the geometry and the Higgs field.

hep-th↗

arXiv2009

Space-time dimensionality from brane collisions

Collisions and subsequent decays of higher dimensional branes leave behind three-dimensional branes and anti-branes, one of which could play the role of our universe. This process also leads to the production of one-dimensional branes and anti-branes, however their number is expected to be suppressed. Brane collisions may also lead to the formation of bound states of branes. Their existence does not alter this result, it just allows for the existence of one-dimensional branes captured within the three-dimensional ones.

hep-th↗

arXiv2008

Tachyonic decay of unstable Dirichlet branes

We consider an unstable bound system of two supersymmetric Dirichlet branes of different dimensionality ($p,p'$ with $p'<p$) embedded in a flat non-compactified IIA or IIB type background. We study the decay, via tachyonic condensation, of such unstable bound states leading to a pair of bound D$(p-1)$, D$p'$-branes. We show that only when the gauge fields carried by the D$p$-brane are localised perependicular to the tachyon direction, then tachyon condensation will indeed take place. We perform our analysis by combining both, the Hamiltonian and the Lagrangian approach.

hep-th↗

arXiv2008

Cusps on cosmic superstrings with junctions

The existence of cusps on non-periodic strings ending on D-branes is demonstrated and the conditions, for which such cusps are generic, are derived. The dynamics of F-, D-string and FD-string junctions are investigated. It is shown that pairs of FD-string junctions, such as would form after intercommutations of F- and D-strings, generically contain cusps. This new feature of cosmic superstrings opens up the possibility of extra channels of energy loss from a string network. The phenomenology of cusps on such cosmic superstring networks is compared to that of cusps formed on networks of their field theory analogues, the standard cosmic strings.

hep-th↗

arXiv2008

Unique factor ordering in the continuum limit of LQC

We show that the factor ordering ambiguities associated with the loop quantisation of the gravitational part of the cosmological Hamiltonian constraint, disappear at the level of Wheeler-DeWitt equation only for a particular choice of lattice refinement model, which coincides with constraints imposed from phenomenological and consistency arguments.

gr-qc↗

arXiv2008

Numerical techniques for solving the quantum constraint equation of generic lattice-refined models in loop quantum cosmology

To avoid instabilities in the continuum semi-classical limit of loop quantum cosmology models, refinement of the underlying lattice is necessary. The lattice refinement leads to new dynamical difference equations which, in general, do not have a uniform step-size, implying complications in their analysis and solutions. We propose a numerical method based on Taylor expansions, which can give us the necessary information to calculate the wave-function at any given lattice point. The method we propose can be applied in any lattice-refined model, while in addition the accuracy of the method can be estimated. Moreover, we confirm numerically the stability criterion which was earlier found following a von Neumann analysis. Finally, the `motion' of the wave-function due to the underlying discreteness of the space-time is investigated, for both a constant lattice, as well as lattice refinement models.

gr-qc↗

arXiv2008

On the possibility of Dark Energy from corrections to the Wheeler-De Witt equation

We present a method for approximating the effective consequence of generic quantum gravity corrections to the Wheeler-DeWitt equation. We show that in many cases these corrections can produce departures from classical physics at large scales and that this behaviour can be interpreted as additional matter components. This opens up the possibility that dark energy (and possible dark matter) could be large scale manifestations of quantum gravity corrections to classical general relativity. As a specific example we examine the first order corrections to the Wheeler-De Witt equation arising from loop quantum cosmology in the absence of lattice refinement and show how the ultimate breakdown in large scale physics occurs.

gr-qc↗

arXiv2007

Lattice Refining LQC and the Matter Hamiltonian

In the context of loop quantum cosmology, we parametrise the lattice refinement by a parameter, $A$, and the matter Hamiltonian by a parameter, $δ$. We then solve the Hamiltonian constraint for both a self-adjoint, and a non-self-adjoint Hamiltonian operator. Demanding that the solutions for the wave-functions obey certain physical restrictions, we impose constraints on the two-dimensional, $(A,δ)$, parameter space, thereby restricting the types of matter content that can be supported by a particular lattice refinement model.

gr-qc↗

arXiv2007

The probability of inflation in Loop Quantum Cosmology

The probability of there being sufficient inflation to solve the fine-tuning associated with the horizon and flatness problems has recently been shown to be exponentially small, within the context of classical general relativity. Here this result is extended by considering loop quantum gravity effects, that are significant at small scales. In addition to accounting for high-energy departures from classicality, it is shown that, in contrast to the classical case, the loop quantum cosmological probability measure is naturally finite, at least in some well defined region. It is also shown that these loop quantum gravity corrections can overcome the classical suppression of the probability only for extremely unnatural choices of ambiguity parameters, implying that single field, slow-roll inflation is exponentially unlikely.

gr-qc↗

arXiv2007

On the Onset of Inflation in Loop Quantum Cosmology

Using a Liouville measure, similar to the one proposed recently by Gibbons and Turok, we investigate the probability that single-field inflation with a polynomial potential can last long enough to solve the shortcomings of the standard hot big bang model, within the semiclassical regime of loop quantum cosmology. We conclude that, for such a class of inflationary models and for natural values of the loop quantum cosmology parameters, a successful inflationary scenario is highly improbable.

gr-qc↗

arXiv2007

Lattice Refining Loop Quantum Cosmology and Inflation

We study the importance of lattice refinement in achieving a successful inflationary era. We solve, in the continuum limit, the second order difference equation governing the quantum evolution in loop quantun cosmology, assuming both a fixed and a dynamically varying lattice in a suitable refinement model. We thus impose a constraint on the potential of a scalar field, so that the continuum approximation is not broken. Considering that such a scalar field could play the role of the inflaton, we obtain a second constraint on the inflationary potential so that there is consistency with the CMB data on large angular scales. For a $m^2ϕ^2/2$ inflationary model, we combine the two constraints on the inflaton potential to impose an upper limit on $m$, which is severely fine-tuned in the case of a fixed lattice. We thus conclude that lattice refinement is necessary to achieve a natural inflationary model.

gr-qc↗

arXiv1994

A Comment on Black Hole Entropy in String Theory

In this note, we extend the string theoretic calculation of the black hole entropy, first performed by Susskind and Uglum, away from the infinite mass limit. It is shown that the result agrees with that obtained from the classical action of string theory, using the Noether charge method developed by Wald. Also shown in the process is the equivalence of two general techniques for finding black hole entropies-the Noether charge method, and the method of conical singularities.

hep-th↗

arXiv1993

Kaluza-Klein Black Holes in String Theory

Exact solutions of heterotic string theory corresponding to four-dimensional magnetic black holes in $N=4$ supergravity are described. The solutions describe the black holes in the throat limit, and consist of a tensor product of an $SU(2)$ WZW orbifold with the linear dilaton vacuum, supersymmetrized to $(1,0)$ world sheet SUSY. One dimension of the $SU(2)$ model is interpreted as a compactified fifth dimension, leading to a four dimensional solution with a Kaluza-Klein gauge field having a magnetic monopole background; this corresponds to a solution in $N=4$ supergravity, since that theory is obtained by dimensional reduction of string theory.

hep-th↗