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A fundamental issue for any quantum cosmological theory is to specify how probabilities can be assigned to various quantum events or sequences of events such as the occurrence of singularities or bounces. In previous work, we have…
We illustrate the crucial role played by decoherence (consistency of quantum histories) in extracting consistent quantum probabilities for alternative histories in quantum cosmology. Specifically, within a Wheeler-DeWitt quantization of a…
Loop quantum cosmology predicts that, in simple models, the big bang singularity of classical general relativity is replaced by a quantum bounce. Because of the extreme physical conditions near the bounce, a natural question is whether the…
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…
We review the application of the consistent (or decoherent) histories formulation of quantum theory to canonical loop quantum cosmology. Conventional quantum theory relies crucially on "measurements" to convert unrealized quantum…
We discuss the way non-perturbative quantization of cosmological spacetimes in loop quantum cosmology provides insights on the physics of Planck scale and the resolution of big bang singularity. In recent years, rigorous examination of…
In Loop Quantum Gravity mathematically rigorous models of full quantum gravity were proposed. In this paper we study a cosmological sector of one of the models describing quantum gravity with positive cosmological constant coupled to…
In this work, we investigate the notion of time and unitarity in the vicinity of a bounce in quantum cosmology, that is, a turning point for the scale factor. Because WKB methods drastically fail near a turning point, the scale factor…
Loop quantum cosmology (LQC) is used to provide concrete evidence in support of the general paradigm underlying spin foam models (SFMs). Specifically, it is shown that: i) the physical inner product in the timeless framework equals the…
We explore the structure of the spin foam-like vertex expansion in loop quantum cosmology and discuss properties of the corresponding amplitudes, with the aim of elucidating some of the expansion's useful properties and features. We find…
Quantum effects are expected to modify the cosmological dynamics of the early universe while maintaining some (potentially discrete) notion of space-time structure. In one approach, loop quantum cosmology, current models are shown here to…
We give an explicit, rigorous framework for calculating quantum probabilities in a model theory of quantum gravity. Specifically, we construct the decoherence functional for the Wheeler-DeWitt quantization of a flat…
The quantum bounce a priori connects several (semi)classical epochs of Universe evolution, however determining if and how well the semiclassicality is preserved in this transition is highly nontrivial. We review the present state of…
General relativity predicts a singularity in the beginning of the universe being called big bang. Recent developments in loop quantum cosmology avoid the singularity and the big bang is replaced by a big bounce. A classical theory of…
Non-perturbative quantum geometric effects in Loop Quantum Cosmology predict a $\rho^2$ modification to the Friedmann equation at high energies. The quadratic term is negative definite and can lead to generic bounces when the matter energy…
Alternative scenarios to the Big Bang singularity have been subject of intense research for several decades by now. Most popular in this sense have been frameworks were such singularity is replaced by a bounce around some minimal…
We investigate the realization of non-singular bouncing cosmologies driven by causal bulk-viscous fluids within General Relativity, $f(R)$ gravity, and Loop Quantum Cosmology. Building on the no-go result of Eckart theory in spatially flat…
The occurrence of singularities where spacetime curvature becomes infinite and geodesic evolution breaks down are inevitable events in classical general relativity (GR) unless one chooses an exotic matter violating weak energy condition.…
Loop quantum cosmology homogeneous models with a massless scalar field show that the big-bang singularity can be replaced by a big quantum bounce. To gain further insight on the nature of this bounce, we study the semi-discrete loop quantum…
These notes are a didactic overview of the non perturbative and background independent approach to a quantum theory of gravity known as loop quantum gravity. The definition of real connection variables for general relativity, used as a…