A brief description of the elements of noncommutative spectral geometry as an approach to unification is presented. The physical implications of the doubling of the algebra are discussed. Some high energy phenomenological as well as various cosmologi
cal consequences are presented. A constraint in one of the three free parameters, namely the one related to the coupling constants at unification, is obtained, and the possible role of scalar fields is highlighted. A novel spectral action approach based upon zeta function regularisation, in order to address some of the issues of the traditional bosonic spectral action based on a cutoff function and a cutoff scale, is discussed.
We briefly discuss constraints on supersymmetric hybrid inflation models and examine the consistency of brane inflation models. We then address the implications for inflationary scenarios resulting from the strong constraints on the cosmic (super)str
ing tension imposed from the most recent cosmic microwave background temperature anisotropies data.
We review a gravitational model based on noncommutative geometry and the spectral action principle. The space-time geometry is described by the tensor product of a four-dimensional Riemanian manifold by a discrete noncommutative space consisting of o
nly two points. With a specific choice of the finite dimensional involutive algebra, the noncommutative spectral action leads to the standard model of electroweak and strong interactions minimally coupled to Einstein and Weyl gravity. We present the main mathematical ingredients of this model and discuss their physical implications. We argue that the doubling of the algebra is intimately related to dissipation and the gauge field structure. We then show how this noncommutative spectral geometry model, a purely classical construction, carries implicit in the doubling of the algebra the seeds of quantization. After a short review on the phenomenological consequences of this geometric model as an approach to unification, we discuss some of its cosmological consequences. In particular, we study deviations of the Friedmann equation, propagation of gravitational waves, and investigate whether any of the scalar fields in this model could play the role of the inflaton.
We present a physical interpretation of the doubling of the algebra, which is the basic ingredient of the noncommutative spectral geometry, developed by Connes and collaborators as an approach to unification. We discuss its connection to dissipation
and to the gauge structure of the theory. We then argue, following t Hoofts conjecture, that noncommutative spectral geometry classical construction carries implicit in its feature of the doubling of the algebra the seeds of quantization.
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.
We study, via numerical experiments, the role of bound states in the evolution of cosmic superstring networks, being composed by p F-strings, q D-strings and (p,q) bound states. We find robust evidence for scaling of all three components of the netwo
rk, independently of initial conditions. The novelty of our numerical approach consists of having control over the initial abundance of bound states. This indeed allows us to identify the effect of bound states on the evolution of the network. Our studies also clearly show the existence of an additional energy loss mechanism, resulting to a lower overall string network energy, and thus scaling of the network. This new mechanism consists of the formation of bound states with an increasing length.
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.
