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The article investigates cosmological applications of $f(Q)$ theories in a non-coincident formalism. We explore a new $f(Q)$ theory dynamics utilizing a non-vanishing affine connection involving a non-constant function…
This Chapter provides an up to date, pedagogical review of some of the most relevant advances in loop quantum cosmology. We review the quantization of homogeneous cosmological models, their singularity resolution and the formulation of…
The renormalization group in effective quantum gravity can be consistently formulated using the Vilkovisky and DeWitt version of effective action and assuming a non-zero cosmological constant. Taking into account that the vacuum counterpart…
The cosmological constant problem is one of the greatest challenges in contemporary physics, since it is deeply rooted in the problematic interplay between quantum fields and gravity. The aim of this work is to review the key conceptual…
We present a line by line derivation of canonical quantum mechanics stemming from the compatibility of the statistical geometry of distinguishable observations with the canonical Poisson structure of Hamiltonian dynamics. This viewpoint can…
We analyze the cosmological solutions to the recently proposed nonlocal quantum effective action for gravity with a cosmological term. We show that the vacuum energy decays with a slow-roll parameter proportional to the anomalous…
We derive the 1-loop effective action of the cubic Galileon coupled to quantum-gravitational fluctuations in a background and gauge-independent manner, employing the covariant framework of DeWitt and Vilkovisky. Although the bare action…
We present a new perspective on early cosmology based on Loop Quantum Gravity. We use projected spinnetworks, coherent states and spinfoam techniques, to implement a quantum reduction of the full Kinematical Hilbert space of LQG, suitable…
Based on modifications inspired from loop quantum gravity (LQG), spherically symmetric models have recently been explored to understand the resolution of classical singularities and the fate of the spacetime beyond. While such…
For a class of solutions of the fundamental difference equation of isotropic loop quantum cosmology, the difference equation can be replaced by a differential equation valid for {\em all} values of the triad variable. The differential…
A general nonperturvative loop quantization procedure for metric modified gravity is reviewed. As an example, this procedure is applied to scalar-tensor theories of gravity. The quantum kinematical framework of these theories is rigorously…
Coupling any interacting quantum mechanical system to gravity in one dimension requires the cosmological constant to belong to the matter energy spectrum and thus to be quantized, even though the gravity sector is free of any quantum…
Quantum groups and non-commutative spaces have been repeatedly utilized in approaches to quantum gravity. They provide a mathematically elegant cut-off, often interpreted as related to the Planck-scale quantum uncertainty in position. We…
A number of recent studies have proposed that linear representations are appropriate for solving nonlinear dynamical systems with quantum computers, which fundamentally act linearly on a wave function in a Hilbert space. Linear…
We develop the canonical formalism for a system of $N$ bodies in lineal gravity and obtain exact solutions to the equations of motion for N=2. The determining equation of the Hamiltonian is derived in the form of a transcendental equation,…
The Hamiltonian constraint of scalar-tensor theories in the Jordan frame is quantised using three quantisation prescriptions in loop quantum cosmology, from which we obtain three different effective Hamiltonian constraints. The…
The continuum limit of loop quantum gravity is still an open problem. Indeed, no proper dynamics in known to start with and we still lack the mathematical tools to study its would-be continuum limit. In the present PhD dissertation, we will…
Coupling any interacting quantum mechanical system to gravity in one (time) dimension requires the cosmological constant to belong to the matter energy spectrum and thus to be quantised, even though the gravity sector is free of any quantum…
A precise interpretation of the Universe wave function is forbidden in the spirit of the Copenhagen School since a precise notion of measure operation cannot be satisfactorily defined. Here we propose a Bohmian interpretation of the…
The study of toy models in loop quantum gravity (LQG), defined as truncations of the full theory, is relevant to both the development of the LQG phenomenology, in cosmology and astrophysics, and the progress towards the resolution of the…