Related papers: Gravity, Geometry and the Quantum
This short review is addressed to cosmologists. General relativity predicts that space-time comes to an end and physics comes to a halt at the big-bang. Recent developments in loop quantum cosmology have shown that these predictions cannot…
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…
In recent years, Loop Quantum Gravity has emerged as a solid candidate for a nonperturbative quantum theory of General Relativity. It is a background independent theory based on a description of the gravitational field in terms of…
General relativity successfully describes space-times at scales that we can observe and probe today, but it cannot be complete as a consequence of singularity theorems. For a long time there have been indications that quantum gravity will…
Applications of Riemannian quantum geometry to cosmology have had notable successes. In particular, the fundamental discreteness underlying quantum geometry has led to a natural resolution of the big bang singularity. However, the precise…
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…
This is a self-contained introduction to quantum Riemannian geometry based on quantum groups as frame groups, and its proposed role in quantum gravity. Much of the article is about the generalisation of classical Riemannian geometry that…
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…
General relativity promotes space-time to a physical, dynamical object subject to equations of motion. Quantum gravity, accordingly, must provide a quantum framework for space-time, applicable on the smallest distance scales. Just like…
Loop Quantum Gravity is a background independent, nonperturbative approach to the quantization of General Relativity. Its application to models of interest in cosmology and astrophysics, known as Loop Quantum Cosmology, has led to new and…
Quantum gravity has matured over the last decade to a theory which can tell in a precise and explicit way how cosmological singularities of general relativity are removed. A branch of the universe "before" the classical big bang is obtained…
Canonical quantum gravity provides insights into the quantum dynamics as well as quantum geometry of space-time by its implications for constraints. Loop quantum gravity in particular requires specific corrections due to its quantization…
Singularities in general relativity such as the big bang and big crunch, and exotic singularities such as the big rip are the boundaries of the classical spacetimes. These events are marked by a divergence in the curvature invariants and…
Cosmology appears as the most promising way to test and constrain quantum gravity theories. Loop quantum gravity is among the most advanced attempts to perform a non-perturbative quantization of general relativity. Its cosmological…
Loop quantum gravity is a physical theory which aims at unifying general relativity and quantum mechanics. It takes general relativity very seriously and modifies it via a quantisation. General relativity describes gravity in terms of…
A set of diverse but mutually consistent results obtained in different settings has spawned a new view of loop quantum gravity and its physical implications, based on the interplay of operator calculations and effective theory: Quantum…
We present a gauge-invariant treatment of singularity resolution using loop quantum gravity techniques with respect to local SU(2) transformations. Our analysis reveals many novel features of quantum geometry which were till now hidden in…
Several examples are known where quantum gravity effects resolve the classical big bang singularity by a bounce. The most detailed analysis has probably occurred for loop quantum cosmology of isotropic models sourced by a free, massless…
Any canonical quantum theory can be understood to arise from the compatibility of the statistical geometry of distinguishable observations with the canonical Poisson structure of Hamiltonian dynamics. This geometric perspective offers a…
We explain how quantum gravity can be defined by quantizing spacetime itself. A pinpoint is that the gravitational constant G = L_P^2 whose physical dimension is of (length)^2 in natural unit introduces a symplectic structure of spacetime…