Related papers: Prescriptions in Loop Quantum Cosmology: A compara…
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…
In Loop Quantum Cosmology, the quantization of the Hamiltonian constraint involves a regularization procedure which is affected by certain ambiguities. Moreover, different regularizations lead to distinct mathematical formulations and,…
The possibility that quantum geometry effects may alleviate the apparent tensions existing at large angular scales in the observations of the Cosmic Microwave Background explains the increasing interest in considering primordial…
Solvable loop quantum cosmology provides a simple model of spatially flat, homogeneous, and isotropic quantum cosmology where the initial singularity is resolved. A close inspection of the literature reveals that there exist two different…
Quantum cosmology in the presence of a fundamental minimal length is analyzed in the context of the flat isotropic and the Taub cosmological models. Such minimal scale comes out from a generalized uncertainty principle and the quantization…
A brief review of various numerical techniques used in loop quantum cosmology and results is presented. These include the way extensive numerical simulations shed insights on the resolution of classical singularities, resulting in the key…
Quantum cosmology is traditionally formulated in a minisuperspace setting, implicitly averaging fields over space to obtain homogeneous models. For universal reasons related to the uncertainty principle, quantum corrections then depend on…
Invited contribution to the Encyclopedia of Mathematical Physics (2nd edition), providing an overview over some main ideas and results in quantum cosmology. Key points: Canonical quantisation of homogeneous, isotropic cosmology; discussion…
This is a technical note on the $i\epsilon$ prescription in cosmology where we consider a self-interacting scalar field in the Poincare patch of the de Sitter space whose Hamiltonian has explicit time dependence. We use both path integral…
We describe quantization schemes for scalar field cosmology in the metric variables with fundamental discreteness imposed with a lattice. The variables chosen for quantization determine the lattice, and each lattice produces distinct…
Recently a number of analytic prescriptions for computing the non-linear matter power spectrum have appeared in the literature. These typically involve resummation or closure prescriptions which do not have a rigorous error control, thus…
In the last decade, progress on quantization of homogeneous cosmological spacetimes using techniques of loop quantum gravity has led to insights on various fundamental questions and has opened new avenues to explore Planck scale physics.…
Inhomogeneities are introduced in loop quantum cosmology using regular lattice states, with a kinematical arena similar to that in homogeneous models considered earlier. The framework is intended to encapsulate crucial features of…
This paper provides a prospectus for a new way of thinking about the wavefunction of the universe: a $\Psi$-epistemic quantum cosmology. We present a proposal that, if successfully implemented, would resolve the cosmological measurement…
Loop quantum cosmological methods are extended to homogeneous models in diagonalized form. It is shown that the diagonalization leads to a simplification of the volume operator such that its spectrum can be determined explicitly. This…
We study the scalar modes of linear perturbations in loop quantum cosmology. This is done on a lattice where each cell is taken to be homogeneous and isotropic and can be quantized via standard homogeneous loop quantum cosmology techniques.…
In quantum cosmology, one applies quantum physics to the whole universe. While no unique version and no completely well-defined theory is available yet, the framework gives rise to interesting conceptual, mathematical and physical…
A homogeneous and isotropic cosmological model with a positive cosmological constant is considered. The matter sector is given by a massless scalar field, which can be used as an internal time to deparametrize the theory. The idea is to…
Based on a more careful canonical analysis, we motivate a reduced quantization - in the sense of superspace quantization - of slightly inhomogeneous cosmology in place of the Dirac quantization in the existing literature, and provide it in…
A complete quantization of a homogeneous and isotropic spacetime with closed spatial sections coupled to a massive scalar field is provided, within the framework of Loop Quantum Cosmology. We identify solutions with their initial data on…