We study cosmological consequences of the noncommutative approach to the standard model. Neglecting the nonminimal coupling of the Higgs field to the curvature, noncommutative corrections to Einsteins equations are present only for inhomogeneous and
anisotropic space-times. Considering the nominimal coupling however, we obtain corrections even for background cosmologies. A link with dilatonic gravity as well as chameleon cosmology are briefly discussed, and potential experimental consequences are mentioned.
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 unstabl
e 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.
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 unif
orm 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.
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.
In the context of loop quantum cosmology, we parametrise the lattice refinement by a parameter, $A$, and the matter Hamiltonian by a parameter, $delta$. We then solve the Hamiltonian constraint for both a self-adjoint, and a non-self-adjoint Hamilton
ian operator. Demanding that the solutions for the wave-functions obey certain physical restrictions, we impose constraints on the two-dimensional, $(A,delta)$, parameter space, thereby restricting the types of matter content that can be supported by a particular lattice refinement model.
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 dy
namically 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 $m^2phi^2/2$ 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.
