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The development of last years in quantum geometrodynamics highlights new problems which were not obvious in its first formulation proposed by Wheeler and DeWitt. At the first stage the main task was to apply known quantization schemes to…
We consider Brans-Dicke cosmology with cosmological constant with negative w parameter and an arbitrary (in general non-vanishing) scale factor at the Big Bang. The field equations describe the flat universe, current observational values…
In the standard model of cosmology, the universe is described by a Robertson-Walker spacetime, while its matter/energy content is modeled by a perfect fluid with three components corresponding to matter/dust, radiation and a cosmological…
We make the cosmological constant, {\Lambda}, into a field and restrict the variations of the action with respect to it by causality. This creates an additional Einstein constraint equation. It restricts the solutions of the standard…
Using a particular form of the quantum K-essence scalar field, we show that in the quantum formalism, a fractional differential equation in the scalar field variable, for some epochs in the Friedmann-Lema\^itre-Robertson-Walker (FLRW) model…
In these notes we address the canonical quantization of the cosmological models which appear as solutions of the low energy effective action of closed bosonic string theory (dilaton models). The analysis is restricted to the quantization of…
A diverse set of observations now compellingly suggest that Universe possesses a nonzero cosmological constant. In the context of quantum-field theory a cosmological constant corresponds to the energy density of the vacuum, and the wanted…
We study the Newtonian cosmology taking into account the leading classical and quantum corrections of order $\mathcal{O}(G^{2})$ in the Newtonian potential. We first derive the modified Friedmann equations starting from the non-relativistic…
The generalized Einstein action is treated quantum mechanically by using a quadratic lagrangian form. The canonical quantization of this action is obtained by using the auxiliary variable to define the generalized momentum. Physical…
Loop quantum cosmology is an application of recent developments for a non-perturbative and background independent quantization of gravity to a cosmological setting. Characteristic properties of the quantization such as discreteness of…
The quantum cosmology of two-dimensional dilaton-gravity models is investigated. A class of models is mapped onto the constrained oscillator-ghost-oscillator model. A number of exact and approximate solutions to the corresponding…
The central equation of quantum gravity is the Wheeler-DeWitt equation. We give an argument suggesting that exact solutions of this equation give a surface in the space of coupling constants. This provides a mechanism for determining the…
Within the framework of loop quantum cosmology, there exists a semi-classical regime where spacetime may be approximated in terms of a continuous manifold, but where the standard Friedmann equations of classical Einstein gravity receive…
Quantization in the minisuperspace of non minimal scalar-tensor theories leads to a partial differential equation which is non separable. Through a conformal transformation we can recast the Wheeler-DeWitt equation in an integrable form,…
Gravitation and the standard model of particle physics are incorporated within a single conformal scalar-tensor theory, where the scalar field is complex. The Higgs field has a dynamical expectation value, as has the Planck mass, but the…
We investigate a cosmological model with a big-brake singularity in the future: while the first time derivative of the scale factor goes to zero, its second time derivative tends to minus infinity. Although we also discuss the classical…
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 study a model of quantum cosmology originating from a classical model of gravitation where a self interacting scalar field is coupled to gravity with the metric undergoing a signature transition. We show that there are dual classical…
We study a classical, noncommutative (NC), Friedmann-Robertson-Walker cosmological model. The spatial sections may have positive, negative or zero constant curvatures. The matter content is a generic perfect fluid. The initial…
Recently it has been claimed that the Wheeler-DeWitt quantization of gravity is unable to avoid cosmological singularities. However, in order to make this assertion, one must specify the underlying interpretation of quantum mechanics which…