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A very first step to develop non-commutative algebraic geometry is the arithmetic of polynomials in non-commuting variables over a commutative field, that is, the study of elements in free associative algebras. This investigation is…
The phase space analysis of cosmological parameters $\Omega_{\phi}$ and $\gamma_{\phi}$ is given. Based on this, the well-known quintessence cosmology is studied with an exponential potential $V(\phi)=V_{0}\exp(-\lambda\phi)$. Given…
We introduce a covariant non-commutative deformation of 3+1-dimensional conformal field theory. The deformation depends on a short-distance scale \ell_p, and thus breaks scale invariance, but preserves all space-time isometries. The…
In the mini-superspace approximation to cosmology, the canonical measure can be used to compute probabilities when a cutoff is introduced in the phase space to regularize the divergent measure. However, the region initially constrained by a…
We revisit a model-independent estimator for cosmic acceleration based on type Ia supernovae distance measurements. This approach does not rely on any specific theory for gravity, energy content or parameterization for the scale factor or…
We consider a simplified model of quantum gravity using a mini-superspace description of an isotropic and homogeneous universe with dust. We derive the corresponding Friedmann equations for the scale factor, which now contain a dependence…
We investigate the consequences of non-minimal gravitational coupling to matter and study how it differs from the case of minimal coupling by choosing certain simple forms for the nature of coupling, The values of the parameters are…
We introduce a cosmological model in the framework of Generalised Massive Gravity. This theory is an extension of non-linear massive gravity with a broken translation symmetry in the St\"uckelberg space. In a recent work, we showed the…
The probability representation, in which cosmological quantum states are described by a standard positive probability distribution, is constructed for minisuperspace models selected by Noether symmetries. In such a case, the tomographic…
We propose a novel extension to the recently developed non-commutative Riemannian foliated branch-cut quantum gravity (BCQG). Based on an extended Faddeev-Jackiw symplectic deformation of the conventional Poisson algebra, we investigate…
We investigate the coupled system of gravity and a scalar with exponential potential. The energy momentum tensor of the scalar field induces a time-dependent cosmological ``constant''. This adjusts itself dynamically to become in the…
In this paper we present the noncommutative Bianchi Class A cosmological models coupled to barotropic perfect fluid. The commutative and noncommutative quantum solution to the Wheeler-DeWitt equation for any factor ordering, to the…
Deterministic dynamical models are discussed which can be described in quantum mechanical terms. In particular, a local quantum field theory is presented which is a supersymmetric classical model. -- The Hilbert space approach of Koopman…
As emphasized by previous studies, proper treatment of the density fluctuation on the fundamental scale of a cosmological simulation volume - the "DC mode" - is critical for accurate modeling of spatial correlations on scales > 10% of…
We present a noncommutative extension of Quantum Cosmology and study the Kantowski-Sachs (KS) cosmological model requiring that the two scale factors of the KS metric, the coordinates of the system, and their conjugate canonical momenta do…
We extend the three-dimensional noncommutative relations of the positions and momenta operators to those in the four dimension. Using the Bopp shift technique, we give the Heisenberg representation of these noncommutative algebras and endow…
This paper investigates the possible cosmological implications of the presence of an antisymmetric tensor field related to a lack of commutatitivity of spacetime coordinates at the Planck era. For this purpose, such a field is promoted to a…
The source of the acceleration of the expansion of the Universe is still unknown. We examine some consequences of the possible scale invariance of the empty space at large scales. The central hypothesis of this work is that, at macroscopic…
We investigate two simplified non-singular cyclic models with a negative time-varying cosmological constant to represent the non-conventional mechanism of negative cosmological constant expected to address the late-time cosmic acceleration.…
General relativity has a Hamiltonian formulation, which formally provides a canonical (Liouville) measure on the space of solutions. In ordinary statistical physics, the Liouville measure is used to compute probabilities of macrostates, and…