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We investigate anisotropic cosmological solutions of the theory with non-minimal couplings between electromagnetic fields and gravity in $Y(R) F^2$ form. After we derive the field equations by the variational principle, we look for…
Inhomogeneous quantum cosmology is modeled as a dynamical system of discrete patches, whose interacting many-body equations can be mapped to a non-linear minisuperspace equation by methods analogous to Bose-Einstein condensation.…
The comprehensive formulation for loop quantum cosmology in the spatially flat, isotropic model was recently constructed. In this paper, the methods are extended to the anisotropic Bianchi I cosmology. Both the precursor and the improved…
A finite and unitary nonlocal formulation of quantum gravity is applied to the cosmological constant problem. The entire functions in momentum space at the graviton-standard model particle loop vertices generate an exponential suppression…
A new model is studied which describes the quantum behavior of transitions through an isotropic quantum cosmological bounce in loop quantum cosmology sourced by a free and massless scalar field. As an exactly solvable model even at the…
A consistent combination of quantum geometry effects rules out a large class of models of loop quantum cosmology and their critical densities as they have been used in the recent literature. In particular, the critical density at which an…
The improved dynamics of loop quantum cosmology is extended to include the Bianchi type II model. Because these space-times admit both anisotropies and non-zero spatial curvature, certain technical difficulties arise over and above those…
This introductory review is addressed to beginning researchers. Some of the distinguishing features of loop quantum gravity are illustrated through loop quantum cosmology of FRW models. In particular, these examples illustrate: i) how…
Aspects of the full theory of loop quantum gravity can be studied in a simpler context by reducing to symmetric models like cosmological ones. This leads to several applications where loop effects play a significant role when one is…
In this paper we study dynamics of the closed FRW model with holonomy corrections coming from loop quantum cosmology. We consider models with a scalar field and cosmological constant. In case of the models with cosmological constant and…
After a brief introduction to classical and quantum gravity we discuss applications of loop quantum gravity in the cosmological realm. This includes the basic formalism and recent results of loop quantum cosmology, and a computation of…
Inhomogeneous cosmological perturbation equations are derived in loop quantum gravity, taking into account corrections in particular in gravitational parts. This provides a framework for calculating the evolution of modes in structure…
The "improved dynamics" of loop quantum cosmology is extended to include anisotropies of the Bianchi I model. As in the isotropic case, a massless scalar field serves as a relational time parameter. However, the extension is non-trivial…
Quantum gravity is expected to be necessary in order to understand situations where classical general relativity breaks down. In particular in cosmology one has to deal with initial singularities, i.e. the fact that the backward evolution…
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…
Loop quantum cosmology predicts that quantum gravity effects resolve the big-bang singularity and replace it by a cosmic bounce. Furthermore, loop quantum cosmology can also modify the form of primordial cosmological perturbations, for…
The relation between an isotropic and an anisotropic model in loop quantum cosmology is discussed in detail, comparing the strict symmetry reduction with a perturbative implementation of symmetry. While the latter cannot be done in a…
Inspired by possible connections between gravity and foundational question in quantum theory, we consider an approach for the adaptation of objective collapse models to a general relativistic context. We apply these ideas to a list of open…
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…
Loop quantum cosmology, the symmetry reduction of quantum geometry for the study of various cosmological situations, leads to a difference equation for its quantum evolution equation. To ensure that solutions of this equation act in the…