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Quantum cosmology describes universe as a relativistic object with an evolution defined by an equation for the energy density corresponding to the least action principle: (Taganov, 2008). In quantum cosmology this equation plays the same…
The inverse scale factor, which in classical cosmological models diverges at the singularity, is quantized in isotropic models of loop quantum cosmology by using techniques which have been developed in quantum geometry for a quantization of…
We re-examine the process of loop quantization for flat isotropic models in cosmology. In particular, we contrast different inequivalent `loop quantizations' of these simple models through their respective successes and limitations and…
We propose an operator constraint equation for the wavefunction of the Universe that admits genuine evolution. While the corresponding classical theory is equivalent to the canonical decomposition of General Relativity, the quantum theory…
Cosmological fluctuations retain a memory of the physics that generated them in their spatial correlations. The strength of correlations varies smoothly as a function of external kinematics, which is encoded in differential equations…
The dynamics of physical theories is usually described by differential equations. Difference equations then appear mainly as an approximation which can be used for a numerical analysis. As such, they have to fulfill certain conditions to…
We review the canonical quantisation of the geometry of the spacetime in the cases of a simply and a non-simply connected manifold. In the former, we analyse the information contained in the solutions of the Wheeler-DeWitt equation and…
A model for a flat isotropic universe with a negative cosmological constant $\Lambda$ and a massless scalar field as sole matter content is studied within the framework of Loop Quantum Cosmology. By application of the methods introduced for…
In loop quantum cosmology, the values of volume fluctuations and correlations determine whether the dynamics of an evolving state exhibits a bounce. Of particular interest are states that are supported only on either the positive or the…
The description of the universe evolving in time according to general relativity is given in comparison with the quantum description of the same universe in terms of semiclassical wave functions. The spacetime geometry is determined by the…
Inspired by the discrete evolution implied by the recent work on loop quantum cosmology, we obtain a discrete time description of usual quantum mechanics viewing it as a constrained system. This description, obtained without any…
Loop quantum cosmology applies techniques derived for a background independent quantization of general relativity to cosmological situations and draws conclusions for the very early universe. Direct implications for the singularity problem…
Despite its great successes in accounting for the current observations, the so called `standard' model of cosmology faces a number of fundamental unresolved questions. Paramount among these are those relating to the nature of the origin of…
Loop quantum cosmology provides an efficient framework to study the evolution of the Universe beyond the classical Big Bang paradigm. Because of holonomy corrections, the singularity is replaced by a "bounce". The dynamics of the background…
Proposing smooth initial conditions is one of the most important tasks in quantum cosmology. On the other hand, the low-energy effective action, appearing in the semiclassical path integral, can get nontrivial quantum corrections near…
Quantum cosmology uses a wave function to model the universe, but finding solutions for this poses a problem as it is difficult to define the boundary conditions or identify the correct path for a path integral. We begin the discussion by…
We develop a quantum-cosmological framework in which the inflationary potential emerges from the structure of the wave function of the universe rather than being postulated. Starting from the Wheeler-DeWitt equation for a flat…
Quantum fluctuations or other moments of a state contribute to energy expectation values and can imply interesting physical effects. In quantum cosmology, they turn out to be important for a discussion of density bounds and instabilities of…
Quantization of a dust-like closed isotropic cosmological model with a cosmological constant is realized by the method of B. DeWitt \cite{1}. It is shown that such quantization leads to interesting results, in particular, to a finite…
Our understanding of quantum field theory rests largely on explicit and controlled calculations in perturbation theory. Because of this, much recent effort has been devoted to improve our grasp of perturbative techniques on cosmological…