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We consider the noncommutative minisuperspace classical and quantum cosmologies.
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We study some consequences of noncommutativity to homogeneous cosmologies by introducing a deformation of the commutation relation between the minisuperspace variables. The investigation is carried out for the Kantowski-Sachs model by means of a comparative study of the universe evolution in four different scenarios: the classical commutative, classical noncommutative, quantum commutative, and quantum noncommutative. The comparison is rendered transparent by the use of the Bohmian formalism of quantum trajectories. As a result of our analysis, we found that noncommutativity can modify significantly the universe evolution, but cannot alter its singular behavior in the classical context. Quantum effects, on the other hand, can originate non-singular periodic universes in both commutative and noncommutative cases. The quantum noncommutative model is shown to present interesting properties, as the capability to give rise to non-trivial dynamics in situations where its commutative counterpart is necessarily static.
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 study the implications of a noncommutative geometry of the minisuperspace variables for the FRW universe with a conformally coupled scalar field. The investigation is carried out by means of a comparative study of the universe evolution in four different scenarios: classical commutative, classical noncommutative, quantum commutative, and quantum noncommutative, the last two employing the Bohmian formalism of quantum trajectories. The role of noncommutativity is discussed by drawing a parallel between its realizations in two possible frameworks for physical interpretation: the NC-frame, where it is manifest in the universe degrees of freedom, and in the C-frame, where it is manifest through theta-dependent terms in the Hamiltonian. As a result of our comparative analysis, we find that noncommutative geometry can remove singularities in the classical context for sufficiently large values of theta. Moreover, under special conditions, the classical noncommutative model can admit bouncing solutions characteristic of the commutative quantum FRW universe. In the quantum context, we find non-singular universe solutions containing bounces or being periodic in the quantum commutative model. When noncommutativity effects are turned on in the quantum scenario, they can introduce significant modifications that change the singular behavior of the universe solutions or that render them dynamical whenever they are static in the commutative case. The effects of noncommutativity are completely specified only when one of the frames for its realization is adopted as the physical one. Non-singular solutions in the NC-frame can be mapped into singular ones in the C-frame.
In this paper, we study a class of symmetry reduced models of $mathcal{N}=1$ supergravity using self-dual variables. It is based on a particular Ansatz for the gravitino field as proposed by DEath et al. We show that the essential part of the constraint algebra in the classical theory closes. In particular, the (graded) Poisson bracket between the left and right supersymmetry constraint reproduces the Hamiltonian constraint. For the quantum theory, we apply techniques from the manifestly supersymmetric approach to loop quantum supergravity, which yields a graded analog of the holonomy-flux algebra and a natural state space. We implement the remaining constraints in the quantum theory. For a certain subclass of these models, we show explicitly that the (graded) commutator of the supersymmetry constraints exactly reproduces the classical Poisson relations. In particular, the trace of the commutator of left and right supersymmetry constraints reproduces the Hamilton constraint operator. Finally, we consider the dynamics of the theory and compare it to a quantization using standard variables and standard minisuperspace techniques.
We demonstrate in two minisuperspace models that a perturbation expansion of quasiclassical Euclidean gravity has a factorial dependence on the order of the term at large orders. This behavior indicates that the expansion is an asymptotic series which is suggestive of an effective field theory. The series may or may not be Borel summable depending on the classical solution expanded around. We assume that only the positive action classical solution contributes to path integrals. We close with some speculative discussion on possible implications of the asymptotic nature of the expansion.
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