Related papers: Noncommutative Geometry and Cosmology
We extend the treatment of quantum cosmology to a manifold with torsion. We adopt a model of Einstein-Cartan-Sciama-Kibble compatible with the cosmological principle. The universe wavefunction will be subject to a $\mathcal{PT}$-symmetric…
A non-commutative multi-dimensional cosmological model is introduced and used to address the issues of compactification and stabilization of extra dimensions and the cosmological constant problem. We show that in such a scenario these…
In this paper, we investigate the effects of non-commutative phase-space on the quintom cosmological model. In that case, we discuss $\Lambda_{1}$, $\Lambda_{2}$ and other cosmological parameters and show that they are associated to…
In this work, a flat Friedmann-Robertson-Walker (FRW) universe with dust and a cosmological constant is quantized. By means of a canonical transformation, the classical Hamiltonian is reduced to that of either a harmonic oscillator or…
We consider astrophysical objects such as main-sequence stars, white-dwarfs and neutron stars in a noncommutative context. Noncommutativity is implemented via a deformed dispersion relation $E^{2}=p^{2}c^{2}(1+\lambda E)^{2}+m^{2}c^{4}$…
A new dynamical paradigm merging quantum dynamics with cosmology is discussed. Time evolution involves a genuine passage of time, which distinguishes the formalism from those where dynamics in space is equivalent to statics in space-time.…
We study dynamics of non-minimally coupled scalar field cosmological models with Higgs-like potentials and a negative cosmological constant. In these models the inflationary stage of the Universe evolution changes into a quasi-cyclic stage…
The cosmological principle asserts that on sufficiently large scales the Universe is homogeneous and isotropic on spatial slices. To deviate from this principle requires a departure from the FLRW ansatz. In this paper we analyze the…
A consistent implementation of quantum gravity is expected to change the familiar notions of space, time and the propagation of matter in drastic ways. This will have consequences on very small scales, but also gives rise to correction…
Perturbations of Kantowski-Sachs models with a positive cosmological constant are considered in a harmonic decomposition, in the framework of gauge invariant 1+3 and 1+1+2 covariant splits of spacetime. Scalar, vector and tensor modes are…
Non-commutative propositions are characteristic of both quantum and non-quantum (sociological, biological, psychological) situations. In a Hilbert space model states, understood as correlations between all the possible propositions, are…
This paper shows how the forms of gauge theory, Hamiltonian mechanics and quantum mechanics arise from a non-commutative framework for calculus and differential geometry. Discrete calculus is seen to fit into this pattern by reformulating…
A new framework for noncommutative complex geometry on quantum homogeneous spaces is introduced. The main ingredients used are covariant differential calculi and Takeuchi's categorical equivalence for faithfully flat quantum homogeneous…
Unlike noncommutative space, when space and time are noncommutative, it seems necessary to modify the usual scheme of quantum mechanics. We propose in this paper a simple generalization of the time evolution equation in quantum mechanics to…
A cosmological model is formulated in the context of a scalar-tensor theory of gravity in which the entire cosmic background evolution is due to a complex scalar field evolving in Minkowski spacetime, such that its (dimensional) modulus is…
A model unifying general relativity with quantum mechanics is further developed. It is based on a noncommutative geometry which supposedly modelled the universe in its pre-Planckian epoch. The geometry is totally nonlocal with no time and…
Cosmological models often contain scalar fields, which can acquire global nonzero expectation values that change with the comoving time. Among the possible consequences of these scalar-field backgrounds, an accelerated cosmological…
In this paper we investigate dynamics of the modified loop quantum cosmology models using dynamical systems methods. Modifications considered come from the choice of the different field strength operator $\hat{F}$ and result in different…
Although cosmic expansion at very small distances is usually dismissed as entirely inconsequential, these extraordinarily small effects may in fact have a real and significant influence on our world. A calculation suggests that the minute…
The algebras of non-relativistic and of classical mechanics are unstable algebraic structures. Their deformation towards stable structures leads, respectively, to relativity and to quantum mechanics. Likewise, the combined relativistic…