Je abstrakter die Wahrheit ist, die du lehren willst, um so mehr mußt du noch die Sinne zu ihr verführen.

(The more abstract the truth you want to teach is, the more you have to seduce to it the senses.)

FRIEDRICH NIETZSCHE

Beyond Good and Evil

The gravitational field equations, for instance in the case of cosmology where one can assume homogeneity and isotropy, involve components of curvature as well as the inverse metric. (Computational methods to derive information from these equations are described in [5].) Since singularities occur, these components will become large in certain regimes, but the equations have been tested only in small curvature regimes. On small length scales such as close to the Big Bang, modifications to the classical equations are not ruled out by observations and can be expected from candidates of quantum gravity. Quantum cosmology describes the evolution of a universe by a constraint equation for a wave function, but some effects can be included already at the level of effective classical equations. In loop quantum gravity, the main modification happens through inverse metric components which, e.g., appear in the kinematic term of matter Hamiltonians. This one modification is mainly responsible for all the diverse effects of loop cosmology.

4.1 Isotropy

4.2 Isotropy: Connection variables

4.3 Isotropy: Implications of a loop quantization

4.4 Isotropy: Effective densities and equations

4.5 Isotropy: Properties and intuitive meaning

4.6 Isotropy: Applications

4.6.1 Collapsing phase

4.6.2 Expansion

4.6.3 Model building

4.6.4 Stability

4.7 Anisotropies

4.8 Anisotropy: Connection variables

4.9 Anisotropy: Applications

4.9.1 Isotropization

4.9.2 Bianchi IX

4.9.3 Isotropic curvature suppression

4.10 Anisotropy: Implications for inhomogeneities

4.11 Inhomogeneities

4.12 Inhomogeneous matter with isotropic quantum geometry

4.13 Inhomogeneity: Perturbations

4.14 Inhomogeneous models

4.15 Inhomogeneity: Results

4.15.1 Matter gradient terms and small-a effects

4.15.2 Matter gradient terms and large-a effects

4.15.3 Non-inflationary structure formation

4.15.4 Stability

4.16 Summary

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